Abstract
In this paper we present a mixed shooting – harmonic balance method for
large linear mechanical systems on which local nonlinearities are imposed. The standard
harmonic balance method (HBM), which approximates the periodic solution
in frequency domain, is very popular as it is well suited for large systems with
many degrees of freedom. However, it suffers from the fact that local nonlinearities
cannot be evaluated directly in the frequency domain. The standard HBM performs
an inverse Fourier transform, then calculates the nonlinear force in time domain and
subsequently the Fourier coefficients of the nonlinear force. The disadvantage of
the HBM is that strong nonlinearities are poorly represented by a truncated Fourier
series. In contrast, the shooting method operates in time-domain and relies on numerical
time-simulation. Set-valued force laws such as dry friction or other strong
nonlinearities can be dealt with if an appropriate numerical integrator is available.
The shooting method, however, becomes infeasible if the system has many states.
The proposed mixed shooting-HBM approach combines the best of both worlds.
The Harmonic Balance Method for Advanced Analysis and Design of Nonlinear Mechanical Systems
