C. Mei

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

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.

Studying the effects of lumped end mass on vibrations of a Timoshenko beam using a wave-based approach

Mast antenna structures and robot arms are often modeled as beams with lumped end masses. In this paper, bending vibrations in beams with lumped masses at boundaries are studied based on the advanced Timoshenko theory. An exact analytical solution is obtained using a wave vibration approach, in which vibrations are described as waves that propagate along a uniform waveguide (such as a beam element) and are reflected and/or transmitted at discontinuities (such as boundaries and lumped mass attachments). The reflection relation corresponding to a bending incident vibration wave at the end mass is derived, which is assembled with propagation and reflection relations at classical boundaries to obtain the modes of vibrations. The effects of lumped end mass on vibrations of a Timoshenko beam are studied in detail.

In-plane Vibrations of Classical Planar Frame Structures — an Exact Wave-based Analytical Solution:

In this paper, classical theories are applied in modeling in-plane vibrations in planar frame structures. An exact analytical solution has been obtained using a wave vibration approach, in which vibrations are described as waves that propagate along a uniform structural element (waveguide) and are reflected and transmitted at discontinuities (such as structural joints). The propagation, reflection, and transmission matrices, as well as the matrix relations between the injected waves and externally applied forces and moments are obtained using classical vibration theories. The coupling effect between bending and longitudinal vibrations is considered in the derivations. Assembling these matrices provides a concise and systematic approach to vibration analysis of complex in-plane coupled bending and longitudinal vibrations of planar frame structures. Numerical examples are presented, with comparisons to results available in the literature.

Differential transformation approach for free vibration analysis of a centrifugally stiffened timoshenko beam

In this paper, the differential transformation approach is applied to analyze the free vibration of centrifugally stiffened Timoshenko beam structures. Such structures involve variable coefficients in the governing equations, which in general cannot be solved analytically in closed form. Both the natural frequencies and the mode shapes are obtained using the differential transformation technique. Numerical examples are presented and results are compared with available results in the literature.

Free vibration analysis of classical single-story multi-bay planar frames

This paper concerns free vibration analysis of single-story multi-bay planar frame structures. An exact analytical solution is obtained using a wave vibration approach, in which vibrations are described as waves propagating along uniform structural elements and are reflected and transmitted at structural discontinuities. The coupling effects between bending and longitudinal vibrations in the multi-bay frames are taken into account. Both natural frequencies and modeshapes are obtained. Numerical examples are presented along with comparisons to results available in the literature.

Effect of material coupling on wave vibration of composite Timoshenko beams

This paper presents the effect of coupling between bending and torsional deformations on vibrations of composite Timoshenko beams from the wave standpoint. The dispersion characteristics and the modes of vibrations are in general affected by material coupling, except those of the torsional modes at low frequencies; and higher-frequency modes are normally more sensitive to material coupling. The wave mode transition phenomenon is also investigated. It is found that like their metallic counterparts, composite Timoshenko beams also exhibit wave mode transition. Furthermore, the transition frequency is found to be unaffected by material coupling. Numerical examples for which comparative results are available in the literature are presented.

Wave Analysis of In-Plane Vibrations of L-Shaped and Portal Planar Frame Structures

This paper concerns in-plane vibration analysis of coupled bending and longitudinal vibrations in L-shaped and portal planar frame structures. An exact analytical solution is obtained using wave vibration approach. The classical Euler-Bernoulli as well as the advanced Timoshenko bending theories are applied in modeling the flexural vibrations in planar frames. Reflection and transmission matrices corresponding to incident waves arriving at the “L” joint from various directions are obtained. A concise and systematic approach to both free and forced vibration analysis of coupled bending and longitudinal vibrations in L-shaped and portal planar frame structures is presented. Results are compared to the Euler-Bernoulli model results available in the literature. Good agreements have been reached.

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

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 beans components. The systematic approach is illustrated through numerical examples for which comparative results are available in the literature.

Effects of rotary inertia, shear deformation, and joint model on vibration characteristics of single-story multi-bay planar frame structures

The effects of rotary inertia, shear deformation, and joint model on vibration characteristics of single-story multi-bay planar frame structures are studied in this paper. An exact analytical solution is obtained using a wave vibration approach, in which vibrations are described as waves propagating along uniform structural elements and being reflected and transmitted at structural discontinuities. Both bending and longitudinal vibrations in the multi-bay frames are taken into account. It is found that rotary inertia and shear deformation play an important role in accurately predicting natural frequencies of multi-bay frames at higher frequencies. It is also found that the choice of joint model affects the predicted natural frequencies.

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

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.