Design and Analysis of an Auto-Parametrically Excited Platform for Active Vibration Control

Abstract

Many researchers have proved the potential of autoparametric system in controlling stability and parametric resonance. In this paper, two different designs for auto-parametrically excited mass-spring-damper systems were studied: one system was controlled by rotational motion of the spring, and the other system was controlled by sliding motion of the spring. The theoretical models were developed to predict the behavior of the systems and also generated stability charts to analyze the systems. For each system, the numerical results from both the nonlinear equation and linearized equation were analyzed and compared. Simulation models were constructed to validate the analytical results. The error between simulation and theoretical results was within 2%. Both theoretical and simulation results displayed that the implementation of autoparametric system could help reduce the resonance by up to 33% and amplify the resonance by up to 34%.

Comparison of Poincaré Normal Forms and Floquet Theory for Analysis of Linear Time Periodic Systems

“…By expressing the updated Eqs. (24) and (25) in the matrix multiplication form, we could obtain the expression forJ matrix for each case. By substituting Eq.…”

“…Moreover, the analytical solution from Normal Forms theory could be used to determine the closed form solution of the L-F transformation matrix, QðtÞ. The application of the proposed approach toward analysis of practical autoparametrically/externally excited systems, such as [24,25] and nonlinear systems will be included in future work.…”