Using Harmonic Balance Method for Solving Frequency Response of Systems With Nonlinear Elastic Foundation

Abstract

The frequency response of the console, discretized by three-dimensional finite elements, excited by a pulsating surface distributed load and mounted on a bilateral nonlinear elastic foundation, reaction forces of which are described by the third-degree polynomial, was investigated. The solution was performed in a program library for solving the problems of steady-state vibration of nonlinear dynamic systems, which is being developed in the MATLAB software. To describe the frequency response curve, the Crisfield's continuous arc length method with the secant predictor was applied. The harmonic balance method using the Alternating Frequency-Time scheme was used to evaluate the non-linear forces in each iteration of the solution to solve the steady-state vibration response in every continuation increment.