A Dihect Parameter Estimation Method for Weak Nonlinear Systems

In this paper a method is presented to identify the parameters of a structure exhibiting weak nonlinear behavior using vibration test data. The identification approach is based on an extension of a linear frequency domain method for the direct identification of incomplete system matrices to the nonlinear case. The basic identification equations are extended by additional stiffness and damping terms desciibing the nonlinear structural behavior. Their contribution to the overall response is governed ky integral multiples of the local response amplitudes. Hence, the method represents a Iinearisation of the full nonlinear equations. The identification equations were basically derived from the well known ‘Harmonic Balance ’ method which is applied here to multi-degree of freedom systems. The choice of an adequate set of nonlinear terms is vem essential to the identification results. To assist this choice common& known detectors findicatars) for the dominant type of the nonlinearity are used. Thqy are based on the fundamental frequency information only. The paper discusses different commonly known sources of weak nonlinear behavior for both simulated and real test cases. It illustrates the ability of the method in conjunction with the indicator functions to extract the UndeAying linear system parameters as well as parameters which account for the nonlinear distortions. NOMENCLATLTRE Physical Prouerties M,D,K mass, damping, stiffness external (excitation) forces displacement, velocity, acceleration real, imaginary part of acceleration frequency response displacement amplitude of harmonic response excitation frequency Modal Properties mass, damping, stiffness external (excitation) forces real, imaginary part of acceleration frequency response right, left hand modal matrix eigenvalues General SDOF, MDOF single, multi degree of freedom