Host: The Japan Society of Mechanical Engineers
Name : Dynamics and Design Conference 2019
Date : August 27, 2019 - August 30, 2019
This paper theoretically investigates localization phenomena using the modal analysis in a nonlinear array with N pendula connected by weak, linear springs when the array is subjected to horizontal harmonic excitation. In the theoretical analysis, the equations of motion for the system are derived in the two different ways, i.e., by using the physical coordinates and the modal coordinates. The equations of motion expressed in a form of the modal coordinates, i.e., a set of the modal equations of motion, form an autoparametric system because only the first mode is directly excited by the external force and the other modes are not directly excited by the external force but are nonlinearly coupled with the first mode. Van der Pol’s method is employed to obtain the solutions of the harmonic oscillations. In the numerical calculations, the frequency response curves of the amplitudes and phase angles in the cases of N=2 and 3 are presented. It is found that localization phenomena can be observed in the physical coordinate system when multiple modes simultaneously appear. The charts of the displacement vectors of the harmonic oscillations are also presented and explain that the localization phenomena are observed as the results of superposing the multiple modes excited by the autoparametric effect.
