Spectral Harmonic Balance in Periodic Responses in Nonlinear Structural Dynamics

Description

The fascinating world is manifested by its unpredictability, sensitivity, and adaptability along its path of change or evolution. In engineering, similar phenomena often lead to unexpected results, e.g., failure even when works are well designed and constructed. It is advantageous to be able to find all possible solutions of the irrationally nonlinear governing equations, albeit approximately. For an initially straight beam, the strain is a function of the curvature, which depends on the negative two-third power of the differential arc length. Harmonic balance using trigonometric series is a common method to formulate a set of nonlinear algebraic equations from the governing differential equations for periodic boundary conditions. The impossibility to express the curvature in trigonometric series accurately leads to various approximation theories. A new formulation method will be introduced in this project to handle irrational nonlinear problems accurately, and some effective solution methods will be suggested to find physically realizable solutions. Emphasis is on multiple solutions and their engineering interpretation and applications.