Modified Energy-Based Time Variational Methods for Obtaining Periodic and Quasi-Periodic Responses

The harmonic Balance Method (HBM) and Time Variational Method (TVM) are two semi-analytical methods used to solve periodically excited dynamical systems. The harmonic Balance Method is modified and extended in several works for solving free vibrations and systems with quasi-periodic responses. Studying the homogeneous response to characterize the system with features like natural frequencies and energy content is very important. In this study, TVM is modified with the addition of energy equations for obtaining multi-frequency responses for multi-DOF autonomous systems and is applied to Duffing oscillator and 2-DOF pendulum system.