Dynamics of linear and nonlinear MDOF systems

This chapter considers the linear and nonlinear dynamic of discrete systems having more than one degree of freedom in the time domain. Linear elastic systems are those that experience small deformations, in which the stiffness is constant. The chapter develops the equation of motion for the simplest multi-degree-of-freedom (MDOF) system. It considers the effect of motion of the reference frame, which could be due to earthquake-induced ground motion. The chapter addresses nonlinearity in the force-displacement response of structural components and geometric effects. It discusses drawbacks associated with using Rayleigh damping for linear systems—mainly that the ß term introduces unrealistically high amounts of damping in higher modes and the a term lacks physical plausibility. As nonlinearity develops, softening causes a reduction in the instantaneous modal frequencies.