Nonlinear Dynamic Analysis Using Harmonic Balance Method

There is a high demand for nonlinear structural dynamics in implicit Finite Element Analysis (FEA). Although such methods are available, there are several obstacles to use them daily. One is their extreme and unpredictable 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 often in contrary to the usual design rules based on frequency domain results. The Harmonic Balance Method (HBM) is a solution for 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 local nonlinearities. This allows to solve contact problems or mounting problems with nonlinear force-deflection curves. The primary results of HBM are in frequency domain. For all calculated frequencies, a solution in time domain is also available for a periodic response. A simplified radiator is used as industrial example. To prove the validity of HBM, 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. Key results of stress and fatigue are presented, and the computation times are analysed to demonstrate the feasibility of the HBM implementation for applications in research and industry. All simulations are performed with the FEA software PERMAS, which contains the HBM among many other analysis methods in structural dynamics.