Free, Forced, And Random Vibrations Of A Beam Composed Of Highly Contrasting Materials

This study deals with free, forced undamped vibration and the random, damped vibration of an inhomogeneous beam composed of two materials with significantly different elastic moduli and material densities. Exact solution is obtained for natural frequencies and the mode shapes using Krylov-Duncan functions, along with the comparison with the results furnished by the Galerkin's method. Random vibrations of the bi-material beams are studied for the first time in the literature for the case of proportional damping. Novel element of this study consists in the unintuitive finding that the response of the bi-material beam may considerably exceed the responses of its homogeneous counterparts, composed of a single material. This finding appears of design significance, suggesting that the natural frequencies of the bi-material beam must be made so as to lie above the cutoff frequency of broad-band cutted white noise. (C) 2020 Elsevier Inc. All rights reserved.