Principle of Stationary Total Potential Energy in Structural Dynamics: Theory and Applications

In this work we derive the principle of stationary total potential energy in structural dynamics firstly presented by the second of the authors and demonstrate its application to the formulation of structural dynamic problems. The analysis procedure is performed in terms of pre-defined potential energy of the vibrating structure. The implementation implies that the entire structural system plus the load system can be regarded as conservative in this study. It will be of interest to note that this principle is an extension of the principle of stationary potential energy in statics to account for dynamic effects. In practice, the proposed theory is used in conjunction with a new matrix assembly technique called the “set-in-right-position” rule also proposed by us to obtain finite element formulations for vibrations of engineering structures. Such an approach enables another way of efficient formulating the equations of motion of a complete finite element model. Finally, several illustrative examples are presented to testify the approach and to discuss the applicability of the present formulation.