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 importa nt to recognise the type of non-linearity actually influencing the system. A procedure, involving structured higher-order FRF analysis based on Volter ra theory is suggested in the present work. to distinguish a polynomial for m of non-linearity from other possible forms. Volterra theory provides conc epts of linear, bilinear, trilinear, etc. kernels, which upon convolution w ith the excitation force and subsequent summation can be employed to repres ent the response of a non-linear system. The kernels of the system are unde rstood as multidimensional unit impulse response functions. The Volterra se ries response representation is employed in this work to facilitate its pro cessing in a structured manner, to extract characteristic features, which c an help in placing the system non-linearity in an appropriate class. The Vo lterra series platform is also employed to make a distinction between symme tric and asymmetric forms of the restoring force function. A multi-tone exc itation 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 illustrate d through numerical simulation. (C) 2001 Academic Press.