Vibration of a Two-Layer“Metal+PZT”Plate Contacting with Viscous Fluid

The present work investigates the mechanically forced vibration of the hydro-elasto-piezoelectric system consisting of a two-layer plate“elastic+PZT”,a compressible viscous fluid,and a rigid wall.It is assumed that the PZT(piezoelectric)layer of the plate is in contact with the fluid and time-harmonic linear forces act on the free surface of the elastic-metallic layer.This study is valuable because it considers for the first time the mechanical vibration of the metal+piezoelectric bilayer plate in contact with a fluid.It is also the first time that the influence of the volumetric concentration of the constituents on the vibration of the hydro-elasto-piezoelectric system is studied.Another value of the present work is the use of the exact equations and relations of elasto-electrodynamics for elastic and piezoelectric materials to describe the motion of the plate layers within the framework of the piecewise homogeneous body model and the use of the linearized Navier-Stokes equations to describe the flow of the compressible viscous fluid.The plane-strain state in the plate and the plane flow in the fluid take place.For the solution of the corresponding boundary-value problem,the Fourier transform is used with respect to the spatial coordinate on the axis along the laying direction of the plate.The analytical expressions of the Fourier transform of all the sought values of each component of the system are determined.The origins of the searched values are determined numerically,after which numerical results on the stress on the fluid and plate interface planes are presented and discussed.These results are obtained for the case where PZT-2 is chosen as the piezoelectric material,steel and aluminum as the elastic metal materials,and Glycerin as the fluid.Analysis of these results allows conclusions to be drawn about the character of the problem parameters on the frequency response of the interfacial stress.In particular,it was found that after a certain value of the vibration frequency,the presence of the metal layer in the two-layer plate led to an increase in the absolute values of the above interfacial stress.

The Interface Stress Field in the Elastic System Consisting of the Hollow Cylinder and Surrounding Elastic Medium Under 3D Non-Axisymmetric Forced Vibration

The paper develops and employs analytical-numerical solution method for the study of the time-harmonic dynamic stress field in the system consisting of the hollow cylinder and surrounding elastic medium under the non-axisymmetric forced vibration of this system.It is assumed that in the interior of the hollow cylinder the point-located with respect to the cylinder axis,non-axisymmetric with respect to the circumferential direction and uniformly distributed time-harmonic forces act.Corresponding boundary value problem is solved by employing of the exponential Fourier transformation with respect to the axial coordinate and by employing of the Fourier series expansion of these transformations.Numerical results on the frequency response of the interface normal stresses are presented and discussed.

The Discrete-Analytical Solution Method for Investigation Dynamics of the Sphere with Inhomogeneous Initial Stresses

The paper deals with a development of the discrete-analytical method for the solution of the dynamical problems of a hollow sphere with inhomogeneous initial stresses.The examinations are made with respect to the problem on the natural vibration of the hollow sphere the initial stresses in which is caused by internal and external uniformly distributed pressure.The initial stresses in the sphere are determined within the scope of the exact equations of elastostatics.It is assumed that after appearing this static initial stresses the sphere gets a dynamical excitation and mechanical behavior of the sphere caused by this excitation is described with the so-called three-dimensional linearized equations of elastic wave propagation in initially stressed bodies.For the solution of these equations,which have variable coefficients,the discrete analytical solution method is developed and applied.In particular,it is established that the convergence of the numerical results with respect to the number of discretization is very acceptable and applicable for the considered type dynamical problems.Numerical results on the influence of the initial stresses on the values of the natural frequencies of the hollow sphere are also presented and these results are discussed.

Forced Vibration of the Non-Homogeneously Pre-Stressed System Consisting of the Hollow Cylinder and Surrounding Medium

The paper deals with the study of the influence of the non-homogeneous prestresses in the system consisting of the hollow cylinder and surrounding elastic medium on the frequency response of this system caused by the time-harmonic ring load acting in the interior of the cylinder.The axisymmetric problem is considered and it is assumed that in the initial state,the system is compressed in the radial direction with homogeneously distributed static forces as a result of which,non-homogeneous pre-stresses(or initial stresses)appear in that.It is also assumed that after these pre-stresses appear in the interior of the cylinder,the point-located(with respect to the axial coordinate directed along the cylinder’s central axis)additional time-harmonic ring load acts.Thus,it is required to determine how the pre-stresses influence the frequency response of the system to the noted additional time-harmonic loading.This influence,which is the non-linear effect,is studied within the scope of the so-called three-dimensional linearized equations and relations of the theory of elastic waves in pre-stressed bodies.The solution to the corresponding boundary value problems is found by employing the discrete analytical solution method and numerical results on the influence of the pre-stresses on the frequency response of the interface stresses which appear as a result of the action of the additional time-harmonic forces,are presented and discussed.In particular,it is established that the pre-stresses mentioned above cause to decrease the magnitude of the interface dynamic stresses appearing as a result of the additional time-harmonic loading.