Amplitude-Dependent Stiffness Method for Studying Frequency and Damping Variations in Nonlinear Dynamical Systems

A method is introduced here for extracting the fundamental backbone branches of the frequency energy plot in which the obtained nonlinear frequencies of the nonlinear dynamical system are plotted with respect to the nonlinear energy content. The proposed method is directly applied to the equations of motion where the solution is not required to be known a priori. The method is based on linearizing the nonlinear coupling force where a scaled amplitude-dependent coupling stiffness force is obtained to replace the original nonlinear coupling stiffness force. Accordingly, the backbone branches in the frequency-nonlinear-energy plot are extracted from the eigensolution of the mass-normalized amplitude-dependent global stiffness matrix of the nonlinear dynamical system. Moreover, the variations in the damping content under the effect of the nonlinear coupling stiffness are also studied. Interesting behavior of damping content under the effect of the amplitude-dependent stiffness has been observed and discussed.