Optimization of mechanical vibration isolation systems with multi-degrees of freedom

An optimization technique of vibration isolation systems with multi-degrees of freedom is developed in this study. The primary goal is to seek a min.-max. point so that the objective function of the system is maximized with respect to a single state variable, the frequency, and at the same time is minimized with respect to multi-control variables, the damping constants. The Newton-Raphson method, which utilizes the second-order derivatives of the objective function, is used for maximization. The Davidon-Fletcher-Powell method is selected for minimization. An iterative technique is developed to improve the solution until the gradients of the objective function are within a prescribed tolerance. A mechanical isolation system with three degrees of freedom is taken as a sample problem for experimental verification. The optimized driving frequency and damping constants are determined by a computer program based on the above-mentioned numerical methods. The experimental test results agree favorably with predicted analytical values.