Dynamic stiffness of randomly parametered beams

A finite element-based methodology is developed for the determination of the dynamic stiffness matrix of Euler-Bernoulli beams with randomly varying flexural and axial rigidity, mass density and foundation elastic modulus. The finite element approximation made employs frequency dependent shape functions and the analysis avoids eigenfunction expansion which, not only eliminates modal truncation errors, but also, restricts the number of random variables entering the formulations. Application of the proposed method is illustrated by considering two problems of wide interest in engineering mechanics, namely, vibration of beams on random elastic foundation and the problem of seismic wave amplification through randomly inhomogeneous soil layers. Satisfactory agreement between analytical solutions and a limited amount of digital simulation results is also demonstrated.