Sound propagation through a discretely inhomogeneous thermoelastic plane layer adjacent to heat-conducting liquids

An analytical solution of the problem of the propagation of a plane sound wave through a discretely inhomogeneous thermoelastic layer adjacent to inviscid heat-conducting liquids is obtained. Results of calculations of the dependences of the transmission coefficient on the wave incidence angle and frequency for discretely inhomogeneous and continuously inhomogeneous thermoelastic layers are given. It is shown that a thermoelastic layer with continuously inhomogeneous thickness can be simulated using a system of homogeneous thermoelastic layers.     

Stability and vibrations of cylindrical shells discretely reinforced with rings

The linearized system of homogeneous equations of motion of cylindrical shells discretely reinforced with quasiregular sets of ring ribs is solved. Approximate formulas for the critical stresses and natural frequencies are presented     

Nonstationary radial electroelastic vibrations of a piezoceramic cylinder under mechanical loading

The radial nonstationary vibrations of a piezoceramic cylinder polarized across the thickness and subjected to mechanical dynamic loading are studied. To solve the initial–boundary-value problem, mesh approximations and difference schemes are used. The electromechanical state of the cylinder under an instantaneously applied constant force is analyzed in detail     

Axisymmetric free vibrations of infinite micropolar thermoelastic plate

The propagation of axisymmetric free vibrations in an infinite homogeneous isotropic micropolar thermoelastic plate without energy dissipation subjected to stress free and rigidly fixed boundary conditions is investigated. The secular equations for homogeneous isotropic micropolar thermoelastic plate without energy dissipation in closed form for symmetric and skew symmetric wave modes of propagation are derived. The different regions of secular equations are obtained. At short wavelength limits, the secular equations for symmetric and skew symmetric modes of wave propagation in a stress free insulated and isothermal plate reduce to Rayleigh surface wave frequency equation. The results for thermoelastic, micropolar elastic and elastic materials are obtained as particular cases from the derived secular equations. The amplitudes of displacement components, microrotation and temperature distribution are also computed during the symmetric and skew symmetric motion of the plate. The dispersion curves for symmetric and skew symmetric modes and amplitudes of displacement components, microrotation and temperature distribution in case of fundamental symmetric and skew symmetric modes are presented graphically. The analytical and numerical results are found to be in close agreement.     

Axisymmetric free vibrations of infinite thermoelastic plate

The propagation of axisymmetric free vibrations in an infinite homogeneous isotropic micropolar thermoelastic plate without energy dissipation subjected to stress free and rigidly fixed boundary conditions is investigated. The secular equations for homogeneous isotropic micropolar thermoelastic plate without energy dissipation in closed form for symmetric and skew symmetric wave modes of propagation are derived. The different regions of secular equations are obtained. At short wavelength limits, the secular equations for symmetric and skew symmetric modes of wave propagation in a stress free insulated and isothermal plate reduce to Rayleigh surface wave frequency equation. The results for thermoelastic, micropolar elastic and elastic materials are obtained as particular cases from the derived secular equations. The amplitudes of displacement components, microrotation and temperature distribution are also computed during the symmetric and skew symmetric motion of the plate. The dispersion curves for symmetric and skew symmetric modes and amplitudes of displacement components, microrotation and temperature distribution in case of fundamental symmetric and skew symmetric modes are presented graphically. The analytical and numerical results are found to be in close agreement.     

Analysis of vibrations in a nonhomogeneous thermoelastic thin annular disk under dynamic pressure

The forced vibration analysis of nonhomogeneous thermoelastic, isotropic, thin annular disk under periodic and exponential types of axisymmetric dynamic pressures applied on its inner boundary has been performed and analytical benchmark solution has been obtained. The material has been assumed to have inhomogeneity according to a simple power law in the radial coordinate. The present analysis has been worked out in the context of generalized theory of thermoelasticity with one relaxation time. The two coupled partial differential equations have been clubbed and solved by employing Laplace transform technique to obtain the solution for radial displacement and temperature change in the space domain. In order to obtain the solution in physical domain, the inversion of the transform has been carried out by using residue calculus. The radial displacement, radial stress, circumferential stress, and temperature change have been computed numerically for copper material annular disk. The numerically computed results have been presented graphically to demonstrate the effect of two different types of dynamic pressure in reference to homogeneous and nonhomogeneous material disk. The results for homogeneous material disk have been deduced and validated with that available in literature. The closed-form solution obtained here is interesting and allows further parametric studies of nonhomogeneous structures.     

A coupled problem of thermoelastic vibrations of a circular plate with exact boundary conditions

Thermoelastic vibrations of a free supported and clamped circular plate caused by a thermal shock upon the plate surface have been analyzed The system of partial differential equations of the coupled system has been reduced to Volterra's first and second kind integral equations in the time domain. In both cases the solutions are given in the.form 4f series of Bessel functions of the first kind     

Influence of discretely arranged longitudinal ribs on the stability and vibrations of open circular cylindrical shells

Open cylindrical shells reinforced with quasiregular sets of longitudinal ribs and hinged at all edges are considered. The effect of the discrete arrangement and number of ribs on the critical stresses that cause instability under longitudinal compression and on the minimum natural frequencies of vibrations is examined. Numerical results are analyzed     

Analysis of the nonaxisymmetric vibrations of flexible ellipsoidal shells discretely reinforced with transverse ribs under nonstationary loads

The problem of forced nonaxisymmetric vibrations of reinforced ellipsoidal shells under nonstationary loads is formulated. A numerical algorithm of solving it is developed and the results obtained are analyzed Translated from Prikladnaya Mekhanika, Vol. 44, No. 10, pp. 63–73, October 2008.     

Non-linear behavior in a discretely forced oscillator

The simulated and experimental responses of a rigid-arm pendulum driven by an external impactor are considered. Here, impact occurs if the trajectory of a rotating impactor intersects that of the pendulum. Using the rotation rate of the impactor as the control parameter, experimental trials have demonstrated much of the dynamic behavior predicted by numerical simulations. The system exhibits chatter (i.e., multiple impacts within a single forcing period), sticking (i.e., contact between the pendulum and the impactor for non-negligible amounts of time), high-order periodicity, and behavior suggestive of chaos. A new convention for classifying periodic motions as well as insights regarding the nature of the coefficient of restitution (COR) in an experimental impacting system are also presented.     

Some non-classical thermoelasticity problems for a rectangular parallelepiped

Meccanica - In the Cartesian system of coordinates, thermoelastic equilibrium of an isotropic homogeneous rectangular parallelepiped is considered. On the lateral faces of a parallelepiped either...     

Multipoint problem for higher-order parabolic equations in a parallelepiped

We study the well-posedness of a problem for a Petrovskii-parabolic equation with coefficients depending on the space coordinates and with multipoint conditions with respect to the time variable. We establish conditions for the existence and uniqueness of the classical solution of the problem. For the proof of the existence of a solution of the problem, the method of divided differences is used. We prove a metric-type theorem on lower bounds for the small denominators that appear in the construction of the solution.     

Natural convection in a closed parallelepiped with a local energy source

An experimental and numerical analysis was performed to investigate the laminar regimes of conjugate thermogravitational convection in a closed parallelepiped with heat-conducting walls of finite thickness in the presence of a local energy source with convective heat exchange with the environment. The numerical studies were performed using the Fluent software. The experimental data and numerical results agree well each other.     

Oscillations of liquid in a vessel in the form of a rectangular parallelepiped

We consider the forced and the free oscillations of a liquid partially filling a cavity in the form of a rectangular parallelepiped. The characteristics of these oscillations are studied for small deformations of the free surface. It is shown that for definite frequencies and amplitudes of two-dimensional translational motions of the parallelepiped the fundamental of the liquid oscillations is excited in the plane perpendicular to the plane of motion of the vessel. The effect of small linear damping of the liquid oscillations on the shape of the boundaries of the principal region of instability of the liquid oscillations is evaluated. Fairly large oscillations of a liquid in a cylinder were considered in [1]. The same problem for a cavity of arbitrary configuration was studied in [2]. We note also that the conclusions of the study presented here are in qualitative agreement with the basic results obtained by a somewhat different method in [3] for a cavity in the form of a right circular cylinder.