Development of a new approach for formulating equations of motion of dynamic systems
In this paper the principle of stationary total potential energy in structural dynamics first presented by the author is thoroughly examined. It is clearly shown that when being used in conjunction with a new matrix assembly technique called the “set-in-right-position” rule also proposed by us, which is inherently different from the most widely used direct stiffness method, the proposed principle is suitable for formulating the finite element equations of motion of the vibrating system. The main advantage of present method lies in its simplicity and efficiency in modeling the dynamic behaviors of more complicated systems that are usually characterized by the presence of very complex layouts as well as the applying of various kinds of external forces. Then, in order to demonstrate the applicability and capability of present method, two illustrated examples have been given. By doing so, one is able to acquire an in-depth understanding on the influence of individual parts of the whole system on its overall dynamic behavior.