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.

Vibration analysis of a stepped laminated composite Timoshenko beam

2005 ◽  
Vol 32 (5) ◽  
pp. 572-581 ◽  
Author(s):  
Xing-Jian Dong ◽  
Guang Meng ◽  
Hong-Guang Li ◽  
Lin Ye
Keyword(s):  
Timoshenko Beam ◽  
Vibration Analysis ◽  
Laminated Composite ◽  
Composite Timoshenko Beam

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.

Medium Frequency Vibration Analysis of Beam Structures Modeled by the Timoshenko Beam Theory

2020 ◽  
Author(s):  
Yichi Zhang ◽  
Bingen Yang
Keyword(s):  
Shear Deformation ◽  
Timoshenko Beam ◽  
Vibration Analysis ◽  
Beam Theory ◽  
Timoshenko Beam Theory ◽  
Bernoulli Beam ◽  
Beam Structure ◽  
Medium Frequency ◽  
Beam Structures ◽  
Euler Bernoulli Beam

Abstract Vibration analysis of complex structures at medium frequencies plays an important role in automotive engineering. Flexible beam structures modeled by the classical Euler-Bernoulli beam theory have been widely used in many engineering problems. A kinematic hypothesis in the Euler-Bernoulli beam theory is that plane sections of a beam normal to its neutral axis remain normal when the beam experiences bending deformation, which neglects the shear deformation of the beam. However, as observed by researchers, the shear deformation of a beam component becomes noticeable in high-frequency vibrations. In this sense, the Timoshenko beam theory, which describes both bending deformation and shear deformation, may be more suitable for medium-frequency vibration analysis of beam structures. This paper presents an analytical method for medium-frequency vibration analysis of beam structures, with components modeled by the Timoshenko beam theory. The proposed method is developed based on the augmented Distributed Transfer Function Method (DTFM), which has been shown to be useful in various vibration problems. The proposed method models a Timoshenko beam structure by a spatial state-space formulation in the s-domain, without any discretization. With the state-space formulation, the frequency response of a beam structure, in any frequency region (from low to very high frequencies), can be obtained in an exact and analytical form. One advantage of the proposed method is that the local information of a beam structure, such as displacements, bending moment and shear force at any location, can be directly obtained from the space-state formulation, which otherwise would be very difficult with energy-based methods. The medium-frequency analysis by the augmented DTFM is validated with the FEA in numerical examples, where the efficiency and accuracy of the proposed method is present. Also, the effects of shear deformation on the dynamic behaviors of a beam structure at medium frequencies are illustrated through comparison of the Timoshenko beam theory and the Euler-Bernoulli beam theory.

Optimal design of laminated composite beam structures

2002 ◽  
Vol 24 (3) ◽  
pp. 205-211 ◽  
Author(s):  
J. B. Cardoso ◽  
L. G. Sousa ◽  
J. A. Castro ◽  
A. J. Valido
Keyword(s):  
Optimal Design ◽  
Composite Beam ◽  
Laminated Composite ◽  
Beam Structures ◽  
Laminated Composite Beam

Stochastic response of an axially loaded composite Timoshenko beam exhibiting bending–torsion coupling

2013 ◽  
Vol 84 (1) ◽  
pp. 109-122 ◽  
Author(s):  
Li Jun ◽  
Shi Chaoxing ◽  
Kong Xiangshao ◽  
Li Xiaobin ◽  
Wu Weiguo
Keyword(s):  
Timoshenko Beam ◽  
Stochastic Response ◽  
Axially Loaded ◽  
Composite Timoshenko Beam
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