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Research Papers

Research on Wave Mode Conversion of Curved Beam Structures by the Wave Approach

[+] Author and Article Information
Huang Xiuchang

e-mail: xchhuang@sjtu.edu.cn

Hua Hongxing

Institute of Vibration, Shock and Noise,
State Key Laboratory of Mechanical System
and Vibration,
Shanghai Jiao Tong University,
Shanghai, PRC 200240

Du Zhipeng

Naval Research Center,
Beijing, PRC 100073

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the Journal of Vibration and Acoustics. Manuscript received November 27, 2011; final manuscript received November 3, 2012; published online April 24, 2013. Assoc. Editor: Jean Zu.

J. Vib. Acoust 135(3), 031014 (Apr 24, 2013) (16 pages) Paper No: VIB-11-1284; doi: 10.1115/1.4023817 History: Received November 27, 2011; Revised November 03, 2012

A general wave approach for the vibration analysis of curved beam structures is presented. The analysis is based on wave propagation, transmission, and reflection, including the effects of both propagating and decaying near-field wave components. A matrix formulation is used that offers a systematic and concise method for tackling free and forced vibrations of complex curved beam structures. To illustrate the effectiveness of the approach, several numerical examples are presented. The predictions made using the wave approach are shown to be in excellent agreement with a conventional finite element analysis, with the advantage of reduced computational costs and good conditioning number of the characteristic equation. The developed wave approach is applied to investigate the free vibration, vibration transmission, and power flow of built-up structures consisting of curved beams, straight beams, and masses, with the aim for designing vibration isolation structure with high attenuation ability. Wave reflection and transmission in the infinite curved beam structure, as well as vibration and energy transmission in coupled finite curved beam structure are investigated. Numerical results show that wave mode conversion takes place for the reflected and transmitted wave propagating through a curved beam, and the power flow in the coupled curved beam structure shows energy attenuation and conversion by curved beam and the discontinuities. The investigation will shed some light on the designing of curved beam structures.

Copyright © 2013 by ASME
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Figures

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Fig. 1

Wave transmission and reflection, force and displacement analysis for general four cases: (a) point discontinuities, (b) general boundaries, (c) changes of section and curvature, and (d) externally applied forces

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Fig. 2

Wave transmission and reflection in coupled curved beams and masses: (a) semi-infinite structure and (b) closed finite structure

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Fig. 3

Wave transmission and reflection in coupled curved beams and straight beams: (a) semi-infinite structure, (b) open finite structure, and (c) closed finite structure

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Fig. 4

Energy transmission and reflection coefficients for the curved beam with single/multiple masses

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Fig. 5

Natural frequencies of the coupled masses and finite curved beams by the wave approach

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Fig. 6

The force/displacement responses at mass 1 and 2 by the wave approach and by Ansys

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Fig. 7

The power flow in the coupled masses and finite curved beams

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Fig. 8

Power transmission and reflection coefficients for different ratio of height or width of straight/curved beam

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Fig. 9

Energy transmission and reflection coefficients versus dimensionless frequency and bending angle

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Fig. 10

The force/displacement responses at 5 and 6 in open structure for various excitations

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Fig. 11

The power flow in the open finite curved beam and straight beam structure for various excitations

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Fig. 12

The force/displacement responses at 5 and 6 in closed structure for various excitations

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Fig. 13

The power flow in closed structure for various excitations

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Fig. 14

The power flow distribution in closed structure (specific frequencies)

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Fig. 15

Definitions of geometry and coordinate system of a curved beam: notation and sign convention

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