P.C.Y. Lee

A two‐dimensional theory for high‐frequency vibrations of piezoelectric crystal plates with or without electrodes

Two‐dimensional equations of motion of successively higher‐order approximations for piezoelectric crystal plates with triclinic symmetry are deduced from the three‐dimensional equations of linear piezoelectricity by expansion in series of trigonometric functions of the thickness coordinate of the plate. These equations, complemented by two additional relations: one, the usual relation of face tractions to the mass of electrodes, and the other relating face charges to face potentials and face displacements, can accommodate either the traction and charge boundary conditions at the faces of the plate without electrodes or the traction and potential boundary conditions at the faces of the plate with electrodes. Dispersion curves are obtained from the first‐ to fourth‐order approximate plate equations for a rotated 45° Y‐cut lithium tantalate plate without electrodes, and these curves are compared with those from the frequency equation of the three‐dimensional equations with close agreement. Solutions of force...

A new two-dimensional theory for vibrations of piezoelectric crystal plates with electroded faces

A system of two-dimensional (2-D) governing equations for piezoelectric plates with general crystal symmetry and with electroded faces is deduced from the three-dimensional (3-D) equations of linear piezoelectricity by expansion in series of trigonometric functions of thickness coordinate. The essential difference of the present derivation from the earlier studies by trigonometrical series expansion is that the antisymmetric in-plane displacements induced by gradients of the bending deflection (the zero-order component of transverse displacement) are expressed by the linear functions of the thickness coordinate, and the rest of displacements are expanded in cosine series of the thickness coordinate. For the electric potential, a sine-series expansion is used for it is well suited for satisfying the electrical conditions at the faces covered with conductive electrodes. A system of approximate first-order equations is extracted from the infinite system of 2-D equations. Dispersion curves for thickness shear...

Thickness vibrations of a piezoelectric plate with dissipation

The three-dimensional (3-D) equations of linear piezoelectricity with quasi-electrostatic approximation are extended to include losses attributed to the acoustic viscosity and electrical conductivity. These equations are used to investigate effects of dissipation on the propagation of plane waves in an infinite solid and forced thickness vibrations in an infinite piezoelectric plate with general symmetry. For a harmonic plane wave propagating in an arbitrary direction in an unbounded solid, the complex eigenvalue problem is solved from which the effective elastic stiffness, viscosity, and conductivity are computed. For the forced thickness vibrations of an infinite plate, the complex coupling factor K*, input admittance Y are derived and an explicit, approximate expression for K* is obtained in terms of material properties. Effects of the viscosity and conductivity on the resonance frequency, modes, admittance, attenuation coefficient, dynamic time constant, coupling factor, and quality factor are calculated and examined for quartz and ceramic barium titanate plates.

Governing equations for a piezoelectric plate with graded properties across the thickness

Two-dimensional first-order governing equations for electroded piezoelectric crystal plates with general symmetry and thickness-graded material properties are deduced from the three-dimensional equations of linear piezoelectricity by Mindlins general procedure of series expansion. Mechanical displacements and thickness-graded material properties, i.e., the elastic stiffnesses, piezoelectric coefficients, dielectric permittivities, and mass density, are expanded in powers of the thickness coordinate, while electric potential is expanded in a special series in order to accommodate the specified electric potentials at electroded faces of the plate. The effects of graded material properties on the piezoelectrically induced stresses or deformations by the applied surface potentials are clearly exhibited in these newly derived equations which reduce to Mindlins first-order equations of elastic anisotropic plates when the material properties are homogeneous. Closed form solutions are obtained from the three-dimensional equations of piezoelectricity and from the present two-dimensional equations for both homogeneous plates and bimorphs of piezoelectric ceramics. Dispersion curves for homogeneous plates and bimorphs and resonance frequencies for bimorph strips with finite width are computed from the solutions of three-dimensional and two-dimensional equations. Comparison of the results shows that predictions from the two-dimensional equations are very close to those from the three-dimensional equations.

Thickness vibrations of piezoelectric plates with dissipation

The three-dimensional equations of linear piezoelectricity with quasi-electrostatic approximation are extended to include losses attributed to the acoustic viscosity and electrical conductivity. These equations are used to investigate the forced thickness vibrations by the thickness excitation in an infinite piezoelectric plate with the most general symmetry. For a harmonic plane wave propagating in an arbitrary direction in an unbounded solid, the complex eigenvalue problem is solved from which the effective elastic stiffness, viscosity, and conductivity are computed from the corresponding frequency-dependent eigenvalues. For the forced thickness vibrations in an infinite plate, the input admittances are obtained and the complex coupling factors are deduced in terms of material properties. Effects of the viscosity and conductivity on the resonance frequencies, modes, attenuation coefficients, time constants and coupling factors are calculated and examined for quartz and ceramic barium titanate plates.

Piezoelectrically forced thickness‐shear and flexural vibrations of contoured quartz resonators

In a previous article a set of first‐order equations of motion is obtained for contoured crystal plates and for frequencies up to and including those of the fundamental thickness‐shear modes. In the present article the governing equations of contoured plates are extended to include the electric potential which is coupled to the mechanical fields by the piezoelectric effect. These equations are, then, employed for the study of piezoelectrically forced thickness‐shear and flexural vibrations of beveled AT‐cut quartz plate, i.e., the plate with a portion of uniform thickness between the two wings of the double wedge. Analytical solutions are obtained by Frobenius method. Displacements, stresses, and electric potential are derivable from six independent functions which are in the form of infinite power series. In addition to the calculations of resonance frequencies and mode shapes, the effects of the contouring on the forced mechanical displacements, electric potential, surface charge, and capacitance ratio ...

Vibrations of AT‐cut quartz strips of narrow width and finite length

A system of one‐dimensional equations of motion for AT‐cut quartz strip resonators with narrow width and for frequencies up to and including the fundamental thickness shear is deduced from the two‐dimensional, first‐order equations for piezoelectric crystal plates by Lee, Syngellakis, and Hou [J. Appl. Phys. 61, 1249 (1987)] by expanding the mechanical displacements and electric potentials in a series of trigonometric functions of the width coordinate. By neglecting the piezoelectric coupling and the weak mechanical coupling through c56, four groups of coupled equations of motion are obtained. For the equations of each group, closed form solutions are obtained and the traction‐free conditions at four edges are accommodated. Dispersion curves and frequency spectrum are computed for quartz strips. The predicted frequency as a function of the length‐to‐thickness ratio and as a function of the width‐to‐thickness ratio of the quartz strips is compared with experimental data with good agreement.

Murine Cytomegalovirus m02 Gene Family Protects against Natural Killer Cell-Mediated Immune Surveillance

ABSTRACT The murine cytomegalovirus m02 gene family encodes putative type I membrane glycoproteins named m02 through m16. A subset of these genes were fused to an epitope tag and cloned into an expression vector. In transfected and murine cytomegalovirus-infected cells, m02, m04, m05, m06, m07, m09, m10, and m12 localized to cytoplasmic structures near the nucleus, whereas m08 and m13 localized to a filamentous structure surrounding the nucleus. Substitution mutants lacking the m02 gene (SMsubm02) or the entire m02 gene family (SMsubm02-16) grew like their wild-type parent in cultured cells. However, whereas SMsubm02 was as pathogenic as the wild-type virus, SMsubm02-16 was markedly less virulent. SMsubm02-16 produced less infectious virus in most organs compared to wild-type virus in BALB/c and C57BL/6J mice, but it replicated to wild-type levels in the organs of immunodeficient γc/Rag2 mice, lacking multiple cell types including natural killer cells, and in C57BL/6J mice depleted of natural killer cells. These results argue that one or more members of the m02 gene family antagonize natural killer cell-mediated immune surveillance.

Plane harmonic waves in an infinite piezoelectric plate with dissipation

In a previous paper, the three-dimensional equations of linear piezoelectricity with quasielectrostatic approximation were extended to include losses attributed to the mechanical damping in solid and the resistance in current conduction. These equations were used to investigate the plane wave propagation in an unbounded solid and forced thickness vibration of an infinite piezoelectric plate. In the present paper, these equations are used to obtain solutions of plane harmonic wave of arbitrary direction in an infinite and dissipative piezoelectric plate with general crystal symmetry. Dispersion curves are computed and plotted for real frequencies and complex wave numbers. All frequency branches are complex for dissipative plate. There are no longer any pure real or pure imaginary or complex conjugate frequency branches as those existing for nondissipative plates. Effects of dissipation on the wave propagation are examined in detail for AT-cut of quartz as well as barium titanate ceramic plate.

Piezoelectric ceramic disks with thickness-graded material properties

A system of two-dimensional, first-order equations for electroded piezoelectric crystal plates with general symmetry and thickness-graded material properties recently was deduced from the three-dimensional equations of linear piezoelectricity. These equations are simplified for the two limiting cases of thickness-graded piezoelectric properties, i.e., the homogeneous plate and bimorph of piezoelectric ceramics. Closed-form solutions are obtained from these reduced equations for the flexural and thickness-shear vibrations and static response of bimorph disks as well as for the extensional and thickness-stretch vibrations of homogeneous disks. Frequency spectra and modes are computed and examined. Resonance frequencies for both homogeneous and bimorph disks of PZT-857 are computed and measured. The comparison of the results shows that the agreement is close.