Wave Reflection and Transmission in Timoshenko Beams and Wave Analysis of Timoshenko Beam Structures

2004 ◽  
Vol 127 (4) ◽  
pp. 382-394 ◽  
Author(s):  
C. Mei ◽  
B. R. Mace
Keyword(s):  
Timoshenko Beam ◽  
Wave Reflection ◽  
General Point ◽  
Timoshenko Beams ◽  
Wave Analysis ◽  
Reflection And Transmission ◽  
Beam Structures ◽  
The Matrix ◽  
Applied Forces ◽  
Transmission And Reflection

This paper concerns wave reflection, transmission, and propagation in Timoshenko beams together with wave analysis of vibrations in Timoshenko beam structures. The transmission and reflection matrices for various discontinuities on a Timoshenko beam are derived. Such discontinuities include general point supports, boundaries, and changes in section. The matrix relations between the injected waves and externally applied forces and moments are also derived. These matrices can be combined to provide a concise and systematic approach to vibration analysis of Timoshenko beams or complex structures consisting of Timoshenko beam components. The approach is illustrated with several numerical examples.

Free and Forced Wave Vibration Analysis of Axially Loaded Materially Coupled Composite Timoshenko Beam Structures

2005 ◽  
Vol 127 (6) ◽  
pp. 519-529 ◽  
Author(s):  
C. Mei
Keyword(s):  
Timoshenko Beam ◽  
Composite Beam ◽  
Vibration Analysis ◽  
Systematic Approach ◽  
Laminated Composite ◽  
General Point ◽  
Beam Structures ◽  
Applied Forces ◽  
Axially Loaded ◽  
Composite Timoshenko Beam

In this paper, wave vibration analysis of axially loaded bending-torsion coupled composite beam structures is presented. It includes the effects of axial force, shear deformation, and rotary inertia; namely, it is for an axially loaded composite Timoshenko beam. The study also includes the material coupling between the bending and torsional modes of deformations that is usually present in laminated composite beam due to ply orientation. From a wave standpoint, vibrations propagate, reflect, and transmit in a structure. The transmission and reflection matrices for various discontinuities on an axially loaded materially coupled composite Timoshenko beam are derived. Such discontinuities include general point supports, boundaries, and changes in section. The matrix relations between the injected waves and externally applied forces and moments are also derived. These matrices can be combined to provide a concise and systematic approach to vibration analysis of axially loaded materially coupled composite Timoshenko beams or complex structures consisting of such beam components. The systematic approach is illustrated through numerical examples for which comparative results are available in the literature.

Global and Local Wave Vibration Characteristics of Materially Coupled Composite Beam Structures

2005 ◽  
Vol 11 (11) ◽  
pp. 1413-1433 ◽  
Author(s):  
C. Mei
Keyword(s):  
Composite Materials ◽  
Vibration Analysis ◽  
Dynamic Performance ◽  
Free Vibration Analysis ◽  
General Point ◽  
The Matrix ◽  
Local Wave ◽  
Vibration Responses ◽  
Applied Forces ◽  
Global And Local

A unique feature of fiber-reinforced composite materials is that it allows structural tailoring for favorable dynamic performance, due to the directional nature of composite materials. The directional nature causes material coupling, which results in coupled vibrational modes and complicates dynamic analysis. Most of the up-to-date composite structure related dynamic studies focus on free vibration analysis. In this paper, the local wave transmission and reflection characteristics at various discontinuities are studied first. Such discontinuities include general point supports, boundaries and change in sections. The matrix relations between the injected waves and externally applied forces and moments are also derived. By assembling these matrices, both free and forced vibration responses of materially coupled composite Euler–Bernoulli beams are obtained. The wave-based vibration analysis approach is found concise and systematic. Numerical examples are given.

scholarly journals Modal Perturbation Method for the Dynamic Characteristics of Timoshenko Beams

2005 ◽  
Vol 12 (6) ◽  
pp. 425-434 ◽  
Author(s):  
Menglin Lou ◽  
Qiuhua Duan ◽  
Genda Chen
Keyword(s):  
Perturbation Method ◽  
Dynamic Characteristics ◽  
Timoshenko Beam ◽  
Natural Frequencies ◽  
Solution Process ◽  
Equation Of Motion ◽  
Timoshenko Beams ◽  
Algebraic Equations ◽  
Nonlinear Algebraic Equations ◽  
Shear Distortion

Timoshenko beams have been widely used in structural and mechanical systems. Under dynamic loading, the analytical solution of a Timoshenko beam is often difficult to obtain due to the complexity involved in the equation of motion. In this paper, a modal perturbation method is introduced to approximately determine the dynamic characteristics of a Timoshenko beam. In this approach, the differential equation of motion describing the dynamic behavior of the Timoshenko beam can be transformed into a set of nonlinear algebraic equations. Therefore, the solution process can be simplified significantly for the Timoshenko beam with arbitrary boundaries. Several examples are given to illustrate the application of the proposed method. Numerical results have shown that the modal perturbation method is effective in determining the modal characteristics of Timoshenko beams with high accuracy. The effects of shear distortion and moment of inertia on the natural frequencies of Timoshenko beams are discussed in detail.

Discontinuity location on a Timoshenko beam by using a novel wave reflection technique

2013 ◽  
Vol 332 (18) ◽  
pp. 4164-4177
Author(s):  
Qiang Fan ◽  
Zhenyu Huang ◽  
Dayue Chen
Keyword(s):  
Timoshenko Beam ◽  
Wave Reflection

Stability of the Size-Dependent and Functionally Graded Curvilinear Timoshenko Beams

2017 ◽  
Vol 12 (4) ◽  
Author(s):  
J. Awrejcewicz ◽  
A. V. Krysko ◽  
S. P. Pavlov ◽  
M. V. Zhigalov ◽  
V. A. Krysko
Keyword(s):  
Differential Equations ◽  
Functionally Graded Material ◽  
Timoshenko Beam ◽  
Stability Loss ◽  
Functionally Graded ◽  
Beam Deflection ◽  
Timoshenko Beams ◽  
Size Dependent ◽  
Rigid Layer ◽  
Graded Material

The size-dependent model is studied based on the modified couple stress theory for the geometrically nonlinear curvilinear Timoshenko beam made from a functionally graded material having its properties changed along the beam thickness. The influence of the size-dependent coefficient and the material grading on the stability of the curvilinear beams is investigated with the use of the setup method. The second-order accuracy finite difference method is used to solve the problem of nonlinear partial differential equations (PDEs) by reducing it to the Cauchy problem. The obtained set of nonlinear ordinary differential equations (ODEs) is then solved by the fourth-order Runge–Kutta method. The relaxation method is employed to solve numerous static problems based on the dynamic approach. Eight different combinations of size-dependent coefficients and the functionally graded material coefficient are used to study the stress-strain responses of Timoshenko beams. Stability loss of the curvilinear Timoshenko beams is investigated using the Lyapunov criterion based on the estimation of the Lyapunov exponents. Beams with/without the size-dependent behavior, homogeneous beams, and functionally graded beams having the same stiffness are investigated. It is shown that in straight-line beams, the size-dependent effect decreases the beam deflection. The same is observed if the most rigid layer is located on the top of the beam. In the curvilinear Timoshenko beam, such a location of the most rigid layer essentially improves the beam strength against stability loss. The observed transition of the largest Lyapunov exponent from a negative to positive value corresponds to the transition from a precritical to postcritical beam state.

scholarly journals Homogenization of very rough three-dimensional interfaces for the poroelasticity theory with Biot's model

2019 ◽  
Author(s):  
Nguyen Thi Kieu ◽  
Pham Chi Vinh ◽  
Do Xuan Tung
Keyword(s):  
Incident Angle ◽  
Three Dimensional ◽  
Homogenization Method ◽  
Reflection And Transmission Coefficients ◽  
Biot Theory ◽  
Rough Interface ◽  
Matrix Formulation ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
The Matrix

In this paper, we carry out the homogenization of a very rough three-dimensional interface separating  two dissimilar generally anisotropic poroelastic solids modeled by the Biot theory. The very rough interface is assumed to be a cylindrical surface that rapidly oscillates between two parallel planes, and the motion is time-harmonic. Using the homogenization method with the matrix formulation of the poroelasicity theory, the explicit  homogenized equations have been derived. Since the obtained  homogenized equations are totally explicit, they are very convenient for solving various practical problems. As an example proving this, the reflection and transmission of SH waves at a very rough interface of tooth-comb type is considered. The closed-form analytical expressions of the reflection and transmission coefficients have been  derived. Based on them, the effect of the incident angle and some material parameters  on the reflection and transmission coefficients are examined numerically.

scholarly journals WAVE ANALYSIS OF A L-BEAM STRUCTURE WITH A BLOCKING MASS

2020 ◽  
Author(s):  
Johnny Tiu ◽  
Richard Bachoo
Keyword(s):  
Systematic Approach ◽  
Building Blocks ◽  
Element Model ◽  
Structural Systems ◽  
Structural Elements ◽  
Wave Analysis ◽  
Beam Structure ◽  
Reflection Matrix ◽  
Geometric Changes ◽  
Transmission And Reflection

The wave vibration approach regards the vibrations present within a structure as waves, whereby each wave flows along a structural member and upon meeting a discontinuity; portions of the incident wave are reflected and transmitted across the discontinuity. The reflected, transmitted and propagating wave transformations are represented mathematically by matrices, which are used to develop a set of wave relation equations at each discontinuity that can be used to describe the frequency response of the system holistically. This method creates a systematic approach of analysing structures by utilizing common cases as building blocks for a specific structure. The L-joint, described as two beams meeting at right angles; is a ubiquitous case for spatial portal and structural frames, which may become geometrically complex. Such structures are well suited to a wave vibration approach due to the large number of geometric changes and the prevalence as well as recurrence of specific cases. In this paper, the L-joint expanded to include a blocking mass, typically employed in structural systems and allows for the isolation and reflection of vibration away from contiguous structural elements. Included are; variance of transmission and reflection matrix components as the size of the blocking mass increases, numerical examples and comparison to a Finite Element Model developed in ANSYS.

scholarly journals Viscous damage model for timoshenko beam structures

1997 ◽  
Vol 34 (30) ◽  
pp. 3953-3976 ◽  
Author(s):  
A.H. Barbat ◽  
S. Oller ◽  
E. Oñate ◽  
A. Hanganu
Keyword(s):  
Timoshenko Beam ◽  
Damage Model ◽  
Beam Structures

Wave Propagation Analysis of an Axially Strained, Rotating Timoshenko Shaft: Part II

1997 ◽  
Author(s):  
Bongsu Kang ◽  
Chin An Tan
Keyword(s):  
Boundary Conditions ◽  
Wave Reflection ◽  
Axial Strain ◽  
Free Vibration Analysis ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
Propagation Analysis ◽  
Geometric Discontinuities ◽  
Bernoulli Models ◽  
Incident Waves

Abstract In this paper, the wave reflection and transmission characteristics of an axially strained, rotating Timoshenko shaft under general support and boundary conditions, and with geometric discontinuities are examined. As a continuation to Part I of this paper (Kang and Tan, 1997), the wave reflection and transmission at point supports with finite translational and rotational constraints are further discussed. The reflection and transmission matrices for incident waves upon general supports and geometric discontinuities are derived. These matrices are combined, with the aid of the transfer matrix method, to provide a concise and systematic approach for the free vibration analysis of multi-span rotating shafts with general boundary conditions. Results on the wave reflection and transmission coefficients are presented for both the Timoshenko and the Euler-Bernoulli models to investigate the effects of the axial strain, shaft rotation speed, shear and rotary inertia.

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