Use of Assumed Modes in Equations Governing Large-Displacement Elastodynamic Plate Behavior

Abstract

The dynamic behavior of multibody systems containing structural elements undergoing large overall rotation and translation as well as small elastic deformations is considered. A systematic procedure, using assumed mode functions and von Kármán-type strain measures, is developed in order to properly account for motion-induced structural stiffness variations during arbitrary overall motion. The procedure is compared in terms of accuracy and efficiency with recently developed imbedded geometric constraint methods involving linear strain-displacement relationships and with more conventional multibody techniques. A numerical example involving a simply supported plate attached to a rigid body (floating frame) undergoing a prescribed large-displacement motion is presented. Extensions to complex multibody systems containing various element types will be discussed.