Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 5252

Search results for: natural frequencies

5252 Modal Analysis of a Cantilever Beam Using an Inexpensive Smartphone Camera: Motion Magnification Technique

Authors: Hasan Hassoun, Jaafar Hallal, Denis Duhamel, Mohammad Hammoud, Ali Hage Diab


This paper aims to prove the accuracy of an inexpensive smartphone camera as a non-contact vibration sensor to recover the vibration modes of a vibrating structure such as a cantilever beam. A video of a vibrating beam is filmed using a smartphone camera and then processed by the motion magnification technique. Based on this method, the first two natural frequencies and their associated mode shapes are estimated experimentally and compared to the analytical ones. Results show a relative error of less than 4% between the experimental and analytical approaches for the first two natural frequencies of the beam. Also, for the first two-mode shapes, a Modal Assurance Criterion (MAC) value of above 0.9 between the two approaches is obtained. This slight error between the different techniques ensures the viability of a cheap smartphone camera as a non-contact vibration sensor, particularly for structures vibrating at relatively low natural frequencies.

Keywords: modal analysis, motion magnification, smartphone camera, structural vibration, vibration modes

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5251 Experimental Modal Analysis of Reinforced Concrete Square Slabs

Authors: M. S. Ahmed, F. A. Mohammad


The aim of this paper is to perform experimental modal analysis (EMA) of reinforced concrete (RC) square slabs. EMA is the process of determining the modal parameters (Natural Frequencies, damping factors, modal vectors) of a structure from a set of frequency response functions FRFs (curve fitting). Although experimental modal analysis (or modal testing) has grown steadily in popularity since the advent of the digital FFT spectrum analyzer in the early 1970’s, studying all members and materials using such method have not yet been well documented. Therefore, in this work, experimental tests were conducted on RC square specimens (0.6m x 0.6m with 40 mm). Experimental analysis is based on freely supported boundary condition. Moreover, impact testing as a fast and economical means of finding the modes of vibration of a structure was used during the experiments. In addition, Pico Scope 6 device and MATLAB software were used to acquire data, analyze and plot Frequency Response Function (FRF). The experimental natural frequencies which were extracted from measurements exhibit good agreement with analytical predictions. It is showed that EMA method can be usefully employed to perform the dynamic behavior of RC slabs.

Keywords: natural frequencies, mode shapes, modal analysis, RC slabs

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5250 Free Vibration Analysis of Composite Beam with Non-Uniform Section Using Analytical, Numerical and Experimental Method

Authors: Kadda Boumediene, Mohamed Ziani


Mainly because of their good ratio stiffness/mass, and in addition to adjustable mechanical properties, composite materials are more and more often used as an alternative to traditional materials in several domains. Before using these materials in practical application, a detailed and precise characterization of their mechanical properties is necessary. In the present work, we will find a dynamic analyze of composite beam (natural frequencies and mode shape), an experimental vibration technique, which presents a powerful tool for the estimation of mechanical characteristics, is used to characterize a dissimilar beam of a Mortar/ natural mineral fiber. The study is completed by an analytic (Rayleigh & Rayleigh-Ritz), experimental and numerical application for non-uniform composite beam of a Mortar/ natural mineral fiber. The study is supported by a comparison between numerical and analytic results as well as a comparison between experimental and numerical results.

Keywords: composite beam, mortar/ natural mineral fiber, mechanical characteristics, natural frequencies, mode shape

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5249 Vibration Absorption Strategy for Multi-Frequency Excitation

Authors: Der Chyan Lin


Since the early introduction by Ormondroyd and Den Hartog, vibration absorber (VA) has become one of the most commonly used vibration mitigation strategies. The strategy is most effective for a primary plant subjected to a single frequency excitation. For continuous systems, notable advances in vibration absorption in the multi-frequency system were made. However, the efficacy of the VA strategy for systems under multi-frequency excitation is not well understood. For example, for an N degrees-of-freedom (DOF) primary-absorber system, there are N 'peak' frequencies of large amplitude vibration per every new excitation frequency. In general, the usable range for vibration absorption can be greatly reduced as a result. Frequency modulated harmonic excitation is a commonly seen multi-frequency excitation example: f(t) = cos(ϖ(t)t) where ϖ(t)=ω(1+α sin⁡(δt)). It is known that f(t) has a series expansion given by the Bessel function of the first kind, which implies an infinity of forcing frequencies in the frequency modulated harmonic excitation. For an SDOF system of natural frequency ωₙ subjected to f(t), it can be shown that amplitude peaks emerge at ω₍ₚ,ₖ₎=(ωₙ ± 2kδ)/(α ∓ 1),k∈Z; i.e., there is an infinity of resonant frequencies ω₍ₚ,ₖ₎, k∈Z, making the use of VA strategy ineffective. In this work, we propose an absorber frequency placement strategy for SDOF vibration systems subjected to frequency-modulated excitation. An SDOF linear mass-spring system coupled to lateral absorber systems is used to demonstrate the ideas. Although the mechanical components are linear, the governing equations for the coupled system are nonlinear. We show using N identical absorbers, for N ≫ 1, that (a) there is a cluster of N+1 natural frequencies around every natural absorber frequency, and (b) the absorber frequencies can be moved away from the plant's resonance frequency (ω₀) as N increases. Moreover, we also show the bandwidth of the VA performance increases with N. The derivations of the clustering and bandwidth widening effect will be given, and the superiority of the proposed strategy will be demonstrated via numerical experiments.

Keywords: Bessel function, bandwidth, frequency modulated excitation, vibration absorber

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5248 Linear Dynamic Stability Analysis of a Continuous Rotor-Disk-Blades System

Authors: F. Rahimi Dehgolan, S. E. Khadem, S. Bab, M. Najafee


Nowadays, using rotating systems like shafts and disks in industrial machines have been increased constantly. Dynamic stability is one of the most important factors in designing rotating systems. In this study, linear frequencies and stability of a coupled continuous flexible rotor-disk-blades system are studied. The Euler-Bernoulli beam theory is utilized to model the blade and shaft. The equations of motion are extracted using the extended Hamilton principle. The equations of motion have been simplified using the Coleman and complex transformations method. The natural frequencies of the linear part of the system are extracted, and the effects of various system parameters on the natural frequencies and decay rates (stability condition) are clarified. It can be seen that the centrifugal stiffening effect applied to the blades is the most important parameter for stability of the considered rotating system. This result highlights the importance of considering this stiffing effect in blades equation.

Keywords: rotating shaft, flexible blades, centrifugal stiffness, stability

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5247 Theoretical Modal Analysis of Freely and Simply Supported RC Slabs

Authors: M. S. Ahmed, F. A. Mohammad


This paper focuses on the dynamic behavior of reinforced concrete (RC) slabs. Therefore, the theoretical modal analysis was performed using two different types of boundary conditions. Modal analysis method is the most important dynamic analyses. The analysis would be modal case when there is no external force on the structure. By using this method in this paper, the effects of freely and simply supported boundary conditions on the frequencies and mode shapes of RC square slabs are studied. ANSYS software was employed to derive the finite element model to determine the natural frequencies and mode shapes of the slabs. Then, the obtained results through numerical analysis (finite element analysis) would be compared with an exact solution. The main goal of the research study is to predict how the boundary conditions change the behavior of the slab structures prior to performing experimental modal analysis. Based on the results, it is concluded that simply support boundary condition has obvious influence to increase the natural frequencies and change the shape of mode when it is compared with freely supported boundary condition of slabs. This means that such support conditions have direct influence on the dynamic behavior of the slabs. Thus, it is suggested to use free-free boundary condition in experimental modal analysis to precisely reflect the properties of the structure. By using free-free boundary conditions, the influence of poorly defined supports is interrupted.

Keywords: natural frequencies, mode shapes, modal analysis, ANSYS software, RC slabs

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5246 Predicting the Frequencies of Tropical Cyclone-Induced Rainfall Events in the US Using a Machine-Learning Model

Authors: Elham Sharifineyestani, Mohammad Farshchin


Tropical cyclones are one of the most expensive and deadliest natural disasters. They cause heavy rainfall and serious flash flooding that result in billions of dollars of damage and considerable mortality each year in the United States. Prediction of the frequency of tropical cyclone-induced rainfall events can be helpful in emergency planning and flood risk management. In this study, we have developed a machine-learning model to predict the exceedance frequencies of tropical cyclone-induced rainfall events in the United States. Model results show a satisfactory agreement with available observations. To examine the effectiveness of our approach, we also have compared the result of our predictions with the exceedance frequencies predicted using a physics-based rainfall model by Feldmann.

Keywords: flash flooding, tropical cyclones, frequencies, machine learning, risk management

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5245 Free Vibration Analysis of Gabled Frame Considering Elastic Supports and Semi-Rigid Connections

Authors: A. Shooshtari, A. R. Masoodi, S. Heyrani Moghaddam


Free vibration analysis of a gabled frame with elastic support and semi-rigid connections is performed by using a program in OpenSees software. Natural frequencies and mode shape details of frame are obtained for two states, which are semi-rigid connections and elastic supports, separately. The members of this structure are analyzed as a prismatic nonlinear beam-column element in software. The mass of structure is considered as two equal lumped masses at the head of two columns in horizontal and vertical directions. Note that the degree of freedom, allocated to all nodes, is equal to three. Furthermore, the mode shapes of frame are achieved. Conclusively, the effects of connections and supports flexibility on the natural frequencies and mode shapes of structure are investigated.

Keywords: natural frequency, mode shape, gabled frame, semi-rigid connection, elastic support, OpenSees software

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5244 Classifying Turbomachinery Blade Mode Shapes Using Artificial Neural Networks

Authors: Ismail Abubakar, Hamid Mehrabi, Reg Morton


Currently, extensive signal analysis is performed in order to evaluate structural health of turbomachinery blades. This approach is affected by constraints of time and the availability of qualified personnel. Thus, new approaches to blade dynamics identification that provide faster and more accurate results are sought after. Generally, modal analysis is employed in acquiring dynamic properties of a vibrating turbomachinery blade and is widely adopted in condition monitoring of blades. The analysis provides useful information on the different modes of vibration and natural frequencies by exploring different shapes that can be taken up during vibration since all mode shapes have their corresponding natural frequencies. Experimental modal testing and finite element analysis are the traditional methods used to evaluate mode shapes with limited application to real live scenario to facilitate a robust condition monitoring scheme. For a real time mode shape evaluation, rapid evaluation and low computational cost is required and traditional techniques are unsuitable. In this study, artificial neural network is developed to evaluate the mode shape of a lab scale rotating blade assembly by using result from finite element modal analysis as training data. The network performance evaluation shows that artificial neural network (ANN) is capable of mapping the correlation between natural frequencies and mode shapes. This is achieved without the need of extensive signal analysis. The approach offers advantage from the perspective that the network is able to classify mode shapes and can be employed in real time including simplicity in implementation and accuracy of the prediction. The work paves the way for further development of robust condition monitoring system that incorporates real time mode shape evaluation.

Keywords: modal analysis, artificial neural network, mode shape, natural frequencies, pattern recognition

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5243 Parametric Analysis and Optimal Design of Functionally Graded Plates Using Particle Swarm Optimization Algorithm and a Hybrid Meshless Method

Authors: Foad Nazari, Seyed Mahmood Hosseini, Mohammad Hossein Abolbashari, Mohammad Hassan Abolbashari


The present study is concerned with the optimal design of functionally graded plates using particle swarm optimization (PSO) algorithm. In this study, meshless local Petrov-Galerkin (MLPG) method is employed to obtain the functionally graded (FG) plate’s natural frequencies. Effects of two parameters including thickness to height ratio and volume fraction index on the natural frequencies and total mass of plate are studied by using the MLPG results. Then the first natural frequency of the plate, for different conditions where MLPG data are not available, is predicted by an artificial neural network (ANN) approach which is trained by back-error propagation (BEP) technique. The ANN results show that the predicted data are in good agreement with the actual one. To maximize the first natural frequency and minimize the mass of FG plate simultaneously, the weighted sum optimization approach and PSO algorithm are used. However, the proposed optimization process of this study can provide the designers of FG plates with useful data.

Keywords: optimal design, natural frequency, FG plate, hybrid meshless method, MLPG method, ANN approach, particle swarm optimization

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5242 Free Vibration of Orthotropic Plate with Four Clamped Edges

Authors: Yang Zhong, Meijie Xu


The explicit solutions for the natural frequencies and mode shapes of the orthotropic rectangular plate with four clamped edges are presented by the double finite cosine integral transform method. In the analysis procedure, the classical orthotropic rectangular thin plate is considered. Because only are the basic dynamic elasticity equations of the orthotropic thin plate adopted, it is not need prior to select the deformation function arbitrarily. Therefore, the solution developed by this paper is reasonable and theoretical. Finally, an illustrative example is given and the results are compared with those reported earlier. This method is found to be easier and effective. The results show reasonable agreement with other available results, but with a simpler and practical approach.

Keywords: rectangular orthotropic plate, four clamped edges, natural frequencies and mode shapes, finite integral transform

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5241 Behavior Fatigue Life of Wind Turbine Rotor with Longitudinal Crack Growth

Authors: S. Lecheb, A. Nour, A. Chellil, H. Mechakra, N. Tchina, H. Kebir


This study concerned the dynamic behavior of the wind turbine rotor. Before all, we have studied the loads applied to the rotor, which allows the knowledge their effect on the fatigue. We also studied the movement of the longitudinal cracked rotor in order to determine stress, strain and displacement. Moreover, to study the issues of cracks in the critical zone ABAQUS software is used, which based to the finite element to give the results. In the first we compared the first six modes shapes between cracking and uncracking of HAWT rotor. In the second part, we show the evolution of six first naturals frequencies with longitudinal crack propagation. Finally, we conclude that the residual change in the naturals frequencies can be used as in shaft crack diagnosis predictive maintenance.

Keywords: wind turbine rotor, natural frequencies, longitudinal crack growth, life time

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5240 Natural Frequency Analysis of a Porous Functionally Graded Shaft System

Authors: Natural Frequency Analysis of a Porous Functionally Graded Shaft System


The vibration characteristics of a functionally graded (FG) rotor model having porosities and micro-voids is investigated using three-dimensional finite element analysis. The FG shaft is mounted with a steel disc located at the midspan. The shaft ends are supported on isotropic bearings. The FG material is composed of a metallic (stainless-steel) and ceramic phase (zirconium oxide) as its constituent phases. The layer wise material property variation is governed by power law. Material property equations are developed for the porosity modelling. Python code is developed to assign the material properties to each layer including the effect of porosities. ANSYS commercial software is used to extract the natural frequencies and whirl frequencies for the FG shaft system. The obtained results show the influence of porosity volume fraction and power-law index, on the vibration characteristics of the ceramic-based FG shaft system.

Keywords: Finite element method, Functionally graded material, Porosity volume fraction, Power law

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5239 Vibration Frequencies Analysis of Nanoporous Graphene Membrane

Authors: Haw-Long Lee, Win-Jin Chang, Yu-Ching Yang


In this study, we use the atomic-scale finite element method to investigate the vibrational behavior of the armchair- and zigzag-structured nanoporous graphene layers with different size under the SFSF and CFFF boundary conditions. The fundamental frequencies computed for the graphene layers without pore are compared with the results of previous studies. We observe very good correspondence of our results with that of the other studies in all the considered cases. For the armchair- and zigzag-structured nanoporous graphene layers under the SFSF and CFFF boundary conditions, the frequencies decrease as the size of the nanopore increase. When the positions of the pore are symmetric with respect to the center of the graphene, the frequency of the zigzag pore graphene is higher than that of the armchair one.

Keywords: atomic-scale finite element method, graphene, nanoporous, natural frequency

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5238 The Effects of the Uniaxial Anisotropy and the Loss Tangent on the Resonant Frequencies in Stacked Rectangular Patches Configuration

Authors: Boualem Mekimah, Abderraouf Messai, Abdelkrim Belhedri


Dielectric substrates have an important attention in the fabrication of microstrip patch antennas. The effects of the uniaxial anisotropy and the loss tangent on resonant frequencies of microstrip patches consist of two perfectly conducting rectangular patches in stacked and offset configuration, embedded in a bilayer medium containing isotropic or uniaxial anisotropic materials. The Green’s functions are discussed in detail and numerical results are validated by comparing the computed results with previously published data. The numerical results show, that the uniaxial anisotropy has more effects on resonant frequencies according to the optical axis. However, the loss tangent of dielectric substrates has almost no effect on resonant frequencies, but it strongly affects the imaginary parts of the resonant frequencies of the antenna. The dielectric constant has no effect on the separation in terms of frequencies.

Keywords: resonant frequencies, loss tangent, microstrip patches, stacked, anisotropic materials, optical axis

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5237 Vibration Based Damage Detection and Stiffness Reduction of Bridges: Experimental Study on a Small Scale Concrete Bridge

Authors: Mirco Tarozzi, Giacomo Pignagnoli, Andrea Benedetti


Structural systems are often subjected to degradation processes due to different kind of phenomena like unexpected loadings, ageing of the materials and fatigue cycles. This is true especially for bridges, in which their safety evaluation is crucial for the purpose of a design of planning maintenance. This paper discusses the experimental evaluation of the stiffness reduction from frequency changes due to uniform damage scenario. For this purpose, a 1:4 scaled bridge has been built in the laboratory of the University of Bologna. It is made of concrete and its cross section is composed by a slab linked to four beams. This concrete deck is 6 m long and 3 m wide, and its natural frequencies have been identified dynamically by exciting it with an impact hammer, a dropping weight, or by walking on it randomly. After that, a set of loading cycles has been applied to this bridge in order to produce a uniformly distributed crack pattern. During the loading phase, either cracking moment and yielding moment has been reached. In order to define the relationship between frequency variation and loss in stiffness, the identification of the natural frequencies of the bridge has been performed, before and after the occurrence of the damage, corresponding to each load step. The behavior of breathing cracks and its effect on the natural frequencies has been taken into account in the analytical calculations. By using a sort of exponential function given from the study of lot of experimental tests in the literature, it has been possible to predict the stiffness reduction through the frequency variation measurements. During the load test also crack opening and middle span vertical displacement has been monitored.

Keywords: concrete bridge, damage detection, dynamic test, frequency shifts, operational modal analysis

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5236 Fracture and Dynamic Behavior of Leaf Spring Suspension

Authors: S. Lecheb, A. Chellil, H. Mechakra, S. Attou, H. Kebir


Although leaf springs are one of the oldest suspension components they are still frequently used, especially in commercial vehicles. Being able to capture the leaf spring characteristics is of significant importance for vehicle handling dynamics studies. The main function of leaf spring is not only to support vertical load but also to isolate road induced vibrations. It is subjected to millions of load cycles leading to fatigue failure. It needs to have excellent fatigue life. The objective of this work is its use of Abaqus software to locate the most stressed areas and predict the areas in which it occurs in fatigue and crack of leaf spring and calculate the stress and frequencies of this model.

Keywords: leaf spring, crack, stress, natural frequencies

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5235 Free Vibration of Axially Functionally Graded Simply Supported Beams Using Differential Transformation Method

Authors: A. Selmi


Free vibration analysis of homogenous and axially functionally graded simply supported beams within the context of Euler-Bernoulli beam theory is presented in this paper. The material properties of the beams are assumed to obey the linear law distribution. The effective elastic modulus of the composite was predicted by using the rule of mixture. Here, the complexities which appear in solving differential equation of transverse vibration of composite beams which limit the analytical solution to some special cases are overcome using a relatively new approach called the Differential Transformation Method. This technique is applied for solving differential equation of transverse vibration of axially functionally graded beams. Natural frequencies and corresponding normalized mode shapes are calculated for different Young’s modulus ratios. MATLAB code is designed to solve the transformed differential equation of the beam. Comparison of the present results with the exact solutions proves the effectiveness, the accuracy, the simplicity, and computational stability of the differential transformation method. The effect of the Young’s modulus ratio on the normalized natural frequencies and mode shapes is found to be very important.

Keywords: differential transformation method, functionally graded material, mode shape, natural frequency

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5234 A Refined Nonlocal Strain Gradient Theory for Assessing Scaling-Dependent Vibration Behavior of Microbeams

Authors: Xiaobai Li, Li Li, Yujin Hu, Weiming Deng, Zhe Ding


A size-dependent Euler–Bernoulli beam model, which accounts for nonlocal stress field, strain gradient field and higher order inertia force field, is derived based on the nonlocal strain gradient theory considering velocity gradient effect. The governing equations and boundary conditions are derived both in dimensional and dimensionless form by employed the Hamilton principle. The analytical solutions based on different continuum theories are compared. The effect of higher order inertia terms is extremely significant in high frequency range. It is found that there exists an asymptotic frequency for the proposed beam model, while for the nonlocal strain gradient theory the solutions diverge. The effect of strain gradient field in thickness direction is significant in low frequencies domain and it cannot be neglected when the material strain length scale parameter is considerable with beam thickness. The influence of each of three size effect parameters on the natural frequencies are investigated. The natural frequencies increase with the increasing material strain gradient length scale parameter or decreasing velocity gradient length scale parameter and nonlocal parameter.

Keywords: Euler-Bernoulli Beams, free vibration, higher order inertia, Nonlocal Strain Gradient Theory, velocity gradient

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5233 Reconfigurable Multiband Meandered Line Antenna

Authors: D. Rama Krishna, Y. Pandu Rangaiah


This paper presents the design of multiband reconfigurable antenna using PIN diodes for four iterations and all the four iterations have been validated by measuring return loss and pattern measurements of developed prototype antenna. The simulated and experimental data have demonstrated the concepts of a multiband reconfigurable antenna by switching OFF and ON of PIN diodes for multiple band frequencies. The technique has taken the advantage of a different number of radiating lengths with the use of PIN diode switches, each configuration resonating at multiband frequencies.

Keywords: frequency reconfigurable, meandered line multiband antenna, PIN diode, multiband frequencies

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5232 Collaborative Early Warning System: An Integrated Framework for Mitigating Impacts of Natural Hazards in the UAE

Authors: Abdulla Al Hmoudi


The impacts and costs of natural disasters on people, properties and the environment is often severe when they occur on a large scale or when not prepared for. Factors such as impacts of climate change, urban growth, poor planning to mention a few, have continued to significantly increase the frequencies and aggravate the impacts of natural hazards across the world; the United Arab Emirates (UAE) inclusive. The lack of deployment of an early warning system, low risk and hazard knowledge and impact of natural hazard experienced in some communities in the UAE have emphasised the need for more effective early warning systems. This paper focuses on the collaborative approach taken to instituting and implementing an early warning system. Using mixed methods 888 people completed the questionnaire and eight people were interviewed in Abu Dhabi. The results indicate that the collaborative approach to early warning system is UAE is needed, but lacks essential principles of the early warning system and currently underutilised. It is recommended that the collaborative early warning system is applied at every stage of the early warning system with the specific responsibility of each stakeholder and actor.

Keywords: community, early warning system, emergency management, UAE

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5231 Molecular Dynamics Simulation of Free Vibration of Graphene Sheets

Authors: Seyyed Feisal Asbaghian Namin, Reza Pilafkan, Mahmood Kaffash Irzarahimi


TThis paper considers vibration of single-layered graphene sheets using molecular dynamics (MD) and nonlocal elasticity theory. Based on the MD simulations, Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS), an open source software, is used to obtain fundamental frequencies. On the other hand, governing equations are derived using nonlocal elasticity and first order shear deformation theory (FSDT) and solved using generalized differential quadrature method (GDQ). The small-scale effect is applied in governing equations of motion by nonlocal parameter. The effect of different side lengths, boundary conditions and nonlocal parameter are inspected for aforementioned methods. Results are obtained from MD simulations is compared with those of the nonlocal elasticity theory to calculate appropriate values for the nonlocal parameter. The nonlocal parameter value is suggested for graphene sheets with various boundary conditions. Furthermore, it is shown that the nonlocal elasticity approach using classical plate theory (CLPT) assumptions overestimates the natural frequencies.

Keywords: graphene sheets, molecular dynamics simulations, fundamental frequencies, nonlocal elasticity theory, nonlocal parameter

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5230 Dynamic Response of Magnetorheological Fluid Tapered Laminated Beams Reinforced with Nano-Particles

Authors: Saman Momeni, Abolghassem Zabihollah, Mehdi Behzad


Non-uniform laminated composite structures are being used in many engineering applications where the structures are subjected to unpredicted vibration. To mitigate the vibration response of these structures, recently, magnetorheological fluid (MR), is added to non-uniform (tapered) thickness laminated composite structures to achieve a new generation of the smart composite as MR tapered beam. However, due to the nature of MR fluid, especially the low stiffness, MR tapered beam exhibit lower stiffness and in turn, lower natural frequencies. To achieve the basic design requirements of the structure without MR fluid, one may need to apply a predefined magnetic energy to the structures, requiring a constant source of energy. In the present work, a passive initial stiffness control of MR tapered beam has been studied. The effects of adding nanoparticles on the dynamic response of MR tapered beam has been investigated. It is observed that adding nanoparticles up to 3% may significantly modify the natural frequencies of the structures and achieve dynamic behavior of the structures before addition of MR fluid. Two Models of tapered structures have been taken into consideration. It is observed that adding only 3% of nanoparticles backs the structures to its initial dynamic behavior.

Keywords: non uniform laminated structures, MR fluid, nanoparticles, vibration, stiffness

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5229 Analyzing Habits of Brushing Teeth in Yuzawa Town, Japan

Authors: Takeo Shibata, Arihito Endo, Akemi Kunimatsu, Chika Hiraga, Yoko Shimizu


Introduction: Yuzawa Town, located in the Niigata prefecture of Japan, is famous for its hot springs. A health promotion program, Yuzawa family health plan, was initiated in 2002. It has been held for fifteen years. We evaluated the profiles of brushing teeth in adults. Subjects: 368 questionnaires were corrected from people who live in Yuzawa town. The range of age was between nineteen and sixty-four years old. Methods: Mann-Whitney’s U test and Kruskal-Wallis test were used to evaluate significant differences in frequencies of brushing teeth per a day. Chi-square test and the adjusted residuals were used to evaluate when they brush their teeth. Results: Women showed greater frequencies of brushing teeth per a day than men. No difference was shown by age. Construction workers showed fewer frequencies of brushing teeth. Specialized technicians, clerical workers, and housewives showed greater frequencies. People who know Yuzawa family health plan, take a regular life, or take a breakfast every day showed greater frequencies. People who think not healthy, don’t care a balance of foods, don’t take yearly health check-up, or smoke showed fewer frequencies. After breakfast, women and specialized technicians showed greater frequencies, and construction workers and self-employed workers showed fewer frequencies. After lunch, clerical workers and specialized technicians showed greater frequencies. There was no significant difference at after waking up, after dinner, and before going to bed. Construction workers showed a lower rate of having a marital partner and having information of health. Conclusion: Gender and occupational differences were shown in frequencies of brushing teeth per a day. A promotion of teeth brushing for male, especially construction workers and self-employed workers, is needed.

Keywords: health promotion, Yuzawa family health plan, brushing teeth, occupational difference

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5228 Application of the Extended Kantorovich Method to Size-Dependent Vibrational Analysis of Fully Clamped Rectangular Micro-Plates

Authors: Amir R. Askari, Masoud Tahani


The objective of the present paper is to investigate the effect of size on the vibrational behavior of fully clamped rectangular micro-plates based on the modified couple stress theory (MCST). To this end, a size-dependent Kirchhoff plate model is considered and the equation of motion which accounts for the effect of residual and couple stress components is derived using the Hamilton's principle. The eigenvalue problem associated with the free vibrations of fully clamped micro-plates is extracted and solved analytically using the extended Kantorovich method (EKM). The present findings are compared and validated by available results in the literature and an excellent agreement between them is observed. A parametric study is also conducted to show the significant effects of couple stress components on natural frequencies of fully clamped micro-plates. It is found that the ratio of MCST natural frequencies to those obtained by the classical theory (CT) only depends on the Poisson's ratio of the plate and is totally independent of plate's aspect ratio for cases with no residual stresses.

Keywords: vibrational analysis, modified couple stress theory, fully clamped rectangular micro-plates, extended Kantorovich method.

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5227 Vibration of a Beam on an Elastic Foundation Using the Variational Iteration Method

Authors: Desmond Adair, Kairat Ismailov, Martin Jaeger


Modelling of Timoshenko beams on elastic foundations has been widely used in the analysis of buildings, geotechnical problems, and, railway and aerospace structures. For the elastic foundation, the most widely used models are one-parameter mechanical models or two-parameter models to include continuity and cohesion of typical foundations, with the two-parameter usually considered the better of the two. Knowledge of free vibration characteristics of beams on an elastic foundation is considered necessary for optimal design solutions in many engineering applications, and in this work, the efficient and accurate variational iteration method is developed and used to calculate natural frequencies of a Timoshenko beam on a two-parameter foundation. The variational iteration method is a technique capable of dealing with some linear and non-linear problems in an easy and efficient way. The calculations are compared with those using a finite-element method and other analytical solutions, and it is shown that the results are accurate and are obtained efficiently. It is found that the effect of the presence of the two-parameter foundation is to increase the beam’s natural frequencies and this is thought to be because of the shear-layer stiffness, which has an effect on the elastic stiffness. By setting the two-parameter model’s stiffness parameter to zero, it is possible to obtain a one-parameter foundation model, and so, comparison between the two foundation models is also made.

Keywords: Timoshenko beam, variational iteration method, two-parameter elastic foundation model

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5226 Heat Transfer Enhancement by Turbulent Impinging Jet with Jet's Velocity Field Excitations Using OpenFOAM

Authors: Naseem Uddin


Impinging jets are used in variety of engineering and industrial applications. This paper is based on numerical simulations of heat transfer by turbulent impinging jet with velocity field excitations using different Reynolds Averaged Navier-Stokes Equations models. Also Detached Eddy Simulations are conducted to investigate the differences in the prediction capabilities of these two simulation approaches. In this paper the excited jet is simulated in non-commercial CFD code OpenFOAM with the goal to understand the influence of dynamics of impinging jet on heat transfer. The jet’s frequencies are altered keeping in view the preferred mode of the jet. The Reynolds number based on mean velocity and diameter is 23,000 and jet’s outlet-to-target wall distance is 2. It is found that heat transfer at the target wall can be influenced by judicious selection of amplitude and frequencies.

Keywords: excitation, impinging jet, natural frequency, turbulence models

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5225 Bridge Damage Detection and Stiffness Reduction Using Vibration Data: Experimental Investigation on a Small Scale Steel Bridge

Authors: Mirco Tarozzi, Giacomo Pignagnoli, Andrea Benedetti


The design of planning maintenance of civil structures often requires the evaluation of their level of safety in order to be able to choose which structure, and in which measure, it needs a structural retrofit. This work deals with the evaluation of the stiffness reduction of a scaled steel deck due to the presence of localized damages. The dynamic tests performed on it have shown the variability of its main frequencies linked to the gradual reduction of its rigidity. This deck consists in a steel grillage of four secondary beams and three main beams linked to a concrete slab. This steel deck is 6 m long and 3 m wide and it rests on two abutments made of concrete. By processing the signals of the accelerations due to a random excitation of the deck, the main natural frequencies of this bridge have been extracted. In order to assign more reliable parameters to the numerical model of the deck, some load tests have been performed and the mechanical property of the materials and the supports have been obtained. The two external beams have been cut at one third of their length and the structural strength has been restored by the design of a bolted plate. The gradual loss of the bolts and the plates removal have made the simulation of localized damage possible. In order to define the relationship between frequency variation and loss in stiffness, the identification of its natural frequencies has been performed, before and after the occurrence of the damage, corresponding to each step. The study of the relationship between stiffness losses and frequency shifts has been reported in this paper: the square of the frequency variation due to the presence of the damage is proportional to the ratio between the rigidities. This relationship can be used to quantify the loss in stiffness of a real scale bridge in an efficient way.

Keywords: damage detection, dynamic test, frequency shifts, operational modal analysis, steel bridge

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5224 Three-Dimensional Vibration Characteristics of Piezoelectric Semi-Spherical Shell

Authors: Yu-Hsi Huang, Ying-Der Tsai


Piezoelectric circular plates can provide out-of-plane vibrational displacements on low frequency and in-plane vibrational displacements on high frequency. Piezoelectric semi-spherical shell, which is double-curvature structure, can induce three-dimensional vibrational displacements over a large frequency range. In this study, three-dimensional vibrational characteristics of piezoelectric semi-spherical shells with free boundary conditions are investigated using three experimental methods and finite element numerical modeling. For the experimental measurements, amplitude-fluctuation electronic speckle pattern interferometry (AF-ESPI) is used to obtain resonant frequencies and radial and azimuthal mode shapes. This optical technique utilizes a full-field and non-contact optical system that measures both the natural frequency and corresponding vibration mode shape simultaneously in real time. The second experimental technique used, laser displacement meter is a point-wise displacement measurement method that determines the resonant frequencies of the piezoelectric shell. An impedance analyzer is used to determine the in-plane resonant frequencies of the piezoelectric semi-spherical shell. The experimental results of the resonant frequencies and mode shapes for the piezoelectric shell are verified with the result from finite element analysis. Excellent agreement between the experimental measurements and numerical calculation is presented on the three-dimensional vibrational characteristics of the piezoelectric semi-spherical shell.

Keywords: piezoelectric semi-spherical shell, mode shape, resonant frequency, electronic speckle pattern interferometry, radial vibration, azimuthal vibration

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5223 Vibration Response of Soundboards of Classical Guitars

Authors: Meng Koon Lee, Mohammad Hosseini Fouladi, Satesh Narayana Namasivayam


Research is focused on the response of soundboards of Classical guitars at frequencies up to 5 kHz as the soundboard is a major contributor to acoustic radiation at high frequencies when compared to the bridge and sound hole. A thin rectangular plate of variable thickness that is simply-supported on all sides is used as an analytical model of the research. This model is used to study the response of the guitar soundboard as the latter can be considered as a modified form of a rectangular plate. Homotopy Perturbation Method (HPM) is selected as a mathematical method to obtain an analytical solution of the 4th-order parabolic partial differential equation of motion of the rectangular plate of constant thickness viewed as a linear problem. This procedure is generalized to the nonlinear problem of the rectangular plate with variable thickness and an analytical solution can also be obtained. Sound power is used as a parameter to investigate the acoustic radiation of soundboards made from spruce using various bracing patterns. The sound power of soundboards made from Malaysian softwood such as damar minyak, sempilor or podo are investigated to determine the viability of replacing spruce as future materials for soundboards of Classical guitars.

Keywords: rectangular plates, analytical solution, homotopy perturbation, natural frequencies

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