Numerical and Experimental Determination of Nonlinear Normal Modes of a Circular Perforated Plate

Abstract

It is commonly known that nonlinearities in structures can lead to large amplitude responses that are not predicted by traditional theories. Thus a linear design could lead to premature failure if the structure actually behaves nonlinearly, or, conversely, nonlinearities could potentially be exploited to reduce stresses relative to the best possible design with a purely linear structure. When examining structures that operate in environments where a nonlinear response is possible, one can gain insight into the free and forced responses of a nonlinear system by determining the structure’s nonlinear normal modes (NNMs). NNMs extend knowledge gained from established linear normal modes (LNMs) into the nonlinear response range by quantifying how the unforced vibration frequency depends on the input energy. Recent works have shown that periodic excitations can be used to isolate a single NNM, providing a means for measuring NNMs in the laboratory. An extension of the modal indicator function can be used to ensure that the measured response is on the desired NNM. The experimentally measured NNMs can then be compared to numerically calculated NNMs for model validation. In this investigation, a circular perforated plate containing a distributed geometric nonlinearity is considered. This plate has demonstrated nonlinear responses when the displacements become comparable to the plate thickness. However, the system is challenging to model because the nonlinear response is potentially sensitive to small geometric features, residual stresses within the structure, and the boundary conditions.