Periodic Vibration Analysis of Nonlinear Structures by Using Response Dependent Nonlinear Modes

Nonlinear effects may play a crucial role, and therefore cannot be ignored in determining forced response of complex mechanical structures. However, predicting nonlinear dynamic behavior of structures accurately within a reasonable computational time is a challenging issue. In this study, steady state harmonic vibration response of large Multi-Degree of Freedom (MDOF) nonlinear systems is obtained by using a novel modal superposition method employing Response Dependent Nonlinear Modes (RDNM). RDNMs defined at each solution point constitute a new set of modes which forms a very strong basis for the nonlinear response space. Calculating the dynamic response of a nonlinear system by using RDNMs decreases the computational burden substantially. Utilizing only one or two RDNMs may be sufficient in the modal superposition method. In the solution, the Describing Function Method is used to obtain a set of nonlinear algebraic equations which are solved by Newton's method with arc-length continuation. The application of the method is demonstrated on a large MDOF system with some case studies by using different nonlinear elements. Computational times and accuracy of the solutions obtained are compared with those of the existing methods for different error criteria