Method of characteristics in analysis of the propagation of electroelastic thickness oscillations in a piezoceramic layer under electric excitation

Abstract

The method of characteristics is used to obtain an analytical solution describing the thickness vibrations of a piezoelectric layer polarized across the thickness and subjected to a nonstationary electric potential. The features of how the vibrations are excited and propagate under electric loading are studied. The dynamic electromechanical state of the layer is analyzed. The electric and mechanical characteristics as functions of time are plotted Introduction. Studying the dynamic electromechanical deformation of piezoceramic bodies is of importance at the stage of development of piezoelectric devices. The vibrations of piezoelectric bodies of various shapes are studied in [1, 5, 6, 9-15, etc.]. The coupling of the electric and mechanical fields allowed for in problems of nonstationary vibrations greatly complicates problem solving, which is why analytic results have been obtained only in a few cases. The problem of longitudinal vibrations of a rod impacted by a massive body at its end is generalized in [4] to the electroelastic case. The problem of vibrations of a piezoceramic layer is solved in [2] using the Laplace transform. The Fourier transform is used in [5] to solve the problem of propagation of an electroelastic pulse through a short-circuited layer in a piezoceramic space. In [1,10], the Laplace transform is used to solve the problem of radial vibrations of piezoceramic cylinders.Here we use the method of characteristics to study the thickness vibrations of a flat piezoceramic layer excited by an electric potential.1. Problem Formulation and the Method of Characteristics. Consider a piezoelectric layer polarized throughout the thickness. Its vibrations are described by the equation of motion and the equation for electric-flux density

The application of second-order approximation of Taylor series in thickness shear vibration analysis of quartz crystal microbalances

“…(3) and (4), into the above boundary conditions, i.e., Eqs. (10), (12) and (13), yields four linear homogeneous algebraic equations for coefficients A 1 , A 2 , A 3 , and A 4 :…”

“…Sometimes, incident current or voltage becomes instable for some reason; for instance, a sudden switching-off caused by the thermal and mechanical shocks, which will disturb resonator operation [11][12][13][14][15][16]. Usually this phenomenon is named as transient effect.…”

“…Another phenomenon, transient effect [11,12], is inevitable during the excitation process of QCM. For instance, the initial switching-on from rest, followed by a sudden switching-off caused by the interruption of incident current, fluctuations in the driving voltage or the frequency, and thermal and mechanical shocks, and so forth.…”