Vibro-Impact Behavior of Two Orthogonal Beams

Abstract

Structural interaction between two beam-like structures is a situation that occurs in piping systems, among other applications relevant to the nuclear, petroleum, biomedical, and automotive industries, for instance. This paper analytically investigates the repetitive impact dynamics of two orthogonal pinned–pinned beams subjected to base excitation at specified frequency and acceleration. The orthogonal beam configuration restricts the contact to a single point, and the contact interface is modeled by a spring. Although many approaches have been developed for multibody dynamics, the constraint and modal mapping method is efficiently applied herein to obtain the forced response through modal analysis. The vibration is described in a piecewise fashion as switching between the linear in-contact and not-in-contact states, and compatibility conditions are applied at their junctions. The development of the conjoined mode shapes and their orthogonality is derived in detail. The contact impulse is used to describ...