Vol. 5, No. 4, 2010

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Spectral element approach to wave propagation in uncertain beam structures

V. Ajith and S. Gopalakrishnan

Vol. 5 (2010), No. 4, 637–659

This paper presents a study on the uncertainty in material parameters of wave propagation responses in metallic beam structures. Special effort is made to quantify the effect of uncertainty in the wave propagation responses at high frequencies. Both the modulus of elasticity and the density are considered uncertain. The analysis is performed using a Monte Carlo simulation (MCS) under the spectral finite element method (SEM). The randomness in the material properties is characterized by three different distributions, the normal, Weibull and extreme value distributions. Their effect on wave propagation in beams is investigated. The numerical study shows that the CPU time taken for MCS under SEM is about 48 times less than for MCS under a conventional one-dimensional finite element environment for 50 kHz loading. The numerical results presented investigate effects of material uncertainties on high frequency modes. A study is performed on the usage of different beam theories and their uncertain responses due to dynamic impulse load. These studies show that even for a small coefficient of variation, significant changes in the above parameters are noticed. A number of interesting results are presented, showing the true effects of uncertainty response due to dynamic impulse load.

MCS, SEM, normal distribution, Weibull distribution, extreme value distribution, wavenumber, group speeds
Received: 28 July 2009
Revised: 1 January 2010
Accepted: 14 January 2010
Published: 8 November 2010
V. Ajith
Department of Aerospace Engineering
Indian Institute of Science
Bangalore 560012
S. Gopalakrishnan
Department of Aerospace Engineering
Indian Institute of Science
Bangalore 560012