Frequency response calculations of a nonlinear structure a comparison of numerical methods
Paper in proceedings, 2014

Mechanical systems having presence of nonlinearities are often represented by nonlinear ordinary differential equations. For most of such equations, exact analytic solutions are not found; thus numerical techniques have to be used. In many applications, among which model calibration can be one, steady-state frequency response functions are the desired quantities to calculate. The objective of this paper is to compare the performance of computations of nonlinear frequency response functions (FRFs) calculated directly within the frequency domain, using the Multi-Harmonic Balance method, with the time-domain methods Runge-Kutta, Newmark and Pseudo Force in State Space (PFSS). The PFSS method is a recently developed state-space based force feedback method. The accuracy and efficiency of the methods are studied and compared using a model of a cantilever beam connected to a non-linear spring at its free end.

Numerical methods

Frequency response function

Multi-harmonic balance

Nonlinear system



Y. Chen

Linnaeus University, Växjö

Andreas Linderholt

Linnaeus University, Växjö

Thomas Abrahamsson


Conference Proceedings of the Society for Experimental Mechanics Series: 32nd IMAC Conference and Exposition on Structural Dynamics, 2014; Orlando, FL; United States; 3 February 2014 through 6 February 2014

2191-5652 (eISSN)

Vol. 2 35-44

Subject Categories

Mechanical Engineering





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