An Improved Way of Detecting the Threshold Value of Chaotic Motion on a Parametrical Excited Rectangular Thin Plate
One dynamical model of a thin rectangular plate subject to in-plate parametrical excitation is proposed based on elastic theory and Galerkin’s approach. At first, the undermined fundamental frequency and normal form method was utilized to study the influence of the disturbing parameters to the fundamental frequency. Secondly, the improved Melnikov expression for the oscillator was built based on the results of the undermined fundamental frequency method and time scale transformation to improve the approximate threshold value of chaotic motion in the Homoclinicity. Finally, the numerical results show the efficiency of the theoretical analysis.
G. Ge and Z. W. Zhu, "An Improved Way of Detecting the Threshold Value of Chaotic Motion on a Parametrical Excited Rectangular Thin Plate", Applied Mechanics and Materials, Vols. 66-68, pp. 833-837, 2011