Investigation on Free Vibration of Buckled Beams

2012 ◽  
Vol 433-440 ◽  
pp. 41-44 ◽  
Author(s):  
Ming Hsu Tsai ◽  
Wen Yi Lin ◽  
Kuo Mo Hsiao ◽  
Fu Mio Fujii
Keyword(s):  
Free Vibration ◽  
Virtual Work ◽  
Beam Theory ◽  
Taylor Series Expansion ◽  
Element Formulation ◽  
Governing Equations ◽  
Nonlinear Beam ◽  
Buckled Beams ◽  
Buckled Beam ◽  
D’Alembert Principle

The objective of this study is to investigate the deformed configuration and free vibration around the deformed configuration of clamped buckled beams by co-rotational finite element formulation. The principle of virtual work, d'Alembert principle and the consistent second order linearization of the nonlinear beam theory are used to derive the element equations in current element coordinates. The governing equations for linear vibration are obtained by the first order Taylor series expansion of the equation of motion at the static equilibrium position of the buckled beam. Numerical examples are studied to investigate the natural frequencies of clamped buckled beams with different slenderness ratios under different axial compression.

scholarly journals Vibration and Instability of Rotating Composite Thin-Walled Shafts with Internal Damping

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Ren Yongsheng ◽  
Zhang Xingqi ◽  
Liu Yanghang ◽  
Chen Xiulong
Keyword(s):  
Virtual Work ◽  
Numerical Study ◽  
Equations Of Motion ◽  
Beam Theory ◽  
Dynamical Analysis ◽  
Design Parameters ◽  
Internal Damping ◽  
Analysis Method ◽  
Governing Equations ◽  
Thin Walled

The dynamical analysis of a rotating thin-walled composite shaft with internal damping is carried out analytically. The equations of motion are derived using the thin-walled composite beam theory and the principle of virtual work. The internal damping of shafts is introduced by adopting the multiscale damping analysis method. Galerkin’s method is used to discretize and solve the governing equations. Numerical study shows the effect of design parameters on the natural frequencies, critical rotating speeds, and instability thresholds of shafts.

Nonlinear Free Vibration of a Beam With Off-Axis Attached Mass

2013 ◽  
Author(s):  
Pezhman A. Hassanpour
Keyword(s):  
Free Vibration ◽  
Multiple Scales ◽  
Equations Of Motion ◽  
Center Of Mass ◽  
Beam Theory ◽  
Governing Equations ◽  
Attached Mass ◽  
Lumped Mass ◽  
Nonlinear Free Vibration ◽  
Euler Bernoulli Beam

A model of a clamped-clamped beam with an attached lumped mass is presented in this paper. The system is modeled using the Euler-Bernoulli beam theory. In the models presented in literature, it is assumed that the center of mass of the attached mass is located on the neutral axis of the beam. In this paper, this assumption is relaxed. The governing equations of motion are derived. It has been shown that the off-axis center of mass of the attached mass generates an amplitude-dependent transverse force in the beam, which introduces a quadratic nonlinearity. The nonlinear governing equations of motion are solved using the Multiple Scales method. The nonlinear free vibration frequencies are determined.

scholarly journals Boundary Characteristic Bernstein Polynomials Based Solution for Free Vibration of Euler Nanobeams

2019 ◽  
Vol 3 (4) ◽  
pp. 99
Author(s):  
Somnath Karmakar ◽  
Snehashish Chakraverty
Keyword(s):  
Free Vibration ◽  
Bernstein Polynomials ◽  
Ritz Method ◽  
Beam Theory ◽  
Nonlocal Elasticity Theory ◽  
Computationally Efficient ◽  
Governing Equations ◽  
Classical Boundary ◽  
Convergence Study ◽  
Euler Bernoulli Beam

This paper is concerned with the free vibration problem of nanobeams based on Euler–Bernoulli beam theory. The governing equations for the vibration of Euler nanobeams are considered based on Eringen’s nonlocal elasticity theory. In this investigation, computationally efficient Bernstein polynomials have been used as shape functions in the Rayleigh-Ritz method. It is worth mentioning that Bernstein polynomials make the computation efficient to obtain the frequency parameters. Different classical boundary conditions are considered to address the titled problem. Convergence of frequency parameters is also tested by increasing the number of Bernstein polynomials in the simulation. Further, comparison studies of the results with existing literature are done after fixing the number of polynomials required from the said convergence study. This shows the efficacy and powerfulness of the method. The novelty of using the Bernstein polynomials is addressed in detail and solutions obtained by this method provide a better representation of the vibration behavior of Euler nanobeams.

Finite element analysis of a Timoshenko beam traversed by a moving vehicle

2009 ◽  
Vol 223 (3) ◽  
pp. 231-243
Author(s):  
M Moghaddas ◽  
R Sedaghati ◽  
E Esmailzadeh ◽  
P Khosravi
Keyword(s):  
Finite Element ◽  
Timoshenko Beam ◽  
Equations Of Motion ◽  
Beam Theory ◽  
Weak Form ◽  
Element Formulation ◽  
Governing Equations ◽  
Element Analysis ◽  
Moving Vehicle ◽  
The Difference

In this study the finite element formulation for the dynamics of a bridge traversed by moving vehicles is presented. The vehicle including the driver and the passenger is modelled as a half-car planner model with six degree of freedom, travelling on the bridge with constant velocity. The bridge is modelled as a uniform beam with simply supported end conditions that obeys the Timoshenko beam theory. The governing equations of motion are derived using the extended Hamilton principle and then transformed into the finite element format by using the weak-form formulation. The Newmark-β method is utilized to solve the governing equations and the results are compared with those reported in the literature. Furthermore, the maximum values of deflection for the Timoshenko and Euler—Bernoulli beams have been compared. The results illustrated that as the velocity of the vehicle increases, the difference between the maximum beam deflections in the two beam models becomes more significant.

Nonlinear Free Vibration of Hyperelastic Beams Based on Neo-Hookean Model

2019 ◽  
Vol 20 (01) ◽  
pp. 2050015 ◽  
Author(s):  
Wei Chen ◽  
Lin Wang ◽  
Huliang Dai
Keyword(s):  
Free Vibration ◽  
Large Strain ◽  
Slenderness Ratio ◽  
Taylor Series Expansion ◽  
Soft Materials ◽  
Free Vibrations ◽  
Phase Portraits ◽  
Governing Equations ◽  
Nonlinear Free Vibration ◽  
Initial Displacement

The investigation of hyperelastic responses of soft materials and structures is essential for understanding of the mechanical behaviors and for the design of soft systems. In this paper, by considering both the material and geometrical nonlinearities, a new neo-Hookean model for the hyperelastic beam is developed with focus on its nonlinear free vibration with large strain deformations. The neo-Hookean model is employed to capture the large strain deformation of the hyperelastic beam. The governing equations of the hyperelastic beam are derived by using Hamilton’s principle. To avoid expensive calculations for solving the nonlinear governing equations, a simplified Taylor-series expansion model is proposed. The effects of two key system parameters, i.e. the initial displacement amplitude and the slenderness ratio, on the nonlinear free vibrations of the hyperelastic beam are numerically analyzed. The bifurcation diagrams, displacement time traces, phase portraits and power spectral diagrams are presented for the nonlinear free vibrations of the hyperelastic beam. For small initial displacement amplitudes, it is found that the hyperelastic beam will undergo limit cycle oscillations, depending on the initial amplitude employed. For initial displacement amplitudes large enough, interestingly, the free vibration of the hyperelastic beam will become quasi-periodic or chaotic, which were rarely reported for the free vibration of linearly elastic beams. Also observed is the traveling wave feature of oscillating shapes of the hyperelastic beam, indicating that higher-order modes of the beam are excited even for free vibrations. All these new features in the nonlinear free vibrations of hyperelastic beams indicate that the material and geometric nonlinearities play a great role in the dynamic analysis of hyperelastic beams.

The effects of shear deformation on the free vibration of elastic beams with general boundary conditions

2009 ◽  
Vol 224 (1) ◽  
pp. 71-84 ◽  
Author(s):  
J Li ◽  
H Hua
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Shear Deformation ◽  
Dynamic Stiffness ◽  
Beam Theory ◽  
Mode Shapes ◽  
Governing Equations ◽  
One Dimensional ◽  
Elastic Beams ◽  
Shear Deformable

Free vibration characteristics of shear deformable elastic beams subjected to different sets of boundary conditions are investigated. The analysis is based on a unified one-dimensional shear deformation beam theory. The governing equations of the elastic beams are obtained by means of Hamilton's principle. Four different boundary conditions are considered. The natural frequencies and mode shapes are obtained by applying the dynamic stiffness method, where the elements of the exact dynamic stiffness matrix are derived by using the analytical solutions of the governing equations of the beam in free vibration. The numerical results for the particular beams with different slenderness ratios are presented and compared with those available in the literature.

Free vibration analysis of angle-ply laminate composite beams by mixed finite element formulation using the Gâteaux differential

2014 ◽  
Vol 21 (2) ◽  
pp. 257-266 ◽  
Author(s):  
Atilla Ozutok ◽  
Emrah Madenci ◽  
Fethi Kadioglu
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Timoshenko Beam ◽  
Mixed Finite Element ◽  
Beam Theory ◽  
Bending Moment ◽  
Vertical Displacement ◽  
Composite Beams ◽  
Differential Method ◽  
Element Formulation

AbstractFree vibration analyses of angle-ply laminated composite beams were investigated by the Gâteaux differential method in the present paper. With the use of the Gâteaux differential method, the functionals were obtained and the natural frequencies of the composite beams were computed using the mixed finite element formulation on the basis of the Euler-Bernoulli beam theory and Timoshenko beam theory. By using these functionals in the mixed-type finite element method, two beam elements, CLBT4 and FSDT8, were derived for the Euler-Bernoulli and Timoshenko beam theories, respectively. The CLBT4 element has 4 degrees of freedom (DOFs) containing the vertical displacement and bending moment as the unknowns at the nodes, whereas the FSDT8 element has 8 DOFs containing the vertical displacement, bending moment, shear force and rotation as unknowns. A computer program was developed to execute the analyses for the present study. The numerical results of free vibration analyses obtained for different boundary conditions were presented and compared with the results available in the literature, which indicates the reliability of the present approach.

Free vibration analysis of composite foils with different ply angles based on beam theory

2021 ◽  
Vol 226 ◽  
pp. 108854
Author(s):  
Hanzhe Zhang ◽  
Qin Wu ◽  
Yunqing Liu ◽  
Biao Huang ◽  
Guoyu Wang
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Free Vibration Analysis ◽  
Beam Theory

Thermal Post-Buckling Analysis of Functionally Graded Composite Plates with Nonlinear Aerodynamic Forces

2010 ◽  
Vol 123-125 ◽  
pp. 280-283
Author(s):  
Chang Yull Lee ◽  
Ji Hwan Kim
Keyword(s):  
Material Properties ◽  
Numerical Solutions ◽  
Virtual Work ◽  
Shear Deformation Theory ◽  
Composite Plates ◽  
Buckling Analysis ◽  
Functionally Graded ◽  
Governing Equations ◽  
Functionally Graded Composite ◽  
Post Buckling

The post-buckling of the functionally graded composite plate under thermal environment with aerodynamic loading is studied. The structural model has three layers with ceramic, FGM and metal, respectively. The outer layers of the sandwich plate are different homogeneous and isotropic material properties for ceramic and metal. Whereas the core is FGM layer, material properties vary continuously from one interface to the other in the thickness direction according to a simple power law distribution in terms of the volume fractions. Governing equations are derived by using the principle of virtual work and numerical solutions are solved through a finite element method. The first-order shear deformation theory and von-Karman strain-displacement relations are based to derive governing equations of the plate. Aerodynamic effects are dealt by adopting nonlinear third-order piston theory for structural and aerodynamic nonlinearity. The Newton-Raphson iterative method applied for solving the nonlinear equations of the thermal post-buckling analysis

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