Nonlinear identification of cantilever beam using free vibration response decay and solving with differential transform method

The linearity is a simplifying assumption in most vibration problems of real mechanical systems which may, is not turn, lead to a considerable error in predicting the system dynamic response. Determining a suitable mathematical model for a nonlinear vibrating system is an important step in order to analyze the structural dynamics behavior efficiently. When the amplitude of vibration is large, the system is said to be geometrically nonlinear. In this paper, the nonlinear identification of a cantilever slender beam undergoing large amplitude free vibration has been investigated. Because of no excitation force in this situation and lack of information about its response, the existing identification methods are not efficient. In present research a new approach based on optimum correction factor of terms having uncertainty is used and identification has been done by using nonlinear free vibration decay. In order to solve the geometrical and inertial nonlinear terms, the method of modified differential transform according to Padé approximation was used and resonant frequency is determined. Also, the resonant frequency of nonlinear system is calculated by generalized variational iteration method and compared with the obtained frequency from the modified differential transform method. Comparison of the current results with those of 4th order Runge-Kutta technique shows good agreement of the two approaches. Finally, Obtained results compared with the experimental results showed good accuracy identifying models for nonlinear beam.