P. Heyliger et Da. Saravanos, EXACT FREE-VIBRATION ANALYSIS OF LAMINATED PLATES WITH EMBEDDED PIEZOELECTRIC LAYERS, The Journal of the Acoustical Society of America, 98(3), 1995, pp. 1547-1557
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.