Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/65726
Title: A double expansion method for the frequency response of finite-length beams with periodic parameters
Authors: Ying, ZG
Ni, YQ
Keywords: Double expansion
Finite periodic beam
Frequency response
Galerkin method
Parameter-varying differential equation
Issue Date: 2017
Publisher: Academic Press
Source: Journal of sound and vibration, 2017, v. 391, p. 180-193 How to cite?
Journal: Journal of sound and vibration 
Abstract: A double expansion method for the frequency response of finite-length beams with periodic distribution parameters is proposed. The vibration response of the beam with spatial periodic parameters under harmonic excitations is studied. The frequency response of the periodic beam is the function of parametric period and then can be expressed by the series with the product of periodic and non-periodic functions. The procedure of the double expansion method includes the following two main steps: first, the frequency response function and periodic parameters are expanded by using identical periodic functions based on the extension of the Floquet-Bloch theorem, and the period-parametric differential equation for the frequency response is converted into a series of linear differential equations with constant coefficients; second, the solutions to the linear differential equations are expanded by using modal functions which satisfy the boundary conditions, and the linear differential equations are converted into algebraic equations according to the Galerkin method. The expansion coefficients are obtained by solving the algebraic equations and then the frequency response function is finally determined. The proposed double expansion method can uncouple the effects of the periodic expansion and modal expansion so that the expansion terms are determined respectively. The modal number considered in the second expansion can be reduced remarkably in comparison with the direct expansion method. The proposed double expansion method can be extended and applied to the other structures with periodic distribution parameters for dynamics analysis. Numerical results on the frequency response of the finite-length periodic beam with various parametric wave numbers and wave amplitude ratios are given to illustrate the effective application of the proposed method and the new frequency response characteristics, including the parameter-excited modal resonance, doubling-peak frequency response and remarkable reduction of the maximum frequency response for certain parametric wave number and wave amplitude. The results have the potential application to structural vibration control.
URI: http://hdl.handle.net/10397/65726
ISSN: 0022-460X
EISSN: 1095-8568
DOI: 10.1016/j.jsv.2016.12.011
Appears in Collections:Journal/Magazine Article

Access
View full-text via PolyU eLinks SFX Query
Show full item record

Page view(s)

14
Checked on Sep 17, 2017

Google ScholarTM

Check

Altmetric



Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.