Modeling dynamic behavior of MDOF systems with multiple bilinear springs

Abstract

A computational scheme is presented in this paper to simulate dynamical behavior of multiple degrees of freedom (MDOF) systems with multiple bilinear springs. In the proposed scheme, a bilinear spring is modeled using by two parallel springs - a primary spring and a secondary spring. The primary spring is an ordinary linear spring having identical stiffness in tension and compression, and is active for tension and compression. The secondary spring, whose stiffness characterizes the bilinearity, is active only during compression. It is employed in connection with the Newmark integration method and the linear complementarity problem (LCP) formulation to obtain time-domain responses of dynamical systems with bilinear springs due to initial disturbances and harmonic excitations. The scheme described in this paper is effective in dealing with the sudden transition from tension to compression and vice versa simultaneously for all bilinear springs. Numerical results for bilinear oscillators with finite bilinearity ratios and impact oscillators with an infinite bilinearity ratio show that the proposed bilinear spring model is accurate, generic and valid for bilinearity ratios ranging from zero to infinity. Orderly and chaotic behavior of viscously damped 3-DOF system under harmonic excitation is studied for a wide range of excitation frequencies and bilinear ratios to demonstrate the effectiveness and applicability of the proposed model for MDOF bilinear systems.