Amplitude-dependent stiffness method for studying frequencyand 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 ob- tained nonlinear frequencies of the nonlinear dynamical system are plotted with respect to the nonlinear energy content. The pro- posed 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 re- place the original nonlinear coupling stiffness force. Accord- ingly, 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 dy- namical system. Moreover, the variations in the damping con- tent under the effect of the nonlinear coupling stiffness are also studied. Interesting behavior of damping content under the ef- fect of the amplitude-dependent stiffness has been observed and discussed.