Explicit expression for precise kineto-elastodynamic analysis

From the principle of the virtual displacement of a flexible body, a new equation for kineto-elastodynamic analysis is developed. It takes into account the nonlinear coupling effects between the gross motion and the elastic deformation. The element equation is explicitly expressed with global variables. It does not contain the time derivative of the transformation matrix. Meanwhile, it has the same form as the general kineto-elastodynamic analysis which is based on the assumption of the instantaneous structure, and the assembly of the system equations is the same too. The general kineto-elastodynamic analysis equation can be directly developed into the new one just by adding several terms. A particularized expression is developed for the analysis of planar link mechanism, and an example is given to illustrate it at last.