Search results for: visco Pasternak foundation

Authors: Hamed Khani Arani, Mohammad Shariyat, Armaghan Mohammadian

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In this research, the free vibration of a rectangular sandwich nano-plate (SNP) made of three smart layers in the visco Pasternak foundation is studied. The core of the sandwich is a piezo magnetic nano-plate integrated with two layers of piezoelectric materials. First-order shear deformation plate theory is utilized to derive the motion equations by using Hamilton’s principle, piezoelectricity, and modified couple stress theory. Elastic medium is modeled by visco Pasternak foundation, where the damping coefficient effect is investigated on the stability of sandwich nano-plate. These equations are solved by the differential quadrature method (DQM), considering different boundary conditions. Results indicate the effect of various parameters such as aspect ratio, thickness ratio, shear correction factor, damping coefficient, and boundary conditions on the dimensionless frequency of sandwich nano-plate. The results are also compared by those available in the literature, and these findings can be used for automotive industry, communications equipment, active noise, stability, and vibration cancellation systems and utilized for designing the magnetostrictive actuator, motor, transducer and sensors in nano and micro smart structures.

Keywords: free vibration, modified couple stress theory, sandwich nano-plate, visco Pasternak foundation

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Authors: Merrimi El Bekkaye, El Bikri Khalid, Benamar Rhali

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In the present paper, the problem of geometrically non-linear free vibration of symmetrically and asymmetrically laminated composite beams (LCB) resting on nonlinear Pasternak elastic Foundation with immovable ends is studied. A homogenization procedure has been performed to reduce the problem under consideration to that of the isotropic homogeneous beams with effective bending stiffness and axial stiffness parameters. This simple formulation is developed using the governing axial equation of the beam in which the axial inertia and damping are ignored. The theoretical model is based on Hamilton’s principle and spectral analysis. Iterative form solutions are presented to calculate the fundamental nonlinear frequency parameters which are found to be in a good agreement with the published results. On the other hand, the influence of the foundation parameters on the nonlinear frequency to the linear frequency ratio of the LCB has been studied. The non-dimensional curvatures associated to the fundamental mode are also given in the case of clamped-clamped symmetrically and asymmetrically laminated composite beams.

Keywords: large vibration amplitudes, laminated composite beam, Pasternak foundation, composite beams

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Authors: Akif Kutlu, Merve Ermis, Nihal Eratlı, Mehmet H. Omurtag

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The objective of this study is to investigate the forced vibration analysis of a planar curved beam lying on elastic foundation by using the mixed finite element method. The finite element formulation is based on the Timoshenko beam theory. In order to solve the problems in frequency domain, the element matrices of two nodded curvilinear elements are transformed into Laplace space. The results are transformed back to the time domain by the well-known numerical Modified Durbin’s transformation algorithm. First, the presented finite element formulation is verified through the forced vibration analysis of a planar curved Timoshenko beam resting on Winkler foundation and the finite element results are compared with the results available in the literature. Then, the forced vibration analysis of a planar curved beam resting on Winkler-Pasternak foundation is conducted.

Keywords: curved beam, dynamic analysis, elastic foundation, finite element method

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Authors: Ali Oveysi Sarabi

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The dimensions of nanostructures are in the range of inter-atomic spacing of the structures which makes them impossible to be modeled as a continuum. Nanoscale size-effects on vibration analysis of nanobeams embedded in an elastic medium is investigated using different types of beam theory. To this end, Eringen’s nonlocal elasticity is incorporated to various beam theories namely as Euler-Bernoulli beam theory (EBT), Timoshenko beam theory (TBT), Reddy beam theory (RBT), and Levinson beam theory (LBT). The surrounding elastic medium is simulated with both Winkler and Pasternak foundation models and the difference between them is studies. Explicit formulas are presented to obtain the natural frequencies of nanobeam corresponding to each nonlocal beam theory. Selected numerical results are given for different values of the non-local parameter, Winkler modulus parameter, Pasternak modulus parameter and aspect ratio of the beam that imply the effects of them, separately. It is observed that the values of natural frequency are strongly dependent on the stiffness of elastic medium and the value of the non-local parameter and these dependencies varies with the value of aspect ratio and mode number.

Keywords: nanobeams, free vibration, nonlocal elasticity, winkler foundation model, Pasternak foundation model, beam theories

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Authors: M. Seguini, D. Nedjar

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In this paper, the nonlinear analysis of Timoshenko beam undergoing moderate large deflections and resting on nonlinear two-parameter random foundation is presented, taking into account the effects of shear deformation, beam’s properties variation and the spatial variability of soil characteristics. The finite element probabilistic analysis has been performed by using Timoshenko beam theory with the Von Kàrmàn nonlinear strain-displacement relationships combined to Vanmarcke theory and Monte Carlo simulations, which is implemented in a Matlab program. Numerical examples of the newly developed model is conducted to confirm the efficiency and accuracy of this later and the importance of accounting for the foundation second parameter (Winkler-Pasternak). Thus, the results obtained from the developed model are presented and compared with those available in the literature to examine how the consideration of the shear and spatial variability of soil’s characteristics affects the response of the system.

Keywords: nonlinear analysis, soil-structure interaction, large deflection, Timoshenko beam, Euler-Bernoulli beam, Winkler foundation, Pasternak foundation, spatial variability

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Authors: Somnath Karmakar, S. Chakraverty

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This work investigates the vibration of nonhomogeneous Timoshenko nanobeam resting on the Winkler-Pasternak foundation. Eringen’s nonlocal theory has been used to investigate small-scale effects. The Differential Quadrature method is used to obtain the frequency parameters with various classical boundary conditions. The nonhomogeneous beam model has been considered, where Young’s modulus and density of the beam material vary linearly and quadratically. Convergence of frequency parameters is also discussed. The influence of mechanical properties and scaling parameters on vibration frequencies are investigated for different boundary conditions.

Keywords: Timoshenko beam, Eringen's nonlocal theory, differential quadrature method, nonhomogeneous nanobeam

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Authors: Ashwini V. Chavan, Sukhanand S. Bhosale

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Challenges of weak soil subgrade are often resolved either by stabilization or reinforcing it. However, it is also practiced to reinforce the granular fill to improve the load-settlement behavior of over weak soil strata. The inclusion of reinforcement in the engineered granular fill provided a new impetus for the development of enhanced Soil-Structure Interaction (SSI) models, also known as mechanical foundation models or lumped parameter models. Several researchers have been working in this direction to understand the mechanism of granular fill-reinforcement interaction and the response of weak soil under the application of load. These models have been developed by extending available SSI models such as the Winkler Model, Pasternak Model, Hetenyi Model, Kerr Model etc., and are helpful to visualize the load-settlement behavior of a physical system through 1-D and 2-D analysis considering beam and plate resting on the foundation respectively. Based on the literature survey, these models are categorized as ‘Reinforced Pasternak Model,’ ‘Double Beam Model,’ ‘Reinforced Timoshenko Beam Model,’ and ‘Reinforced Kerr Model.’ The present work reviews the past 30+ years of research in the field of SSI models for reinforced foundation systems, presenting the conceptual development of these models systematically and discussing their limitations. Special efforts are taken to tabulate the parameters and their significance in the load-settlement analysis, which may be helpful in future studies for the comparison and enhancement of results and findings of physical models.

Keywords: geosynthetics, mathematical modeling, reinforced foundation, soil-structure interaction, ground improvement, soft soil

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Authors: Neslihan Genckal, Reha Gursoy, Vedat Z. Dogan

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In this study, dynamic responses of composite plates on elastic foundations subjected to impact and moving loads are investigated. The first order shear deformation (FSDT) theory is used for moderately thick plates. Pasternak-type (two-parameter) elastic foundation is assumed. Elastic foundation effects are integrated into the governing equations. It is assumed that plate is first hit by a mass as an impact type loading then the mass continues to move on the composite plate as a distributed moving loading, which resembles the aircraft landing on airport pavements. Impact and moving loadings are modeled by a mass-spring-damper system with a wheel. The wheel is assumed to be continuously in contact with the plate after impact. The governing partial differential equations of motion for displacements are converted into the ordinary differential equations in the time domain by using Galerkin’s method. Then, these sets of equations are solved by using the Runge-Kutta method. Several parameters such as vertical and horizontal velocities of the aircraft, volume fractions of the steel rebar in the reinforced concrete layer, and the different touchdown locations of the aircraft tire on the runway are considered in the numerical simulation. The results are compared with those of the ABAQUS, which is a commercial finite element code.

Keywords: elastic foundation, impact, moving load, thick plate

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Authors: Benselama Khadidja, El Meiche Noureddine

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This paper presents the effect of hybridization material on the variation of non-dimensional critical buckling load with different cross-ply laminates plate resting on elastic foundations of Winkler and Pasternak types subjected to combine uniaxial and biaxial loading by using two variable refined plate theories. Governing equations are derived from the Principle of Virtual Displacement; the formulation is based on a new function of shear deformation theory taking into account transverse shear deformation effects vary parabolically across the thickness satisfying shear stress-free surface conditions. These equations are solved analytically using the Navier solution of a simply supported. The influence of the various parameters geometric and material, the thickness ratio, and the number of layers symmetric and antisymmetric hybrid laminates material has been investigated to find the critical buckling loads. The numerical results obtained through the present study with several examples are presented to verify and compared with other models with the ones available in the literature.

Keywords: buckling, hybrid cross-ply laminates, Winkler and Pasternak, elastic foundation, two variables plate theory

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Authors: N. E.Sam, S. R.Singh

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Pipeline infrastructure are a valuable asset to the country that help in transporting fluid and gas from one place to another and contribute in keeping the country functioning both physically and economically. During seismic activity, additional loads are acted on the buried pipelines becoming a salient parameter to be studied in soil pipe interaction. Winkler Beam Theory is a commonly used approach for design of underground buried structures however this theory does not take into account shear and dynamic loading parameters in consideration. Shear can be addressed in Pasternak Theory – an improved model of Winkler Theory. However dynamic loading condition and horizontal displacement is not considered in either method. A comprehensive critical review between Winkler Beam Method, Pasternak Method and Three-Dimensional Method in finite element analysis is to be done in this paper for seismic forces. Study of the influence of depth and displacement of soil in correspondence to stiffness value and influence of horizontal displacement for design of underground structures is considered.

Keywords: finite element, pasternak theory, seismic, soil-structure interaction, three-dimensional theory, winkler theory

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Authors: Gholamhosein Khosravi, Mohammad Azadi, Hamidreza Ghezavati

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In this paper, vibration of a nonlinear composite beam is analyzed and then an active controller is used to control the vibrations of the system. The beam is resting on a Winkler-Pasternak elastic foundation. The composite beam is reinforced by single walled carbon nanotubes. Using the rule of mixture, the material properties of functionally graded carbon nanotube-reinforced composites (FG-CNTRCs) are determined. The beam is cantilever and the free end of the beam is under follower force. Piezoelectric layers are attached to the both sides of the beam to control vibrations as sensors and actuators. The governing equations of the FG-CNTRC beam are derived based on Euler-Bernoulli beam theory Lagrange- Rayleigh-Ritz method. The simulation results are presented and the effects of some parameters on stability of the beam are analyzed.

Keywords: carbon nanotubes, vibration control, piezoelectric layers, elastic foundation

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Authors: Y. Rae, A. Benaarbia, J. Hughes, Wei Sun

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This paper describes an elasto-visco-plastic computational modelling method which can be used to assess the cyclic plasticity responses of high temperature structures operating under thermo-mechanical loadings. The material constitutive equation used is an improved unified multi-axial Chaboche-Lemaitre model, which takes into account non-linear kinematic and isotropic hardening. The computational methodology is a three-dimensional framework following an implicit formulation and based on a radial return mapping algorithm. The associated user material (UMAT) code is developed and calibrated across isothermal hold-time low cycle fatigue tests for a typical turbine rotor steel for use in finite element (FE) implementation. The model is applied to a realistic industrial gas turbine rotor, where the study focuses its attention on the deformation heterogeneities and critical high stress areas within the rotor structure. The potential improvements of such FE visco-plastic approach are discussed. An integrated life assessment procedure based on R5 and visco-plasticity modelling, is also briefly addressed.

Keywords: unified visco-plasticity, thermo-mechanical, turbine rotor, finite element modelling

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Authors: V. Keim, J. Spachtholz, J. Hammer

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The importance of fibre reinforced plastics continually increases due to the excellent mechanical properties, low material and manufacturing costs combined with significant weight reduction. Today, components are usually designed and calculated numerically by using finite element methods (FEM) to avoid expensive laboratory tests. These programs are based on material models including material specific deformation characteristics. In this research project, material models for short glass fibre reinforced plastics are presented to simulate the visco-elasto-plastic deformation behaviour. Prior to modelling specimens of the material EMS Grivory HTV-5H1, consisting of a Polyphthalamide matrix reinforced by 50wt.-% of short glass fibres, are characterized experimentally in terms of the highly time dependent deformation behaviour of the matrix material. To minimize the experimental effort, the cyclic deformation behaviour under tensile and compressive loading (R = −1) is characterized by isothermal complex low cycle fatigue (CLCF) tests. Combining cycles under two strain amplitudes and strain rates within three orders of magnitude and relaxation intervals into one experiment the visco-elastic deformation is characterized. To identify visco-plastic deformation monotonous tensile tests either displacement controlled or strain controlled (CERT) are compared. All relevant modelling parameters for this complex superposition of simultaneously varying mechanical loadings are quantified by these experiments. Subsequently, two different material models are compared with respect to their accuracy describing the visco-elasto-plastic deformation behaviour. First, based on Chaboche an extended 12 parameter model (EVP-KV2) is used to model cyclic visco-elasto-plasticity at two time scales. The parameters of the model including a total separation of elastic and plastic deformation are obtained by computational optimization using an evolutionary algorithm based on a fitness function called genetic algorithm. Second, the 12 parameter visco-elasto-plastic material model by Launay is used. In detail, the model contains a different type of a flow function based on the definition of the visco-plastic deformation as a part of the overall deformation. The accuracy of the models is verified by corresponding experimental LCF testing.

Keywords: complex low cycle fatigue, material modelling, short glass fibre reinforced polyphthalamides, visco-elasto-plastic deformation

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Authors: Sharad Singh, Ajay Kumar Sinha

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Coupled dampers like viscoelastic-frictional dampers for supplemental damping are a newer technique. In this paper, innovative Visco-frictional damping models have been presented and investigated. This paper attempts to couple frictional and fluid viscous dampers into a single unit of supplemental dampers. Visco-frictional damping model is developed by series and parallel coupling of frictional and fluid viscous dampers using Maxwell and Kelvin-Voigat models. The time analysis has been performed using numerical simulation on an SDOF system with varying fundamental periods, subject to a set of 12 ground motions. The simulation was performed using the direct time integration method. MATLAB programming tool was used to carry out the numerical simulation. The response behavior has been analyzed for the varying time period and added damping. This paper compares the response reduction behavior of the two modes of coupling. This paper highlights the performance efficiency of the suggested damping models. It also presents a mathematical modeling approach to visco-frictional dampers and simultaneously suggests the suitable mode of coupling between the two sub-units.

Keywords: hysteretic damping, Kelvin model, Maxwell model, parallel coupling, series coupling, viscous damping

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Authors: Nicolas Bae, Theodore L. Karavasilis

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Increasingly, a large number of new and existing tall buildings are required to improve their resilient performance against strong winds and earthquakes to minimize direct, as well as indirect damages to society. Those advent stationary functions of tall building structures in metropolitan regions can be severely hazardous, in socio-economic terms, which also increase the requirement of advanced seismic performance. To achieve these progressive requirements, the seismic reinforcement for some old, conventional buildings have become enormously costly. The methods of increasing the buildings’ resilience against wind or earthquake loads have also become more advanced. Up to now, vibration control devices, such as the passive damper system, is still regarded as an effective and an easy-to-install option, in improving the seismic resilience of buildings at affordable prices. The main purpose of this paper is to examine 1) the optimization of the shape of visco plastic brace damper (VPBD) system which is one of hybrid damper system so that it can maximize its energy dissipation capacity in tall buildings against wind and earthquake. 2) the verification of the seismic performance of the visco plastic brace damper system in tall buildings; up to forty-storey high steel frame buildings, by comparing the results of Non-Linear Response History Analysis (NLRHA), with and without a damper system. The most significant contribution of this research is to introduce the optimized hybrid damper system that is adequate for high rise buildings. The efficiency of this visco plastic brace damper system and the advantages of its use in tall buildings can be verified since tall buildings tend to be affected by wind load at its normal state and also by earthquake load after yielding of steel plates. The modeling of the prototype tall building will be conducted using the Opensees software. Three types of modeling were used to verify the performance of the damper (MRF, MRF with visco-elastic, MRF with visco-plastic model) 22-set seismic records used and the scaling procedure was followed according to the FEMA code. It is shown that MRF with viscous, visco-elastic damper, it is superior effective to reduce inelastic deformation such as roof displacement, maximum story drift, roof velocity compared to the MRF only.

Keywords: tall steel building, seismic retrofit, viscous, viscoelastic damper, performance based design, resilience based design

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Authors: Sheryl Avendaño, Miguel Ospina, Hebert Montegranario

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Full Wave Inversion (FWI) is a variant of seismic tomography for obtaining velocity profiles by an optimization process that combine forward modelling (or solution of wave equation) with the misfit between synthetic and observed data. In this research we are modelling wave propagation in a visco-acoustic medium in the frequency domain. We apply finite differences for the numerical solution of the wave equation with a mix between usual and rotated grids, where density depends on velocity and there exists a damping function associated to a linear dissipative medium. The velocity profiles are obtained from an initial one and the data have been modeled for a frequency range 0-120 Hz. By an iterative procedure we obtain an estimated velocity profile in which are detailed the remarkable features of the velocity profile from which synthetic data were generated showing promising results for our method.

Keywords: seismic inversion, full wave inversion, visco acoustic wave equation, finite diffrence methods

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Authors: Azmat Hussain

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Great Taj Mahal is built on well foundation. Well foundation can be constructed on the dry bed or after making sand Island. Cassions are relatively easy to construct provide sinking operations are smooth without much hindrance. Well foundation have many constructional difficulties, viz prolonged sinking period, tilting etc. These problems become worse and take more time when working season is winter. Especially in Indian Areas like Jammu & Kashmir (Srinagar) where technology lacks. The only thing Engineers can do is to wait till working conditions become suitable. A case study is presented in the paper exploring the feasibility of pile foundation.

Keywords: well foundation, pile foundation, equipments used, pile construction

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Authors: Christopher Giehl, Anja Allabar, Daniela Ehgartner

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Rotational rheometry is standard practice for the viscosity measurement of molten glass, neglecting the viscoelastic properties of this material, especially at temperatures approaching the glass transition. Oscillatory rheometry serves as a powerful toolbox for glass melt characterization beyond viscosity measurements. Heating and cooling rates and the time-dependent visco-elastic behavior influence the temperature where materials undergo the glass transition. This study presents quantitative thermo-mechanical visco-elasticity measurements on three samples in the Na-K-Al-Si-O system. The measurements were performed with a Furnace Rheometer System combined with an air-bearing DSR 502 measuring head (Anton Paar) and a Pt90Rh10 measuring geometry. Temperature ramps were conducted in rotation and oscillation, and the (complex) viscosity values were compared to calculated viscosity values based on sample composition. Furthermore, temperature ramps with different frequencies were conducted, also revealing the frequency-dependence of the shear loss modulus G’’ and the shear storage modulus G’. Here, lower oscillatory frequency results in lower glass transition temperature, as defined by the G’-G’’ crossover point. This contribution demonstrates that oscillatory rheometry serves as a powerful toolbox beyond viscosity measurements, as it considers the visco-elasticity of glass melts quantifying viscous and elastic moduli. Further, it offers a strong definition of Tg beyond the 10^12 Pas concept, which cannot be utilized with rotational viscometry data.

Keywords: frequency dependent glass transition, Na-K-Al-Si-O glass melts, oscillatory rheometry, visco-elasticity

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Authors: Harvinder Kaur

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Rayleigh–Ritz method is a broadly used classical method for the calculation of the natural vibration frequency of a structure in the second or higher order. Here it is used to construct a mathematical model of relative study of the thermal effect on free transverse vibrations of clamped (c-c-c-c type) visco-elastic rectangular plate with linearly and exponentially thickness variations respectively in two directions. Researchers in the field of Engineering always make an effort for better designs of mechanical structures. In-depth study of the vibration behavior of tapered plates with diverse thickness variation under high temperature would ultimately help to finalize the accurate design of a structure. The perfect tapered structure saves weight and as well as expenses. In the present paper, the comparison has been done for deflection and time period corresponding to the first two modes of vibrations of clamped plate for various values of aspect ratio, thermal constants, and taper constants of both the cases.

Keywords: Rayleigh-Ritz Method, tapered plates, transverse vibration, thermal constant, visco-elasticity

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Authors: D. Latha, V. Sunitha, Samson Mathew

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In India, most of the pavement is laid by bituminous road and the consumption of binder is high for pavement construction and also modified binders are used to satisfy any specific pavement requirement. Since the binders are visco-elastic material which is having the mechanical properties of binder transition from visco-elastic solid to visco-elastic fluid. In this paper, two different protocols were used to measure the viscosity property of binder using a Brookfield Viscometer and there is a need to find the appropriate mixing and compaction temperatures of various types of binders which can result in complete aggregate coating and adequate field density of HMA mixtures. The aim of this work is to find the transition temperature from Non-Newtonian behavior to Newtonian behavior of the binder by adopting a steady shear protocol and the shear rate ramp protocol. The transition from non-Newtonian to Newtonian can occur through an increase of temperature and shear of the material. The test has been conducted for unmodified binder VG 30. The transition temperature was found in the unmodified binder VG is 120oC. So the application of both modified binder and unmodified binder in the pavement construction needs to be studied properly by considering temperature and traffic loading factors of the respective project site.

Keywords: unmodified and modified binders, Brookfield viscometer, transition temperature, steady shear and shear rate protocol

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Authors: Uchegbu Nneka Nkechi, Okoye Ogochukwu Peace

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The evaluation of the visco-elastic properties and microbial quality of a formulated oat-based dietetic food were investigated. Oat flour, pumpkin seed flour, carrot flour and skimmed milk powder were blended in varying proportions to formulate a product with codes OCF, which contains 70% oat flour, 10 % carrot flour, 10 % pumpkin seed flour and 10% skimmed milk powder, OCF which contains 65 % oat flour, 10 % carrot flour, 10 % pumpkin seed flour and 15 % skimmed milk powder, OCF which contains 60 % oat flour, 10 % carrot flour, 10 % pumpkin seed flour and 20 % skimmed milk powder, OCF which contains 55 % oat flour, 10 % carrot flour, 10 % pumpkin seed flour and 25 % skimmed milk powder and OF with 95 % oat as the commercial control. All the samples were assessed for their proximate composition, microbial quality and visco-elastic properties. The moisture content was highest at sample OF (10.73%) and lowest at OCF (7.10%) (P<0.05). Crude protein ranged from 13.38%-22.86%, with OCF having the highest (P<0.05) protein content and OF having the lowest. Crude fat was 3.74% for OCF and 6.31% for OF. Crude fiber ranged from 3.58% - 17.39% with OF having the lowest (P<0.05) fiber content and OCF having the highest. Ash content was 1.30% for OCF and 2.75% for OCF. There was no mold growth in the samples. The total viable ml/wl count ranged from 1.5×10³ cfu/g - 2.6×10³ cfu/g, with OCF having the lowest and OF having the highest (P<0.05) total viable count. The peak viscosity of the sample ranged from 75.00 cP-2895.00 cP, with OCF having the lowest and OF having the highest value. The final viscosity was 130.50 cP in OCF and 3572.50 cP in OF. The setback viscosity was 58.00 cP in OCF and 1680.50 cP in OF. The peak time was 6.93 mins in OCF to 5.57 mins in OF. There was no pasting temperature for all samples except the OF, which had 86.43. Sample OF was the highest in terms of overall acceptability. This study showed that the oat-based composite flour produced had a nutritional profile that would be acceptable for the aged population.

Keywords: dietetic, pumpkin, visco-elastic, microbial

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Authors: Prasad Pokkunuri

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Visco-elastic materials combine the stress response properties of both solids and fluids and have found use in a variety of damping applications – both vibrational and acoustic. Defense and automotive applications, in particular, are subject to high impact and shock loading – for example: aircraft landing gear, firearms, and shock absorbers. Field responsive fluids – a class of smart materials – are the preferred choice of energy absorbents because of their controllability. These fluids’ stress response can be controlled by the application of a magnetic or electric field, in a closed loop. Their rheological properties – elasticity, plasticity, and viscosity – can be varied all the way from that of a liquid such as water to a hard solid. This work presents a simplified model to study the impulse response behavior of such fluids for use in recoil damping systems. The well-known Burger’s equation, in conjunction with various visco-elastic constitutive models, is used to represent fluid behavior. The Kelvin-Voigt, Upper Convected Maxwell (UCM), and Oldroyd-B constitutive models are implemented in this study. Using these models in a one-dimensional framework eliminates additional complexities due to geometry, pressure, body forces, and other source terms. Using a finite difference formulation to numerically solve the governing equation(s), the response to an initial impulse is studied. The disturbance is confined within the problem domain with no-inflow, no-outflow boundary conditions, and its decay characteristics studied. Visco-elastic fluids typically involve a time-dependent stress relaxation which gives rise to interesting behavior when subjected to an impulsive load. For particular values of viscous damping and elastic modulus, the fluid settles into a stable oscillatory state, absorbing and releasing energy without much decay. The simplified formulation enables a comprehensive study of different modes of system response, by varying relevant parameters. Using the insights gained from this study, extension to a more detailed multi-dimensional model is considered.

Keywords: Burgers Equation, Impulse Response, Recoil Damping Systems, Visco-elastic Fluids

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Authors: Mogens Saberi

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This paper presents different design approaches for the design of turbine foundations. In the design process, several unknown factors must be considered such as the soil stiffness at the site. The main static and dynamic loads are presented and the results of a dynamic simulation are presented for a turbine foundation that is currently being built. A turbine foundation is an important part of a power plant since a non-optimal behavior of the foundation can damage the turbine itself and thereby stop the power production with large consequences.

Keywords: dynamic turbine design, harmonic response analysis, practical turbine design experience, concrete foundation

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Authors: Anyeres N. Atehortua Jimenez, J. David Lambraño, Juan Carlos Muñoz

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Navier-Stokes equations (NSE), which describe the dynamics of a fluid, have an important application on modeling waves used for data inversion techniques as full waveform inversion (FWI). In this work a linearized version of NSE and its variables, neglecting deviatoric terms of stress tensor, is presented. In order to get a theoretical modeling of pressure p(x,t) and wave velocity profile c(x,t), a wave equation of visco-acoustic medium (VAE) is written. A change of variables p(x,t)=q(x,t)h(ρ), is made on the equation for the VAE leading to a well known Klein-Gordon equation (KGE) describing waves propagating in variable density medium (ρ) with dispersive term α^2(x). KGE is reduced to a Poisson equation and solved by proposing a specific function for α^2(x) accounting for the energy dissipation and dispersion. Finally, an integral form solution is derived for p(x,t), c(x,t) and kinematics variables like particle velocity v(x,t), displacement u(x,t) and bulk modulus function k_b(x,t). Further, it is compared this visco-acoustic formulation with another form broadly used in the geophysics; it is argued that this formalism is more general and, given its integral form, it may offer several advantages from the modern parallel computing point of view. Applications to minimize the errors in modeling for FWI applied to oils resources in geophysics are discussed.

Keywords: Navier-Stokes equations, modeling, visco-acoustic, inversion FWI

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Authors: Dodi Ikhsanshaleh

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When subjected to dynamic load, foundation oscillates in the way that depends on the soil behaviour, the geometry and inertia of the foundation and the dynamic exctation. The practical guideline to analysis block-type foundation excitated by dynamic load from vibrating machine is presented. The analysis use Lumped Mass Parameter Method to express dynamic properties such as stiffness and damping of soil. The numerical examples are performed on design block-type foundation supporting gas turbine compressor which is important equipment package in gas processing plant

Keywords: block foundation, dynamic load, lumped mass parameter

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Authors: Zicheng Wang

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Offshore wind energy provides a huge potential for the expansion of renewable energies to the coastal countries. High demands are required concerning the shape and type of foundations for offshore wind turbines (OWTs) to find an economically, technically and environmentally-friendly optimal solution. A promising foundation concept is the hybrid foundation system, which consists of a steel plate attached to the outer side of a hollow steel pipe pile. In this study, the bearing behavior of a large diameter foundation is analyzed using a 3-dimensional finite element (FE) model. Non-linear plastic soil behavior is considered. The results of the numerical simulations are compared to highlight the priority of the hybrid foundation to the conventional monopile foundation.

Keywords: hybrid foundation system, mechanical parameters, plastic soil behaviors, numerical simulations

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Authors: Abdelazim Makki Ibrahim, Esamaldeen Ali

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This study aims at analysing the load settlement behavior and predict the bearing capacity of piled raft foundation a series of finite element models with different foundation configurations and stiffness were established. Numerical modeling is used to study the behavior of the piled raft foundation due to the complexity of piles, raft, and soil interaction and also due to the lack of reliable analytical method that can predict the behavior of the piled raft foundation system. Simple analytical models are developed to predict the average settlement and the load sharing between the piles and the raft in piled raft foundation system. A simple example to demonstrate the applications of these charts is included.

Keywords: finite element, pile-raft foundation, method, PLAXIS software, settlement

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Authors: Mauricio Terceros, Jann-Eike Saathoff, Martin Achmus

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In non-cohesive soil, onshore wind turbines are often found on shallow foundations with a circular or octagonal shape. For the current generation of wind turbines, shallow foundations with very large breadths are required. The foundation support costs thus represent a considerable portion of the total construction costs. Therefore, an economic optimization of the type of foundation is highly desirable. A conceivable alternative foundation type would be a pier foundation, which combines the load transfer over the foundation area at the pier base with the transfer of horizontal loads over the shaft surface of the pier. The present study aims to evaluate the load-bearing behavior of a pier foundation based on comprehensive parametric studies. Thereby, three-dimensional numerical simulations of both pier and shallow foundations are developed. The evaluation of the results focuses on the rotational stiffnesses of the proposed soil-foundation systems. In the design, the initial rotational stiffness is decisive for consideration of natural frequencies, whereas the rotational secant stiffness for a maximum load is decisive for serviceability considerations. A systematic analysis of the results at different load levels shows that the application of the typical pier foundation is presumably limited to relatively small onshore wind turbines.

Keywords: onshore wind foundation, pier foundation, rotational stiffness of soil-foundation system, shallow foundation

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Authors: Carlos A. Vega-Posada, Jeisson Alejandro Higuita-Villa, Julio C. Saldarriaga-Molina

Abstract:

This paper presents a simplified analytical approach to conduct elastic stability and second-order lateral stiffness analyses of beam-column elements (i.e., piles) with generalized end-boundary conditions embedded on a homogeneous or non-homogeneous Pasternak foundation. The solution is derived using the well-known Differential Transformation Method (DTM), and it consists simply of solving a system of two linear algebraic equations. Using other conventional approaches to solve the governing differential equation of the proposed element can be cumbersome and the solution challenging to implement, especially when the non-homogeneity of the soil is considered. The proposed formulation includes the effects of i) any rotational or lateral transverse spring at the ends of the pile, ii) any external transverse load acting along the pile, iii) soil non-homogeneity, and iv) the second-parameter of the elastic foundation (i.e., shear layer connecting the springs at the top). A parametric study is conducted to investigate the effects of different modulus of subgrade reactions, degrees of non-homogeneities, and intermediate end-boundary conditions on the pile response. The same set of equations can be used to conduct both elastic stability and static analyses. Comprehensive examples are presented to show the simplicity and practicability of the proposed method.

Keywords: elastic stability, second-order lateral stiffness, soil-non-homogeneity, pile analysis

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Authors: K. Karuppasamy

Abstract:

In this paper analysis of an infinite beam resting on multilayer tensionless extensible geosynthetic reinforced granular fill - poor soil system overlying soft soil strata under moving the load with constant velocity is presented. The beam is subjected to a concentrated load moving with constant velocity. The upper reinforced granular bed is modeled by a rough membrane embedded in Pasternak shear layer overlying a series of compressible nonlinear Winkler springs representing the underlying the very poor soil. The multilayer tensionless extensible geosynthetic layer has been assumed to deform such that at the interface the geosynthetic and the soil have some deformation. Nonlinear behavior of granular fill and the very poor soil has been considered in the analysis by means of hyperbolic constitutive relationships. Governing differential equations of the soil foundation system have been obtained and solved with the help of appropriate boundary conditions. The solution has been obtained by employing finite difference method by means of Gauss-Siedel iterative scheme. Detailed parametric study has been conducted to study the influence of various parameters on the response of soil – foundation system under consideration by means of deflection and bending moment in the beam and tension mobilized in the geosynthetic layer. These parameters include the magnitude of applied load, the velocity of the load, damping, the ultimate resistance of the poor soil and granular fill layer. The range of values of parameters has been considered as per Indian Railways conditions. This study clearly observed that the comparisons of multilayer tensionless extensible geosynthetic reinforcement with poor foundation soil and magnitude of applied load, relative compressibility of granular fill and ultimate resistance of poor soil has significant influence on the response of soil – foundation system. However, for the considered range of velocity, the response has been found to be insensitive towards velocity. The ultimate resistance of granular fill layer has also been found to have no significant influence on the response of the system.

Keywords: infinite beams, multilayer tensionless extensible geosynthetic, granular layer, moving load and nonlinear behavior of poor soil

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