Modal characteristics of beams with extensional piezoelectric actuators

Thesis submitted in partial fulfillment of the requirement of the degree of Master of Science in Mechanical Engineering Riyadh,KSA 1427-HIn this thesis we will study the case in which piezoelectric (PZT5H) is bonded on the surface of the beam (extension mode). This extension mode consists of two layer of piezoelectric actuators between them orthotropic material (composite material). Those layers can be bonded along the beam or at local position on the beam. This structure can contain one pair or two pairs of piezoelectric actuators or n pairs of piezoelectric actuators and it can be symmetric or unsymmetric about its mid-plane. The purpose of this study is to find the exact natural frequencies and mode shapes associated with the flexural motion for various combinations of boundary conditions. The analytical solutions will be obtained with the aid of the state-space approach. To formulate the models, Euler Bernoulli beam theory (CBT), first-order beam theory (FOBT) and higher-order beam theory (HOBT) will be used. The equations of motion and associated boundary conditions are derived for the beam models using Hamilton’s principle. Perfect bonding of the piezoelectric actuator to the beam substructure was assumed. In addition the effects of varying some parameters for the symmetric and unsymmetric cross-ply laminated beam are presented for different type of piezoelectric actuators cases. By using higher order beam theory the effect of length-to-thickness ratio, number of layers and actuators thickness on the nondimensional frequencies are investigated when the piezoelectric actuators bonded along the beam surface, also first order beam theory is used to present the effect of actuators position and length on the nondimensional frequencies when one pair and two pairs of piezoelectric actuators are bonded respectively at a local position on the beam surface