Nonlinear Dynamic Analysis Using Harmonic Balance Method

Abstract

There is for sure a high demand for nonlinear structural dynamics in implicit Finite Element Analysis (FEA). Although such methods are available, there are severe obstacles to use them daily. One is their extreme and not predictable computation time, which makes it often impossible to get results in time. Another point is the restriction of the methods to the time domain, which is in many cases in contrary to the usual design rules based on frequency domain results.

The Harmonic Balance Method (HBM) is a solution for at least an important sub-class of analysis cases, which resolves the two mentioned obstacles. As a starting point, we define HBM as a frequency response analysis with nonlinear elements like springs, dampers, or control elements. This allows to solve contact problems or mounting problems with nonlinear force-deflection curves. In fact, the HBM is a method in frequency domain, but an alternating use of frequency domain and time domain is necessary to cope with the nonlinearities. The primary results are in frequency domain. For all calculated frequencies, a solution in time domain is also available for a periodic response.

The paper will use a simplified radiator as industrial example to demonstrate the HBM. To prove the validity of the HBM procedure, a comparison with a linear frequency response analysis is performed, which shows same results. Then, rubber bushes and contact are added to the model as nonlinearities. Sufficient damping is applied to avoid multiple solutions for any frequency in the observed frequency range. Then, key results of stress and fatigue are presented. Finally, the computation times are analyzed to demonstrate the feasibility of the described process for practical applications in research and industry.

All simulations are performed with the FEA software PERMAS, which contains the HBM among other analysis methods in structural dynamics.