Flexural vibrations of discontinuous layered elastically bonded beams

Abstract

This paper addresses the dynamic flexural behavior of layered elastically bonded beams carrying an arbitrary number of elastic translational supports and rotational joints. The beams are referred to as discontinuous for the discontinuities of response variables at the application points of supports/joints. The Euler-Bernoulli hypothesis is assumed to hold for each layer separately, and a linear constitutive relation between the horizontal interlayer slip and the interlaminar shear force is considered. Based on the theory of generalized functions to handle the discontinuities of response variables due to supports/joints, exact beam modes are obtained from a characteristic equation built as determinant of a 6 × 6 matrix, regardless of the number of supports/joints. On using pertinent orthogonality condition for the deflection modes, the dynamic response of the beam is derived in time domain. Remarkably, all response variables are presented in a closed analytical form. Two numerical applications illustrate the efficiency of the proposed method.