Modal analysis of nonlinear systems with classical and non-classical damping

Abstract

In the dynamic analysis and design of structures and equipment, the behavior of various components beyond the linear range is often of interest. A nonlinear vibration analysis is time consuming, particularly if many configurations or loading conditions have to be considered in order to arrive at representative values for design. The selection of an efficient and yet accurate analysis procedure is therefore extremely important. Two mode-superposition procedures are presented for the dynamic analysis of nonlinear structures with classical (proportional) and non-classical (non-proportional) damping. The nonlinearity at each time step is treated as a pseudo force. Undamped eigensolution and complex modes are used to uncouple the equations of motion for classical and non-classical damping cases. A recursive procedure based on the exact solution of the differential equation is used to obtain the modal responses. The advantages of the proposed method of computing the response over the existing integration techniques are: (a) the simplicity of the procedure, (b) a substantial reduction in computational time, (c) the possibility of using fewer modes to achieve the desired accuracy, and (d) the adaptability of the procedure to parallel processing machines which will further reduce the computational time.