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1 2009

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Analysis of Vibrations of Autoparametric System with Springly Coupled Pendulums

Sado D., Gajos K.

Machine Dynamics Problems

2009

Vol. 33, No. 3

91-101

The nonlinear dynamics of a three degree of freedom autoparametrical vibration system with two coupled pendulums in the neighborhood internal and external resonances is presented in this work. It was assumed that the main body is suspended by an element characterized by linear elasticity and linear damping force and is excited harmonicaly in the vertical direction. The two pendulums connected by spring are mounted to the main body. It is assumed, that the motion of the pendulums are damped by viscotic resistive forces. Solutions for the system response are presented for specific values of the uncoupled normal frequency. Analytical solutions have been obtained by using multiple scales method. This method is used to construct first-order non-linear ordinary differential equations governing the modulation of the amplitudes and phases. Steady state solutions are computed for selected values of the systems parameters.