Stiffness Non-Linearity Classification Through Structured Response Component Analysis Using Volterra Series
Most non-linear analysis problems, consider only the Duffing oscillator as a representative case. In engineering analysis, it is however, also important to recognise the type of non-linearity actually influencing the system. A procedure, involving structured higher-order FRF analysis based on Volterra theory is suggested in the present work, to distinguish a polynomial form of non-linearity from other possible forms. Volterra theory provides concepts of linear, bilinear, trilinear, etc. kernels, which upon convolution with the excitation force and subsequent summation can be employed to represent the response of a non-linear system. The kernels of the system are understood as multidimensional unit impulse response functions. The Volterra series response representation is employed in this work to facilitate its processing in a structured manner, to extract characteristic features, which can help in placing the system non-linearity in an appropriate class. The Volterra series platform is also employed to make a distinction between symmetric and asymmetric forms of the restoring force function. A multi-tone excitation procedure is further suggested, through which higher-order kernels of the system can be constructed for identification of the structure of the polynomial representing the restoring force. The procedures are illustrated through numerical simulation.