Quantifying the Local Kinematic Effect in Actuated Plates via Strain Energy Distribution

This article examines the distribution of strain energy in the various component materials of actuated plates and investigates the manner in which the strain energy distribution is influenced by the actuated span-to-thickness ratio and the thickness of the adhesive bond layer. Furthermore, the article investigates the effect of modeling choices (e.g., kinematic assumptions and mesh density) on the predicted magnitude and mode of the dominant strain energy form in each component material. These computed parameters can be used to quantify the overall efficiency of an actuated plate in addition to aiding the understanding of the local mechanics that govern the process. The focus problem consists of a square aluminum plate with a single symmetric pair of surface-mounted piezoceramic actuators that are used to produce in-plane extension or bending in the aluminum plate. The behavior of the actuated plate is examined over a range of plate thicknesses and adhesive bond layer thicknesses by using a series of finite element models that feature different levels of kinematic complexity and different levels of two-dimensional (2-D) mesh density. The results of the study emphasize the need for discrete layer kinematics in determining the magnitude and mode of the dominant strain energy form in each constituent material; however, these computed parameters are shown to be rather insensitive to changes in 2-D mesh density. Most importantly, the study confirms the existence and quantifies the magnitude of the local kinematic effect, whereby a portion of the available actuation energy is diverted to the production of localized transverse shear deformation and transverse normal deformation, thus reducing the amount of actuation energy available to produce in-plane deformation in the structural substrate.