Development of Nonlinear Building Block Approach

A nonlinear building block approach (NLBBA) is proposed to evaluate frequency response characteristics of nonlinear structure systems including springs with nonlinear stiffness and clearances at slide or bearing as occur in actual systems. The advantage of the building block approach (BBA) was that dynamic performance of the total linear system can be evaluated by analyzing and synthesizing the performance of subsystems. In this paper the method was extensively developed to investigate systems with nonlinearities. The describing function was adopted to represent nonlinearity in the system equations. The compliance could be obtained by solving nonlinear simultaneous algebraic equations for multi-degrees-of-freedom system with multinonlinearities. The method was applied to a beam supported by nonlinear springs and a spindle of a machine tool. The evaluated compliance could quantitatively show effects of the nonlinearity such as transfer of the natural frequency, variance of the compliance at the natural frequency, and jump phenomena for sweep of the excitation frequency. The results of the application agreed well with those obtained by step-by-step integration in the time domain (time historical analysis) which is generally used, and also agreed well with the empirical phenomenon of the stability to the self-excited chatter. The computation time could be significantly shortened by the proposed method.