Axial–bending coupling vibration of mass eccentric double-beam system with discrete elastic connections

The existence of mass eccentricity will lead to the energy transfer between axial and flexural vibrations of a beam. To study the coupling properties of a double-Timoshenko beam system, a non-uniform coupled double-beam system is modeled in which the upper beam is typical and the lower beam is mass eccentric simulated by a non-uniform two-layer Timoshenko beam. By incorporating Hamilton’s principle and spectral element method, the axial–bending coupled governing equations of the system are derived and the approach can also be easily used to analyze the influences of the parameters and other coupled beam systems. Both the free and forced vibration results of a double-beam system by this method are consistent with the corresponding finite element model’s and thus this method is validated. The coupled properties and their mechanism are revealed. The influences of axial and transverse flexible connection on the coupling properties including free and forced vibration are investigated. A systematic matching principle of reducing the vibration of the coupled system is proposed.

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Longitudinal and Transverse Coupling Dynamic Properties of a Timoshenko Beam with Mass Eccentricity

International Journal of Structural Stability and Dynamics ◽

10.1142/s0219455417500778 ◽

2017 ◽

Vol 17 (07) ◽

pp. 1750077 ◽

Cited By ~ 7

Author(s):

Zhiyang Lei ◽

Jinpeng Su ◽

Hongxing Hua

Keyword(s):

Timoshenko Beam ◽

Control Method ◽

Dynamic Properties ◽

Element Model ◽

Spectral Element ◽

Coupling Mechanism ◽

Beam Model ◽

Coupling Coefficients ◽

Coupling Vibration ◽

Mass Eccentricity

Non-uniform mass distribution on a beam will lead to the coupling between lateral and axial vibrations of the beam. To simulate the mass eccentricity, a double-layered Timoshenko beam model is developed. Based on Hamilton’s principle, the coupled governing equations are derived and mass and stiffness coupling coefficients are also derived. Moreover, the spectral element method (SEM), with high frequency accuracy by employing the dynamic shape functions, is utilized to study the dynamic properties of the beam. In addition, a corresponding finite element model is established to verify the SEM model. The coupling vibration characteristics are investigated and the coupling mechanism is revealed. Furthermore, the effects of mass non--uniformity on the free vibration and forced vibration of the beam with classical and flexible boundary conditions are analyzed. Finally, an optimal control method for reducing the contributions of bending modes under the axial excitation is presented with the results displayed.

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Forced vibration analysis of Timoshenko double-beam system under compressive axial load by means of Green's functions

Journal of Sound and Vibration ◽

10.1016/j.jsv.2019.115001 ◽

2020 ◽

Vol 464 ◽

pp. 115001 ◽

Cited By ~ 6

Author(s):

X. Zhao ◽

B. Chen ◽

Y.H. Li ◽

W.D. Zhu ◽

F.J. Nkiegaing ◽

...

Keyword(s):

Forced Vibration ◽

Vibration Analysis ◽

Axial Load ◽

Green's Functions ◽

Green’S Functions ◽

Beam System ◽

Double Beam ◽

Compressive Axial Load ◽

Forced Vibration Analysis

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Effects of Cable on the Dynamics of a Cantilever Beam with Tip Mass

Shock and Vibration ◽

10.1155/2016/7698729 ◽

2016 ◽

Vol 2016 ◽

pp. 1-10 ◽

Cited By ~ 4

Author(s):

Yi-Xin Huang ◽

Hao Tian ◽

Yang Zhao

Keyword(s):

Cantilever Beam ◽

Spectral Element Method ◽

Natural Frequencies ◽

Spectral Element ◽

Mode Shapes ◽

Beam System ◽

Double Beam ◽

Tip Mass ◽

Beam Mode ◽

Element Method

The dynamic effects of cable attachment on a cantilever beam with tip mass are investigated by an improved Chebyshev spectral element method. The cabled beam is modeled as a double-beam system connected by springs at several discrete locations. By utilizing high order Chebyshev polynomials as basis functions and meshing the system at the locations of connections, precise numerical results of the natural frequencies and mode shapes can be obtained using only a few elements. The accuracy of this method is validated through comparing the results of finite element method and those of spectral element method in literature. The validated method is implemented to investigate the effects of parameters, including spring stiffness, number of connections, density, and Young’s modulus of cable. The results show that the mode shapes of the cabled beam system can be classified into two types: beam mode shapes and cable mode shapes, according to their main deformation. Their corresponding natural frequencies change in very different ways with the variation of system parameters. This work can be applied to optimize the dynamic characteristics of precise spacecraft structures with cable attachments.

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Stability for the Timoshenko Beam System with Local Kelvin–Voigt Damping

Acta Mathematica Sinica English Series ◽

10.1007/s10114-003-0256-4 ◽

2004 ◽

Vol 21 (3) ◽

pp. 655-666 ◽

Cited By ~ 25

Author(s):

Hong Liang Zhao ◽

Kang Sheng Liu ◽

Chun Guo Zhang

Keyword(s):

Timoshenko Beam ◽

Beam System

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Exact dynamic characteristic analysis of a double-beam system interconnected by a viscoelastic layer

Composites Part B Engineering ◽

10.1016/j.compositesb.2018.11.043 ◽

2019 ◽

Vol 163 ◽

pp. 272-281 ◽

Cited By ~ 20

Author(s):

Fei Han ◽

Danhui Dan ◽

Wei Cheng

Keyword(s):

Dynamic Characteristic ◽

Viscoelastic Layer ◽

Characteristic Analysis ◽

Beam System ◽

Double Beam

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Boundary control of a Timoshenko beam system with input dead-zone

International Journal of Control ◽

10.1080/00207179.2014.1003098 ◽

2015 ◽

Vol 88 (6) ◽

pp. 1257-1270 ◽

Cited By ~ 19

Author(s):

Wei He ◽

Tingting Meng ◽

Jin-Kun Liu ◽

Hui Qin

Keyword(s):

Boundary Control ◽

Timoshenko Beam ◽

Dead Zone ◽

Beam System

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Wave-Induced Vibrations of an Axial-Loaded Immersed Timoshenko Beam Carrying an Eccentric Tip Mass with Rotary Inertia

Journal of Ship Research ◽

10.5957/jsr.2010.54.1.15 ◽

2010 ◽

Vol 54 (01) ◽

pp. 15-33

Author(s):

Jong-Shyong Wu ◽

Chin-Tzu Chen

Keyword(s):

Closed Form ◽

Timoshenko Beam ◽

Forced Vibration ◽

Natural Frequencies ◽

Closed Form Solution ◽

Form Solution ◽

Rotary Inertia ◽

Mode Shapes ◽

Mode Superposition Method ◽

Tip Mass

Under the specified assumptions for the equation of motion, the closed-form solution for the natural frequencies and associated mode shapes of an immersed "Euler-Bernoulli" beam carrying an eccentric tip mass possessing rotary inertia has been reported in the existing literature. However, this is not true for the immersed "Timoshenko" beam, particularly for the case with effect of axial load considered. Furthermore, the information concerning the forced vibration analysis of the foregoing Timoshenko beam caused by wave excitations is also rare. Therefore, the first purpose of this paper is to present a technique to obtain the closed-form solution for the natural frequencies and associated mode shapes of an axial-loaded immersed "Timoshenko" beam carrying eccentric tip mass with rotary inertia by using the continuous-mass model. The second purpose is to determine the forced vibration responses of the latter resulting from excitations of regular waves by using the mode superposition method incorporated with the last closed-form solution for the natural frequencies and associated mode shapes of the beam. Because the determination of normal mode shapes of the axial-loaded immersed "Timoshenko" beam is one of the main tasks for achieving the second purpose and the existing literature concerned is scarce, the details about the derivation of orthogonality conditions are also presented. Good agreements between the results obtained from the presented technique and those obtained from the existing literature or conventional finite element method (FEM) confirm the reliability of the presented theories and the developed computer programs for this paper.

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