A New Method for Determining the Steady State Response of Mechanical Systems With Structural Flexibility

A new method is developed for determining the steady state response of mechanical systems with structural flexibility. The main advantage of the developed method is that the effects of structural flexibilities as well as the steady state response of the system can be determined without the need for the commonly performed dynamics modeling and computer simulations. The method is developed based on “tracing” the “propagation” of the effects of high frequency motion requirements on the dynamic response characteristics of machines with structural flexibility, particularly those with closed-loop kinematics structures. The method considers harmonic motion transmissibility characteristics of machines with structural flexibility. Of particular interest is the high frequency motion “filtering” action of the structural elements with flexibility. The method readily illustrates the effects of structural and joint flexibilities on the dynamic behavior of machines without requiring complex dynamics modeling and computer simulation. In addition, it clearly identifies the physics of the problem and the mechanisms with which link and joint flexibilities affect the kinematics and dynamics of high speed machinery in general and those with closed-loop structures in particular. As an example, the method is applied to a four-bar linkage mechanism with longitudinally flexible coupler link. The obtained steady state response is shown to be highly accurate as compared to those obtained by computer simulation. A number of related issues of interest are discussed.