An efficient computational method for vibration analysis of unsymmetric piecewise-linear dynamical systems with multiple degrees of freedom

Abstract

This paper presents an efficient computational method for determining vibrational responses of piecewise-linear dynamical systems with multiple degrees of freedom (MDOF) and an arbitrary number of gap-activated springs. A time-domain solution is obtained using the Bozzak–Newmark numerical integration scheme. At each time step, an auxiliary displacement vector, complementary to the contact force vector, is introduced. With the help of a simple transformation, the vibration problem is reduced to a standard linear complementarity problem (LCP) for which an accurate solution can be obtained. Responses of an SDOF system with a gap-activated spring and a 3-DOF system with three gap-activated springs under harmonic excitations are obtained using the proposed method, and compared with the results in the literature. Good agreement is observed. The proposed method has also been successfully applied to a piecewise linear dynamical system with 1000 DOF’s and 1000 gap-activated springs under harmonic excitations.