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A wavelet-based method for the forced vibration analysis of piecewise linear single- and multi-DOF systems with application to cracked beam dynamics

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Title A wavelet-based method for the forced vibration analysis of piecewise linear single- and multi-DOF systems with application to cracked beam dynamics
 
Creator JOGLEKAR, DM
MITRA, M
 
Subject HARMONIC-BALANCE METHOD
BREATHING CRACK
FINITE-ELEMENT
NONLINEAR BEHAVIOR
DAMAGE DETECTION
CANTILEVER BEAM
CLOSING CRACK
FATIGUE-CRACK
PROPAGATION
IDENTIFICATION
 
Description The present investigation outlines a method based on the wavelet transform to analyze the vibration response of discrete piecewise linear oscillators, representative of beams with breathing cracks. The displacement and force variables in the governing differential equation are approximated using Daubechies compactly supported wavelets. An iterative scheme is developed to arrive at the optimum transform coefficients, which are back transformed to obtain the time domain response. A time integration scheme, solving a linear complementarity problem at every time step, is devised to validate the proposed wavelet based method. Applicability of the proposed solution technique is demonstrated by considering several test cases involving a cracked cantilever beam modeled as a bilinear SDOF system subjected to a harmonic excitation. In particular, the presence of higher order harmonics, originating from the pieccwise linear behavior, is confirmed in all the Lest cases. Parametric study involving the variations in the crack depth, and crack location is performed to bring out their effect on the relative strengths of higher order harmonics. Versatility of the method is demonstrated by considering the cases such as mixed frequency excitation and an MDOF oscillator with multiple bilinear springs. In addition to purporting the wavelet based method as a viable alternative to analyze the response of piecewise linear oscillators, the proposed method can be easily extended to solve inverse problems unlike the other direct time integration schemes. (C) 2015 Elsevier Ltd. All rights reserved.
 
Publisher ACADEMIC PRESS LTD- ELSEVIER SCIENCE LTD
 
Date 2016-01-15T04:31:12Z
2016-01-15T04:31:12Z
2015
 
Type Article
 
Identifier JOURNAL OF SOUND AND VIBRATION, 358,217-235
0022-460X
1095-8568
http://dx.doi.org/10.1016/j.jsv.2015.07.034
http://dspace.library.iitb.ac.in/jspui/handle/100/17763
 
Language en