Showing papers on "Timoshenko beam theory published in 2006"
TL;DR: In this article, the elastic buckling analysis of micro- and nano-rods/tubes based on Eringen's nonlocal elasticity theory and the Timoshenko beam theory is concerned.
Abstract: This paper is concerned with the elastic buckling analysis of micro- and nano-rods/tubes based on Eringen's nonlocal elasticity theory and the Timoshenko beam theory. In the former theory, the small scale effect is taken into consideration while the effect of transverse shear deformation is accounted for in the latter theory. The governing equations and the boundary conditions are derived using the principle of virtual work. Explicit expressions for the critical buckling loads are derived for axially loaded rods/tubes with various end conditions. These expressions account for a better representation of the buckling behaviour of micro- and nano-rods/tubes where small scale effect and transverse shear deformation effect are significant. By comparing it with the classical beam theories, the sensitivity of the small scale effect on the buckling loads may be observed.
378 citations
TL;DR: The use of the Timoshenko beam model for free vibration analysis of multi-walled carbon nanotubes (CNTs) is discussed in this paper, where the authors show that the frequencies are significantly overpredicted by the Euler beam theory when the length-to-diameter ratios are small and when considering high vibration modes.
241 citations
TL;DR: In this paper, the existence of low frequency gaps in Timoshenko beams with local resonators was investigated theoretically and experimentally, and it was shown that low frequency flexural vibration gap is indicated by the complex band structure calculated with transfer matrix theory for an infinite beam, as well as the frequency response function calculated with the finite element method for a finite Timoshenko beam with finite local resonance.
Abstract: Flexural vibration in Timoshenko beams with periodically attached local resonators is studied theoretically and experimentally. The existence of a low frequency flexural vibration gap is indicated by the complex band structure calculated with transfer matrix theory for an infinite beam, as well as the frequency response function calculated with the finite element method for a finite Timoshenko beam with finite local resonators. This finite Timoshenko beam was manufactured and vibration experiments generated an experimental frequency response function curve showing a vibration gap as expected. The existence of low frequency gaps in Timoshenko beams with local resonators provides a method of flexural vibration control of beams.
224 citations
TL;DR: In this paper, an analytical method that uses Timoshenko beam theory for calculating the tool point FRF of a given combination by using the receptance coupling and structural modification methods is presented.
Abstract: Regenerative chatter is a well-known machining problem that results in unstable cutting process, poor surface quality and reduced material removal rate. This undesired self-excited vibration problem is one of the main obstacles in utilizing the total capacity of a machine tool in production. In order to obtain a chatter-free process on a machining center, stability diagrams can be used. Numerically or analytically, constructing the stability lobe diagram for a certain spindle–holder–tool combination implies knowing the system dynamics at the tool tip; i.e., the point frequency response function (FRF) that relates the dynamic displacement and force at that point. This study presents an analytical method that uses Timoshenko beam theory for calculating the tool point FRF of a given combination by using the receptance coupling and structural modification methods. The objective of the study is two fold. Firstly, it is aimed to develop a reliable mathematical model to predict tool point FRF in a machining center so that chatter stability analysis can be done, and secondly to make use of this model in studying the effects of individual bearing and contact parameters on tool point FRF so that better approaches can be found in predicting contact parameters from experimental measurements. The model can also be used to study the effects of several spindle, holder and tool parameters on chatter stability. In this paper, the mathematical model, as well as the details of obtaining the system component (spindle, holder and tool) dynamics and coupling them to obtain the tool point FRF are given. The model suggested is verified by comparing the natural frequencies of an example spindle–holder–tool assembly obtained from the model with those obtained from a finite element software. r 2006 Elsevier Ltd. All rights reserved.
208 citations
TL;DR: In this paper, a study of free vibration of Timoshenko beams and Mindlin plates is presented based on a new numerical scheme, where collocation by radial basis functions and pseudospectral methods are combined to produce highly accurate results.
153 citations
TL;DR: In this article, the bending of a Timoshenko beam resting on a Kerr-type three-parameter elastic foundation is introduced, its governing differential equations are formulated and analytically solved, and the solutions are discussed and applied to particular problems.
139 citations
TL;DR: In this paper, the authors studied the wave characteristics in carbon nanotubes (CNTs) via beam theories and compared the applicability of the two beam models from the numerical simulations, and showed the significance of applying an appropriate continuum model in studying the wave propagation in CNTs.
135 citations
TL;DR: In this article, the scale effect on transverse wave propagation in double-walled carbon nanotubes (DWNTs) is studied via nonlocal elastic continuous models. And the diameter-dependent dispersion relations for DWNTs via the nonlocal continuum models are observed as well.
124 citations
TL;DR: In this paper, a theoretical formulation of the linear elastic in-plane and torsional behavior of corrugated web I-girders under inplane loads is presented, and the results for a simply supported span subjected to a uniformly distributed load are presented.
Abstract: A theoretical formulation of the linear elastic in-plane and torsional behavior of corrugated web I-girders under in-plane loads is presented. A typical corrugated web steel I-girder consists of two steel flanges welded to a corrugated steel web. Under a set of simplifying assumptions, the equilibrium of an infinitesimal length of a corrugated web I-girder is studied, and the cross-sectional stresses and stress resultants due to primary bending moment and shear are deduced. The analysis shows that a corrugated web I-girder will twist out-of-plane simultaneously as it deflects in-plane under the action of in-plane loads. In the paper, the in-plane bending behavior is analyzed using conventional beam theory, whereas the out-of-plane torsional behavior is analyzed as a flange transverse bending problem. The results for a simply supported span subjected to a uniformly distributed load are presented. Finally, finite element analysis results are presented and compared to the theoretical results for validation.
118 citations
TL;DR: In this article, a force-based two-dimensional element based on the Timoshenko beam theory was proposed to predict the failure of reinforced concrete (RC) structures under monotonic and cyclic loading.
Abstract: The response of reinforced concrete (RC) structures is often governed by shear failure. This article reports on a study of RC plane frames under monotonic and cyclic loading, including axial, bending, and shear effects. The authors introduce a force-based two-dimensional (2D) element based on the Timoshenko beam theory. The element formulation is general and yields the exact solution within the Timoshenko beam theory. The authors use a simple, nonlinear, shear force-shear deformation law at the section level, together with a classical fiber section for the axial and bending effects. The authors validate their hypotheses through comparisons with experimental data on the shear performance of bridge columns. A case example using a viaduct that collapsed during the 1995 Kobe earthquake is presented. The results highlight the importance of accounting for the limited shear capacity of the piers in predicting the failure mechanism of the structure.
115 citations
TL;DR: In this article, a finite element based model of spindle, tool holder and cutting tool is presented which uses Timoshenko beam theory to obtain the frequency response of the system when gyroscopic terms are included.
Abstract: Dynamic stability of machine tools during operations is dependent on many parameters including the spindle speed. In high and ultra high speed machining, the gyroscopic effect on the spindle dynamics becomes more pronounced and can affect the borders of stability of the rotating system. In this paper, a finite element based model of spindle, tool holder and cutting tool is presented which uses Timoshenko beam theory to obtain the frequency response of the system when gyroscopic terms are included. Using this response, the stability of a high speed spindle system in the presence of gyroscopic effect is investigated. It is shown that the gyroscopic effects lower the critical depth of cut in high speed milling.
TL;DR: A review of contributions and views on the second spectrum of Timoshenko beam theory over the past two decades, together with some new results, are presented in this article, where a simple relationship between the so-called Ostrogradski energy and the mechanical energy is derived for hinged-hinged end conditions.
TL;DR: In this article, a displacement-based 4-node quadrilateral element RDKQ-NL20 and a displacement based 4-Node Quadrilateral Plane Element (QPE) is proposed for geometrically nonlinear analysis of thin to moderately thick laminated composite plates.
Book•
01 Jan 2006
TL;DR: In this paper, the authors present a method for the integration of two-dimensional components in a finite element solution, based on the Green-Gauss Theorem, and evaluate its performance on a set of problems: 1.1 Lagrange Interpolation for Second-Order Problems, 2.2 Finite Element Formulation for Antisymmetric Loading Terms, 3.3 Multi-Factor Adjustment of Stresses, 4.4 Numerical Integration using Gauss Quadrature, and 5.5 Evaluation of Surface Integrals.
Abstract: CONTENTS OF THE BOOK WEB SITE. PREFACE. 1 ESSENTIAL BACKGROUND. 1.1 Steps in a Finite Element Solution. 1.1.1 Two-Node Uniform Bar Element. 1.2 Interpolation Functions. 1.2.1 Lagrange Interpolation for Second-Order Problems. 1.2.2 Hermite Interpolation for Fourth-Order Problems. 1.2.3 Lagrange Interpolation for Rectangular Elements. 1.2.4 Triangular Elements. 1.3 Integration by Parts. 1.3.1 Gauss's Divergence Theorem. 1.3.2 Green-Gauss Theorem. 1.3.3 Green-Gauss Theorem as Integration by Parts in Two Dimensions. 1.4 Numerical Integration Using Gauss Quadrature. 1.4.1 Gauss Quadrature for One-Dimensional Integrals. 1.4.2 Gauss Quadrature for Area Integrals. 1.4.3 Gauss Quadrature for Volume Integrals. 1.5 Mapped Elements. 1.5.1 Restrictions on Mapping of Areas. 1.5.2 Derivatives of the Assumed Solution. 1.5.3 Evaluation of Area Integrals. 1.5.4 Evaluation of Boundary Integrals. Problems. 2 ANALYSIS OF ELASTIC SOLIDS. 2.1 Governing Equations. 2.1.1 Stresses. 2.1.2 Strains. 2.1.3 Constitutive Equations. 2.1.4 Temperature Effects and Initial Strains. 2.1.5 Stress Equilibrium Equations. 2.2 General Form of Finite Element Equations. 2.2.1 Weak Form. 2.2.2 Finite Element Equations. 2.3 Tetrahedral Element. 2.3.1 Interpolation Functions for a Tetrahedral Element. 2.3.2 Tetrahedral Element for Three-Dimensional Elasticity. 2.4 Mapped Solid Elements. 2.4.1 Interpolation Functions for an Eight-Node Solid Element. 2.4.2 Interpolation Functions for a 20-Node Solid Element. 2.4.3 Evaluation of Derivatives. 2.4.4 Integration over Volume. 2.4.5 Evaluation of Surface Integrals. 2.4.6 Evaluation of Line Integrals. 2.4.7 Complete Mathematica/MATLAB Implementations. 2.5 Stress Calculations. 2.5.1 Optimal Locations for Calculating Element Stresses. 2.5.2 Interpolation-Extrapolation of Stresses. 2.5.3 Average Nodal Stresses. 2.5.4 Iterative Improvement in Stresses. 2.6 Static Condensation. 2.7 Substructuring. 2.8 Patch Test and Incompatible Elements. 2.8.1 Convergence Requirements. 2.8.2 Extra Zero-Energy Modes. 2.8.3 Patch Test for Plane Elasticity Problems. 2.8.4 Quadrilateral Element with Additional Bending Shape Functions. 2.9 Computer Implementation: fe2Quad. Problems. 3 SOLIDS OF REVOLUTION. 3.1 Equations of Elasticity in Cylindrical Coordinates. 3.2 Axisymmetric Analysis. 3.2.1 Potential Energy. 3.2.2 Finite Element Equations. 3.2.3 Three-Node Triangular Element. 3.2.4 Mapped Quadrilateral Elements. 3.3 Unsymmetrical Loading. 3.3.1 Fourier Series Representation of Loading. 3.3.2 Finite Element Formulation for Symmetric Loading Terms. 3.3.3 Finite Element Formulation for Antisymmetric Loading Terms. Problems. 4 MULTIFIELD FORMULATIONS FOR BEAM ELEMENTS. 4.1 Euler-Bernoulli Beam Theory. 4.2 Mixed Beam Element Based on EBT. 4.3 Timoshenko Beam Theory. 4.4 Displacement-Based Beam Element for TBT. 4.5 Shear Locking in Displacement-Based Beam Elements for TBT. 4.5.1 Possible Remedies for Shear Locking. 4.6 Mixed Beam Element Based on TBT. 4.7 Four-Field Beam Element for TBT. 4.8 Linked Interpolation Beam Element for TBT. 4.9 Concluding Remarks. Problems. 5 MULTIFIELD FORMULATIONS FOR ANALYSIS OF ELASTIC SOLIDS. 5.1 Governing Equations. 5.2 Displacement Formulation. 5.3 Stress Formulation. 5.4 Mixed Formulation. 5.5 Assumed Stress Field For Mixed Formulation. 5.5.1 Minimum Number of Stress Parameters. 5.5.2 Optimum Number of Stress Parameters. 5.5.3 Suggested Procedure for Determining Appropriate Stress Interpolation. 5.6 Analysis of Nearly Incompressible Solids. 5.6.1 Deviatoric and Volumetric Stresses and Strains. 5.6.2 Poisson Ratio Locking in the Displacement-Based Finite Elements. 5.6.3 Mixed Formulation for Nearly Incompressible Solids. 5.6.4 Finite Element Equations. 5.6.5 Assumed Pressure Solution. 5.6.6 Quadrilateral Elements for Planar Problems. Problems. 6 PLATES AND SHELLS. 6.1 Kirchhoff Plate Theory. 6.1.1 Equilibrium Equations. 6.1.2 Stress Computations. 6.1.3 Weak Form for Displacement-Based Formulation. 6.1.4 General Form of Kirchhoff Plate Element Equations. 6.2 Rectangular Kirchhoff Plate Elements. 6.2.1 MZC (Melosh, Zienkiewicz, and Cheung) Rectangular Plate Element. 6.2.2 Patch Test for Plate Elements. 6.2.3 BFS (Bogner, Fox, and Schmit) Rectangular Plate Element. 6.3 Triangular Kirchhoff Plate Elements. 6.3.1 BCIZ (Bazeley, Cheung, Irons, and Zienkiewicz) Triangular Plate Element. 6.3.2 Conforming Triangular Plate Elements. 6.4 Mixed Formulation for Kirchhoff Plates. 6.5 Mindlin Plate Theory. 6.6 Displacement-Based Finite Elements for Mindlin Plates. 6.6.1 Weak Form. 6.6.2 General Form of Mindlin Plate Element Equations. 6.6.3 Heterosis Element. 6.7 Multifield Elements for Mindlin Plates. 6.8 Analysis of Shell Structures. 6.8.1 Transformation Matrix. 6.8.2 Transformed Equations. Problems. 7 INTRODUCTION TO NONLINEAR PROBLEMS. 7.1 Nonlinear Differential Equation. 7.1.1 Approximate Solutions Using the Classical Form of the Galerkin Method. 7.1.2 Finite Element Solution. 7.2 Solution Procedures for Nonlinear Problems. 7.2.1 Constant Stiffness Iteration. 7.2.2 Load Increments. 7.2.3 Arc-Length Method. 7.3 Linearization and Directional Derivative. 7.3.1 Examples of Linearization. Problems. 8 MATERIAL NONLINEARITY. 8.1 Analysis of Axially Loaded Bars. 8.1.1 Weak Form. 8.1.2 Two-Node Finite Element. 8.1.3 One-Dimensional Plasticity. 8.1.4 Ramberg-Osgood Model. 8.2 Nonlinear Analysis of Trusses. 8.3 Material Nonlinearity in General Solids. 8.3.1 General Form of Finite Element Equations. 8.3.2 General Formulation for Incremental Stress-Strain Equations. 8.3.3 State Determination Procedure. 8.3.4 von Mises Yield Criterion and the Associated Hardening Models. Problems. 9 GEOMETRIC NONLINEARITY. 9.1 Basic Continuum Mechanics Concepts. 9.1.1 Deformation Gradient. 9.1.2 Green-Lagrange Strains. 9.1.3 Cauchy and Piola-Kirchhoff Stresses. 9.2 Governing Differential Equations and Weak Forms. 9.3 Linearization of the Weak Form. 9.4 General Form of Element Tangent Matrices. 9.4.1 State Determination and Check for Convergence. 9.5 Constitutive Equations. 9.5.1 Kirchhoff Material. 9.5.2 Compressible Neo-Hookean Material. 9.6 Computations For a Planar Analysis. 9.7 Deformation-Dependent Loading. 9.7.1 Linearized External Virtual Work for Pressure Loading: General Three-Dimensional Case. 9.7.2 Linearized External Virtual Work for Pressure Loading: Planar Case. 9.8 Linearized Buckling Analysis. 9.8.1 Buckling Load for Trusses. 9.9 Appendix: Double Contraction of Tensors. 9.9.1 Double Contraction of Two Second-Order Tensors. 9.9.2 Double Contraction of a Fourth-Order Tensor with a Second-Order Tensor. Problems. 10 CONTACT PROBLEMS. 10.1 Simple Normal Contact Example. 10.1.1 Direct Solution. 10.1.2 Solution Using Normal Contact Constraint. 10.2 Contact Example Involving Friction. 10.2.1 Solution of a Beam Problem with No Frictional Resistance. 10.2.2 Frictional Constraint Function. 10.2.3 Solution of a Beam Problem with Large Frictional Resistance. 10.2.4 Solution of a Beam Problem with Small Frictional Resistance. 10.3 General Contact Problems. 10.3.1 Contact Point and Gap Calculations. 10.3.2 Forces on the Contact Surface. 10.3.3 Lagrange Multiplier Weak Form. 10.3.4 Penalty Formulation. Problems. BIBLIOGRAPHY. INDEX.
TL;DR: In this paper, a phenomenological enhancement is proposed, which makes these models causal, and the main idea behind this enhancement is that a partial differential equation that governs dynamic behaviour of a causal gradient elasticity model must be of the same order with respect to spatial coordinate and with respect time.
TL;DR: In this paper, a systematic approach to solving the eigenvalue problems associated with the uniform Timoshenko beam model is presented, and the natural frequencies and modes of the pinned-pinned and cantilever beam are discussed.
TL;DR: In this article, a flap-wise bending vibration analysis of a rotating cantilever Timoshenko beam was performed using the differential transform method (DTM) and the Hamiltonian approach was used to obtain the governing equations of motion.
Abstract: Purpose – To perform the flapwise bending vibration analysis of a rotating cantilever Timoshenko beam.Design/methodology/approach – Kinetic and potential energy expressions are derived step by step. Hamiltonian approach is used to obtain the governing equations of motion. Differential transform method (DTM) is applied to solve these equations.Findings – It is observed that the ρIΩ2θ term which is ignored by many researchers and which becomes more important as the rotational speed parameter increases must be included in the formulation.Originality/value – Kinetic and potential energy expressions for rotating Timoshenko beams are derived clearly step by step. It is the first time, for the best of author's knowledge, that DTM has been applied to the blade type rotating Timoshenko beams.
TL;DR: In this article, the buckling analysis of cross-ply laminated beams subjected to different sets of boundary conditions is considered, and the critical buckling loads are obtained by applying the Ritz method where the three displacement components are expressed in a series of simple algebraic polynomials.
TL;DR: In this paper, an analytical method is developed to present the dynamic response of a cracked cantilever beam subject to a concentrated moving load, where the cracked beam system is modeled as a two-span beam and each span of the continuous beam is assumed to obey Euler-Bernoulli beam theory.
TL;DR: In this article, a modified transfer matrix method for analyzing the coupling lateral and torsional vibrations of the symmetric rotor bearing system with an external torque was developed, where Euler's angles were used to describe the orientations of the shaft element and disk.
TL;DR: In this paper, a hybrid method is introduced for the calibration of the spring constants of atomic force microscopy cantilevers, based on the minimization of the difference between the modelled and experimentally determined full-field displacement maps of the surface of the cantilever in motion at several resonant frequencies.
Abstract: A hybrid method is introduced for the calibration of the spring constants of atomic force microscopy cantilevers. It is based on the minimization of the difference between the modelled and experimentally determined full-field displacement maps of the surface of the cantilever in motion at several resonant frequencies. The dynamic mechanical response of the cantilever to periodic motion is measured in a vacuum by means of a scanning vibrometer. Given the dimensions of the cantilever, the obtained surface displacements together with analytical or numerical models are used to resolve the physical unknowns of the probe. These are the elastic properties of the cantilever, and the residual stress state built up during the deposition of the reflective coating on the backside of the cantilever. The scanning vibrometry experiment allows the precise determination of the first ten resonant frequencies and the modes associated. After optimization of the elastic properties and the surface stress, the relative agreement between all resonant frequencies is better than 1% with the finite element model and 2% with the Timoshenko beam equation. The agreement between surface displacements is also excellent when the damping constant of the system has been determined, except for the first lateral mode, which exhibits strong coupling to a reflection of the first torsional mode. Because all the displacements at resonance are known, it is possible to decouple these modes, and the result is shown to compare well with the model. The cantilever being fully characterized (geometry, materials, residual stress state and boundary conditions), it is straightforward to deduce all its spring constants, in the linear and nonlinear elastic regimes.
TL;DR: In this article, a thermal post-buckling analysis of FGM (Functionally Graded Material) Timoshenko beams subjected to transversely non-uniform temperature rise is presented.
Abstract: Analysis of thermal post-buckling of FGM (Functionally Graded Material) Timoshenko beams subjected to transversely non-uniform temperature rise is presented. By accurately considering the axial extension and transverse shear deformation in the sense of theory of Timoshenko beam, geometrical nonlinear governing equations including seven basic unknown functions for functionally graded beams subjected to mechanical and thermal loads were formulated. In the analysis, it was assumed that the material properties of the beam vary continuously as a power function of the thickness coordinate. By using a shooting method, the obtained nonlinear boundary value problem was numerically solved and thermal buckling and post-buckling response of transversely non-uniformly heated FGM Timoshenko beams with fixed-fixed edges were obtained. Characteristic curves of the buckling deformation of the beam varying with thermal load and the power law index are plotted. The effects of material gradient property on the buckling deformation and critical temperature of beam were discussed in details. The results show that there exists the tension-bend coupling deformation in the uniformly heated beam because of the transversely non-uniform characteristic of materials.
TL;DR: In this paper, the quadrilateral area co-ordinate method was used to formulate a new 4-node, 12-dof element, named AC-MQ4, for the Mindlin-Reissner plate bending problem.
Abstract: The quadrilateral area co-ordinate method is used to formulate a new quadrilateral element for Mindlin–Reissner plate bending problem. Firstly, an independent shear field is assumed based on the locking-free Timoshenko's beam formulae; secondly, a fourth-order deflection field is assumed by introducing some generalized conforming conditions; thirdly, the rotation field is determined by the strain–displacement relations. Furthermore, a hybrid post-processing procedure is suggested to improve the stress/internal force solutions. Following this procedure, a new 4-node, 12-dof quadrilateral element, named AC-MQ4, is successfully constructed. Since all formulations are expressed by the area co-ordinates, element AC-MQ4 presents some different, but beneficial characters when compared with other usual models. Numerical examples show the new element is free of shear locking, insensitive to mesh distortion, and possesses excellent accuracy in the analysis of both thick and thin plates. It has also been demonstrated that the area co-ordinate method, the generalized conforming condition method, and the hybrid post-processing procedure are efficient tools for developing simple, effective and reliable finite element models. Copyright © 2005 John Wiley & Sons, Ltd.
14 Jun 2006
TL;DR: In this paper, the Timoshenko beam model is extended with a small amount of Kelvin-Voigt (KV) damping, which models internal material friction rather than viscous interaction with the environment and is present in every realistic material.
Abstract: In this paper we present the first extension of the backstepping methods that we have developed so far for control of parabolic PDEs (thermal, fluid, and chemical reaction dynamics) to second-order PDE systems (often referred loosely as hyperbolic) which model flexible structures and acoustics. We introduce controller and observer designs capable of adding damping to a model of beam dynamics using actuation only at the beam base and using sensing only at the beam tip. We present our designs for the Timoshenko beam model (the most advanced in the catalog of beam models, which also includes the simplest Euler-Bernoulli, as well as the Rayleigh and "shear" beam models) under the assumption that the beam is "slender." We allow the presence of a small amount of Kelvin-Voigt (KV) damping, which models internal material friction (rather than viscous interaction with the environment) and is present in every realistic material, though our method also applies in the completely undamped case. The closed-loop system with our backstepping boundary feedback is equivalent to a model of a string immersed in viscous fluid, with increased stiffness, supported on one end by a spring of high stiffness and on the other end by a damper. Such a closed loop system is very well damped and achieves the same excellent damping performance as the previous damping feedbacks which apply actuation at the free end of the beam. To ease the reader into the ideas, we first present the same method for a wave equation (string) with one free end and with a small amount of KV damping and then pursue the development for the Timoshenko beam model
TL;DR: In this paper, the dynamic response of viscoelastic Timoshenko beams under a moving harmonic load is studied by using Lagrange equations, and convergence studies are made by comparing them with exact solutions based on the Euler-Bernoulli beam theory obtained for the special cases of the investigated problem.
TL;DR: In this paper, it is conjectured that pseudo-second spectrum contributions arising when evanescent waves become propagating above the cut-off frequency ω co = κ AG / ρ I can corrupt the frequency predictions of Timoshenko beam theory.
TL;DR: In this paper, the effects of axial loading, shear deformation and rotary inertia on the axially loaded cracked Timoshenko beam were analyzed and the transmission and reflection matrices for various discontinuities were derived.
TL;DR: In this paper, the free vibration of a cantilever Timoshenko beam with a rigid tip mass is analyzed, where the mass center of the attached mass need not be coincident with its attachment point to the beam.
TL;DR: In this paper, different numerical methods for modal analysis of stepped piezoelectric beams modeled by the Euler-Bernoulli beam theory are compared with the solution of the exact transcendental eigenvalue problem for the infinite dimensional system.
01 Jan 2006
TL;DR: In this article, a flexural-torsional analysis of composite box beams is presented based on the classical lamination theory and accounts for the coupling of flexural and torsional responses for arbitrary laminate stacking sequence configurations.
Abstract: This paper presents a flexural–torsional analysis of composite box beams. A general analytical model applicable to thin-walled box section composite beams subjected to vertical and torsional load is developed. This model is based on the classical lamination theory, and accounts for the coupling of flexural and torsional responses for arbitrary laminate stacking sequence configurations, i.e. unsymmetric as well as symmetric. Governing equations are derived from the principle of the stationary value of total potential energy. Numerical results are obtained for thin-walled composites beams under vertical and torsional loading, addressing the effects of fiber angle and laminate stacking sequence.