**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**1980

# Search results for: Timoshenko beam theory

##### 1980 Mechanical Buckling of Engesser-Timoshenko Beams with a Pair of Piezoelectric Layers

**Authors:**
A. R. Nezamabadi,
M. Karami Khorramabadi

**Abstract:**

**Keywords:**
Mechanical Buckling,
Engesser-Timoshenko
beam theory - Piezoelectric layer.

##### 1979 Mechanical Buckling of Functionally Graded Engesser-Timoshenko Beams Located on a Continuous Elastic Foundation

**Authors:**
M. Karami Khorramabadi,
A. R. Nezamabadi

**Abstract:**

**Keywords:**
Mechanical Buckling,
Functionally graded beam- Engesser-Timoshenko beam theory

##### 1978 Vibration Analysis of Functionally Graded Engesser- Timoshenko Beams Subjected to Axial Load Located on a Continuous Elastic Foundation

**Authors:**
M. Karami Khorramabadi,
A. R. Nezamabadi

**Abstract:**

This paper studies free vibration of functionally graded beams Subjected to Axial Load that is simply supported at both ends lies on a continuous elastic foundation. The displacement field of beam is assumed based on Engesser-Timoshenko beam theory. The Young's modulus of beam is assumed to be graded continuously across the beam thickness. Applying the Hamilton's principle, the governing equation is established. Resulting equation is solved using the Euler's Equation. The effects of the constituent volume fractions and foundation coefficient on the vibration frequency are presented. To investigate the accuracy of the present analysis, a compression study is carried out with a known data.

**Keywords:**
Functionally Graded Beam,
Free Vibration,
Elastic
Foundation,
Engesser-Timoshenko Beam Theory.

##### 1977 Multivariable Control of Smart Timoshenko Beam Structures Using POF Technique

**Authors:**
T.C. Manjunath,
B. Bandyopadhyay

**Abstract:**

**Keywords:**
Smart structure,
Timoshenko theory,
Euler-Bernoulli
theory,
Periodic output feedback control,
Finite Element Method,
State space model,
Vibration control,
Multivariable system,
Linear
Matrix Inequality

##### 1976 Vibration Suppression of Timoshenko Beams with Embedded Piezoelectrics Using POF

**Authors:**
T. C. Manjunath,
B. Bandyopadhyay

**Abstract:**

**Keywords:**
Smart structure,
Timoshenko beam theory,
Periodic
output feedback control,
Finite Element Method,
State space model,
SISO,
Embedded sensors and actuators,
Vibration control.

##### 1975 Modeling and FOS Feedback Based Control of SISO Intelligent Structures with Embedded Shear Sensors and Actuators

**Authors:**
T. C. Manjunath,
B. Bandyopadhyay

**Abstract:**

**Keywords:**
Smart structure,
Timoshenko beam theory,
Fast output sampling feedback control,
Finite Element Method,
State space model,
SISO,
Vibration control,
LMI

##### 1974 Forced Vibration of a Planar Curved Beam on Pasternak Foundation

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

**Abstract:**

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.

##### 1973 Free Vibration Analysis of Functionally Graded Beams

**Authors:**
Gholam Reza Koochaki

**Abstract:**

**Keywords:**
Functionally graded beam,
Free vibration,
Hamilton's principle.

##### 1972 Mathematical Modeling of SISO based Timoshenko Structures – A Case Study

**Authors:**
T.C. Manjunath,
Student Member,
B. Bandyopadhyay

**Abstract:**

This paper features the mathematical modeling of a single input single output based Timoshenko smart beam. Further, this mathematical model is used to design a multirate output feedback based discrete sliding mode controller using Bartoszewicz law to suppress the flexural vibrations. The first 2 dominant vibratory modes is retained. Here, an application of the discrete sliding mode control in smart systems is presented. The algorithm uses a fast output sampling based sliding mode control strategy that would avoid the use of switching in the control input and hence avoids chattering. This method does not need the measurement of the system states for feedback as it makes use of only the output samples for designing the controller. Thus, this methodology is more practical and easy to implement.

**Keywords:**
Smart structure,
Timoshenko beam theory,
Discretesliding mode control,
Bartoszewicz law,
Finite Element Method,
State space model,
Vibration control,
Mathematical model,
SISO.

##### 1971 Evaluation of Dynamic Behavior of a Rotor-Bearing System in Operating Conditions

**Authors:**
Mohammad Hadi Jalali,
Behrooz Shahriari,
Mostafa Ghayour,
Saeed Ziaei-Rad,
Shahram Yousefi

**Abstract:**

Most flexible rotors can be considered as beam-like structures. In many cases, rotors are modeled as one-dimensional bodies, made basically of beam-like shafts with rigid bodies attached to them. This approach is typical of rotor dynamics, both analytical and numerical, and several rotor dynamic codes, based on the finite element method, follow this trend. In this paper, a finite element model based on Timoshenko beam elements is utilized to analyze the lateral dynamic behavior of a certain rotor-bearing system in operating conditions.

**Keywords:**
Finite element method,
Operational deflection shape,
Timoshenko beam elements,
Unbalance response.

##### 1970 Vibration of a Beam on an Elastic Foundation Using the Variational Iteration Method

**Authors:**
Desmond Adair,
Kairat Ismailov,
Martin Jaeger

**Abstract:**

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.

##### 1969 Critical Buckling Load of Carbon Nanotube with Non-Local Timoshenko Beam Using the Differential Transform Method

**Authors:**
Tayeb Bensattalah,
Mohamed Zidour,
Mohamed Ait Amar Meziane,
Tahar Hassaine Daouadji,
Abdelouahed Tounsi

**Abstract:**

In this paper, the Differential Transform Method (DTM) is employed to predict and to analysis the non-local critical buckling loads of carbon nanotubes with various end conditions and the non-local Timoshenko beam described by single differential equation. The equation differential of buckling of the nanobeams is derived via a non-local theory and the solution for non-local critical buckling loads is finding by the DTM. The DTM is introduced briefly. It can easily be applied to linear or nonlinear problems and it reduces the size of computational work. Inﬂuence of boundary conditions, the chirality of carbon nanotube and aspect ratio on non-local critical buckling loads are studied and discussed. Effects of nonlocal parameter, ratios L/d, the chirality of single-walled carbon nanotube, as well as the boundary conditions on buckling of CNT are investigated.

**Keywords:**
Boundary conditions,
buckling,
non-local,
the differential transform method.

##### 1968 Molecular Dynamics Simulation for Buckling Analysis at Nanocomposite Beams

**Authors:**
Babak Safaei,
A. M. Fattahi

**Abstract:**

**Keywords:**
Nanocomposites,
molecular dynamics simulation,
axial buckling,
generalized differential quadrature (GDQ).

##### 1967 A Study on Application of Elastic Theory for Computing Flexural Stresses in Preflex Beam

**Authors:**
Nasiri Ahmadullah,
Shimozato Tetsuhiro,
Masayuki Tai

**Abstract:**

This paper presents the step-by-step procedure for using Elastic Theory to calculate the internal stresses in composite bridge girders prestressed by the Preflexing Technology, called Prebeam in Japan and Preflex beam worldwide. Elastic Theory approaches preflex beams the same way as it does the conventional composite girders. Since preflex beam undergoes different stages of construction, calculations are made using different sectional and material properties. Stresses are calculated in every stage using the properties of the specific section. Stress accumulation gives the available stress in a section of interest. Concrete presence in the section implies prestress loss due to creep and shrinkage, however; more work is required to be done in this field. In addition to the graphical presentation of this application, this paper further discusses important notes of graphical comparison between the results of an experimental-only research carried out on a preflex beam, with the results of simulation based on the elastic theory approach, for an identical beam using Finite Element Modeling (FEM) by the author.

**Keywords:**
Composite girder,
elastic theory,
preflex beam,
prestressing.

##### 1966 Dynamic Response of Strain Rate Dependent Glass/Epoxy Composite Beams Using Finite Difference Method

**Authors:**
M. M. Shokrieh,
A. Karamnejad

**Abstract:**

**Keywords:**
Composite beam,
Finite difference method,
Progressive damage modeling,
Strain rate.

##### 1965 Dynamic Modeling of Underplateform Damper used in Turbomachinery

**Authors:**
Vikas Rastogi,
Vipan Kumar,
Loveleen Kumar Bhagi

**Abstract:**

**Keywords:**
Turbine blade vibrations,
Friction dampers,
Timoshenko Beam,
Bond graph modeling.

##### 1964 Stability of Functionally Graded Beams with Piezoelectric Layers Based on the First Order Shear Deformation Theory

**Authors:**
M. Karami Khorramabadi,
A. R. Nezamabadi

**Abstract:**

Stability of functionally graded beams with piezoelectric layers subjected to axial compressive load that is simply supported at both ends is studied in this paper. The displacement field of beam is assumed based on first order shear deformation beam theory. Applying the Hamilton's principle, the governing equation is established. The influences of applied voltage, dimensionless geometrical parameter, functionally graded index and piezoelectric thickness on the critical buckling load of beam are presented. To investigate the accuracy of the present analysis, a compression study is carried out with a known data.

**Keywords:**
Stability,
Functionally graded beam,
First order
shear deformation theory,
Piezoelectric layer.

##### 1963 Vibration Control of a Functionally Graded Carbon Nanotube-Reinforced Composites Beam Resting on Elastic Foundation

**Authors:**
Gholamhosein Khosravi,
Mohammad Azadi,
Hamidreza Ghezavati

**Abstract:**

**Keywords:**
Carbon nanotubes,
vibration control,
piezoelectric layers,
elastic foundation.

##### 1962 Stability of Homogeneous Smart Beams based on the First Order Shear Deformation Theory Located on a Continuous Elastic Foundation

**Authors:**
A. R. Nezamabadi,
M. Karami Khorramabadi

**Abstract:**

**Keywords:**
Stability,
Homogeneous beam- Piezoelectric layer

##### 1961 The Effects of Various Boundary Conditions on Thermal Buckling of Functionally Graded Beamwith Piezoelectric Layers Based on Third order Shear Deformation Theory

**Authors:**
O. Miraliyari

**Abstract:**

This article attempts to analyze functionally graded beam thermal buckling along with piezoelectric layers applying based on the third order shearing deformation theory considering various boundary conditions. The beam properties are assumed to vary continuously from the lower surface to the upper surface of the beam. The equilibrium equations are derived using the total potential energy equations, Euler equations, piezoelectric material constitutive equations and third order shear deformation theory assumptions. In order to fulfill such an aim, at first functionally graded beam with piezoelectric layers applying the third order shearing deformation theory along with clamped -clamped boundary conditions are thoroughly analyzed, and then following making sure of the correctness of all the equations, the very same beam is analyzed with piezoelectric layers through simply-simply and simply-clamped boundary conditions. In this article buckling critical temperature for functionally graded beam is derived in two different ways, without piezoelectric layer and with piezoelectric layer and the results are compared together. Finally, all the conclusions obtained will be compared and contrasted with the same samples in the same and distinguished conditions through tables and charts. It would be noteworthy that in this article, the software MAPLE has been applied in order to do the numeral calculations.

**Keywords:**
Thermal buckling,
functionally graded beam,
piezoelectric layer,
various boundary conditions.

##### 1960 Longitudinal Vibration of a Micro-Beam in a Micro-Scale Fluid Media

**Authors:**
M. Ghanbari,
S. Hossainpour,
G. Rezazadeh

**Abstract:**

In this paper, longitudinal vibration of a micro-beam in micro-scale fluid media has been investigated. The proposed mathematical model for this study is made up of a micro-beam and a micro-plate at its free end. An AC voltage is applied to the pair of piezoelectric layers on the upper and lower surfaces of the micro-beam in order to actuate it longitudinally. The whole structure is bounded between two fixed plates on its upper and lower surfaces. The micro-gap between the structure and the fixed plates is filled with fluid. Fluids behave differently in micro-scale than macro, so the fluid field in the gap has been modeled based on micro-polar theory. The coupled governing equations of motion of the micro-beam and the micro-scale fluid field have been derived. Due to having non-homogenous boundary conditions, derived equations have been transformed to an enhanced form with homogenous boundary conditions. Using Galerkin-based reduced order model**,** the enhanced equations have been discretized over the beam and fluid domains and solve simultaneously in order to obtain force response of the micro-beam. Effects of micro-polar parameters of the fluid as characteristic length scale, coupling parameter and surface parameter on the response of the micro-beam have been studied.

**Keywords:**
Micro-polar theory,
Galerkin method,
MEMS,
micro-fluid.

##### 1959 Nonlinear Finite Element Modeling of Deep Beam Resting on Linear and Nonlinear Random Soil

**Authors:**
M. Seguini,
D. Nedjar

**Abstract:**

**Keywords:**
Finite element method,
geometric nonlinearity,
material nonlinearity,
soil-structure interaction,
spatial variability.

##### 1958 High Sensitivity Crack Detection and Locating with Optimized Spatial Wavelet Analysis

**Authors:**
A. Ghanbari Mardasi,
N. Wu,
C. Wu

**Abstract:**

In this study, a spatial wavelet-based crack localization technique for a thick beam is presented. Wavelet scale in spatial wavelet transformation is optimized to enhance crack detection sensitivity. A windowing function is also employed to erase the edge effect of the wavelet transformation, which enables the method to detect and localize cracks near the beam/measurement boundaries. Theoretical model and vibration analysis considering the crack effect are first proposed and performed in MATLAB based on the Timoshenko beam model. Gabor wavelet family is applied to the beam vibration mode shapes derived from the theoretical beam model to magnify the crack effect so as to locate the crack. Relative wavelet coefficient is obtained for sensitivity analysis by comparing the coefficient values at different positions of the beam with the lowest value in the intact area of the beam. Afterward, the optimal wavelet scale corresponding to the highest relative wavelet coefficient at the crack position is obtained for each vibration mode, through numerical simulations. The same procedure is performed for cracks with different sizes and positions in order to find the optimal scale range for the Gabor wavelet family. Finally, Hanning window is applied to different vibration mode shapes in order to overcome the edge effect problem of wavelet transformation and its effect on the localization of crack close to the measurement boundaries. Comparison of the wavelet coefficients distribution of windowed and initial mode shapes demonstrates that window function eases the identification of the cracks close to the boundaries.

**Keywords:**
Edge effect,
scale optimization,
small crack locating,
spatial wavelet.

##### 1957 Study of Coupled Lateral-Torsional Free Vibrations of Laminated Composite Beam: Analytical Approach

**Authors:**
S.H. Mirtalaie,
M.A. Hajabasi

**Abstract:**

In this paper, an analytical approach is used to study the coupled lateral-torsional vibrations of laminated composite beam. It is known that in such structures due to the fibers orientation in various layers, any lateral displacement will produce a twisting moment. This phenomenon is modeled by the bending-twisting material coupling rigidity and its main feature is the coupling of lateral and torsional vibrations. In addition to the material coupling, the effects of shear deformation and rotary inertia are taken into account in the definition of the potential and kinetic energies. Then, the governing differential equations are derived using the Hamilton-s principle and the mathematical model matches the Timoshenko beam model when neglecting the effect of bending-twisting rigidity. The equations of motion which form a system of three coupled PDEs are solved analytically to study the free vibrations of the beam in lateral and rotational modes due to the bending, as well as the torsional mode caused by twisting. The analytic solution is carried out in three steps: 1) assuming synchronous motion for the kinematic variables which are the lateral, rotational and torsional displacements, 2) solving the ensuing eigenvalue problem which contains three coupled second order ODEs and 3) imposing different boundary conditions related to combinations of simply, clamped and free end conditions. The resulting natural frequencies and mode shapes are compared with similar results in the literature and good agreement is achieved.

**Keywords:**
Free vibration,
laminated composite beam,
material coupling,
state space.

##### 1956 Forced Vibration of a Fiber Metal Laminated Beam Containing a Delamination

**Authors:**
Sh. Mirhosseini,
Y. Haghighatfar,
M. Sedighi

**Abstract:**

Forced vibration problem of a delaminated beam made of fiber metal laminates is studied in this paper. Firstly, a delamination is considered to divide the beam into four sections. The classic beam theory is assumed to dominate each section. The layers on two sides of the delamination are constrained to have the same deflection. This hypothesis approves the conditions of compatibility as well. Consequently, dynamic response of the beam is obtained by the means of differential transform method (DTM). In order to verify the correctness of the results, a model is constructed using commercial software ABAQUS 6.14. A linear spring with constant stiffness takes the effect of contact between delaminated layers into account. The attained semi-analytical outcomes are in great agreement with finite element analysis.

**Keywords:**
Delamination,
forced vibration,
finite element modelling,
natural frequency.

##### 1955 Sub-Impact Phenomenon of Elasto-Plastic Free-Free Beam during a Strike

**Authors:**
H. Rong,
X. C. Yin,
J. Yang,
Y. N. Shen

**Abstract:**

**Keywords:**
beam,
sub-impact,
elastic-plastic deformation,
finite difference method.

##### 1954 Control of Vibrations in Flexible Smart Structures using Fast Output Sampling Feedback Technique

**Authors:**
T.C. Manjunath,
B. Bandyopadhyay

**Abstract:**

**Keywords:**
Smart structure,
Finite element method,
State spacemodel,
Euler-Bernoulli theory,
SISO model,
Fast output sampling,
Vibration control,
LMI

##### 1953 Flexure of Cantilever Thick Beams Using Trigonometric Shear Deformation Theory

**Authors:**
Yuwaraj M. Ghugal,
Ajay G. Dahake

**Abstract:**

A trigonometric shear deformation theory for flexure of thick beams, taking into account transverse shear deformation effects, is developed. The number of variables in the present theory is same as that in the first order shear deformation theory. The sinusoidal function is used in displacement field in terms of thickness coordinate to represent the shear deformation effects. The noteworthy feature of this theory is that the transverse shear stresses can be obtained directly from the use of constitutive relations with excellent accuracy, satisfying the shear stress free conditions on the top and bottom surfaces of the beam. Hence, the theory obviates the need of shear correction factor. Governing differential equations and boundary conditions are obtained by using the principle of virtual work. The thick cantilever isotropic beams are considered for the numerical studies to demonstrate the efficiency of the. Results obtained are discussed critically with those of other theories.

**Keywords:**
Trigonometric shear deformation,
thick beam,
flexure,
principle of virtual work,
equilibrium equations,
stress.

##### 1952 Flexure of Simply Supported Thick Beams Using Refined Shear Deformation Theory

**Authors:**
Yuwaraj M. Ghugal,
Ajay G. Dahake

**Abstract:**

A trigonometric shear deformation theory for flexure of thick beams, taking into account transverse shear deformation effects, is developed. The number of variables in the present theory is same as that in the first order shear deformation theory. The sinusoidal function is used in displacement field in terms of thickness coordinate to represent the shear deformation effects. The noteworthy feature of this theory is that the transverse shear stresses can be obtained directly from the use of constitutive relations with excellent accuracy, satisfying the shear stress free conditions on the top and bottom surfaces of the beam. Hence, the theory obviates the need of shear correction factor. Governing differential equations and boundary conditions are obtained by using the principle of virtual work. The thick simply supported isotropic beams are considered for the numerical studies to demonstrate the efficiency of the results obtained is discussed critically with those of other theories.

**Keywords:**
Trigonometric shear deformation,
thick beam,
flexure,
principle of virtual work,
equilibrium equations,
stress.

##### 1951 Out-of-Plane Free Vibrations of Circular Rods

**Authors:**
Faruk Fırat Çalım,
Nurullah Karaca,
Hakan Tacettin Türker

**Abstract:**

**Keywords:**
Circular rod,
Out-of-plane free vibration analysis,
Transfer Matrix Method.