Eigen Value Approach to Generalized Thermoelastic Interactions in an Unbounded Body with Circular Cylindrical Cavity without Energy Dissipation

The theory of generalized thermoelasticity in the context of the Green-Naghdi model -II (thermoelasticity without energy dissipation) is studied for an infinite circular cylindrical cavity subjected to two different cases of thermoelastic interactions when the radial stress is zero for (a) maintaining constant temperature and (b) temperature is varying exponentially with time. The Laplace transform from time variable is used to the governing equations to formulate a vector matrix differential equation which is then solved by the eigen value approach. Numerical computations for the displacement component, temperature distribution and components of thermal stress have been made and presented graphically.

Sound Radiation of the Resonator in the Form of a Vibrating Circular Plate Embedded in the Outlet of the Circular Cylindrical Cavity

The Neumann axisymmetric boundary value problem is considered for a vibrating thin clamped circular plate embedded in the flat rigid screen in the outlet of the circular cylindrical cavity. It is assumed that the two pistons, one cylindrical and the other one annular/circular, are vibrating inside the cavity with the same single frequency and different initial phases. The pistons are the only sources of excitation of the fluid. The acoustic pressure difference on both sides of the plate forces its vibrations. The acoustic waves are radiated into the half-space above it. A rigorous theoretical analysis of sound radiation has been performed based on the exact solution of the problem of free vibrations of the plate. The system of three coupled partial differential equations is solved. They are the two Helmholtz equations for the cavity and for the half-space, and the equation of motion of the plate. Consequently, the acoustic pressure distribution in both spaces is presented as well as the acoustic power radiated.

The Scattering of Circular Cylindrical Cavity with Time-Harmonic SH Waves in Infinite Strip Region

The scattering of time harmonic SH waves by arbitrary positions of circular cylindrical cavity is studied in continuous, homogeneous, isotropic, elastic strip region. In this paper, the completely analytical expression of total wave field is explicitly presented and the dynamic stress distribution is symbolically visualized in the strip region. The total wave field is divided into four sub wave fields, incident wave field and scattering wave field by the upper bound, the lower bound and the cylindrical bound, on big arc supposition. Specific wave functions are employed for each wave field expansion in series, such as circular cylindrical functions, respectively. Corresponding infinite linear algebraic equations are constructed by means of solving coefficients of Fourier series expansion on each sub wave field. Coefficients of cylindrical function expansion of each sub wave field are determined by truncated equations, which are reduced number of coefficients on pre-given computational accuracy. Numerical results graphically describe the dynamic stress concentration factor around the circumference of the cavity and the normalized dynamic stress along the cross section directly above the cavity.

Modeling of the Eigenfield of a Prestressed Hyperelastic Membrane Encapsulating a Liquid

A spectral boundary problem on the eigenfield of an inflated/deflated stretched circular membrane, which is clamped to a circular cylindrical cavity filled with a liquid, is examined. The paper presents an operator formulation of the problem and proposes a new semi-analytical approximate method. The method captures singular behavior of the solution in the pole and at the fastening contour of the membrane.