EXACT FREE-VIBRATION ANALYSIS OF LAMINATED PLATES WITH EMBEDDED PIEZOELECTRIC LAYERS

Exact solutions are developed for predicting the coupled electromechan ical vibration characteristics of simply supported laminated piezoelec tric plates, composed of orthorhombic layers. The three-dimensional eq uations of motion and the charge equation are solved using the assumpt ions of the linear theory of piezoelectricity. The through-thickness d istributions for the displacements and electrostatic potential are fun ctions of eight constants for each layer of the laminate. Enforcing th e continuity and surface conditions results in a linear system of equa tions representing the behavior of the complete laminate. The determin ant of this system must be zero at a resonant frequency. The natural f requencies are found numerically by first incrementally stepping throu gh the frequency spectrum and refining the final frequencies using bis ection. Representative frequencies and mode shapes are presented for a variety of lamination schemes and aspect ratios. (C) 1995 Acoustical Society of America.