Mode Responses of Dynamically Loaded Structures

Instantaneous mode responses of dynamically loaded elastic, viscous, ideally plastic and rigid, viscoplastic structures are defined and characterized by variational criteria with isometric constraints. Under some loading conditions, the instantaneous mode responses would coincide with the natural mode solutions of those problems. For the case of a rigid, perfectly plastic problem, it is believed that the criterion for an instantaneous mode response would yield simultaneously the true limit load and the true collapse mechanism of the limit analysis. Examples of beams and plates of various materials subjected to uniformly distributed, rectangular pulse load or impulsive loading are given to illustrate the instantaneous mode responses which are then compared with exact solutions.