A DRBEM model for harbor oscillation with the effect of energy dissipation

Abstract

In this study, the numerical scheme of dual reciprocity boundary element method (DRBEM) is adopted to investigate the resonant problem in a harbor while considering the effect of energy dissipation. The numerical model employed the mild slope equation as a basic equation. To avoid complicated procedures for solving the equation, DRBEM is used to improve numerical efficiency. Computation results are compared with the existing experimental data and other theoretical results. It shows that the present model is valid and effective to solve the harbor oscillation problem.     

Dispersion of surface waves at a dielectric-high temperature superconductor interface with allowance for energy dissipation

The dispersion characteristics of surface waves at a dielectric-high temperature superconductor (HTSC) interface have been studied with allowance for energy dissipation. Conditions of the existence of surface waves and the corresponding dispersion relations are determined at temperatures below the HTSC critical temperature. The frequency dependences of the penetration depth in each medium and the free path of surface polaritons are described. In the frequency range studied, these quantities can vary within several orders of magnitude.     

A two-dimensional problem for a fibre-reinforced anisotropic thermoelastic half-space with energy dissipation

The theory of thermoelasticity with energy dissipation is employed to study plane waves in a fibre-reinforced anisotropic thermoelastic half-space. We apply a thermal shock on the surface of the half-space which is taken to be traction free. The problem is solved numerically using a finite element method. Moreover, the numerical solutions of the non-dimensional governing partial differential equations of the problem are shown graphically. Comparisons are made with the results predicted by Green–Naghdi theory of the two types (GNII without energy dissipation) and (GNIII with energy dissipation). We found that the reinforcement has great effect on the distribution of field quantities. Results carried out in this paper can be used to design various fibre-reinforced anisotropic thermoelastic elements under thermal load to meet special engineering requirements.     

On the anisotropic piezoelastic contact problem for an elliptical punch

Summary This paper firstly conducts a systematic investigation of the problem of a rigid punch indenting an anisotropic piezoelectric half-space. The Fourier transform method is employed to the mixed boundary value problem. Using the principle of linear superposition, the resulting transformed (algebraic) equations, whose right-hand sides contain both pressure and electric displacement terms, can be solved by superposing the solutions of two sets of algebraic equations, one containing pressure and another containing electric displacement. For an arbitrarily shaped punch, two governing equations are derived, which can be solved numerically. In the case of transversely isotropic piezoelectric media, the two governing equations are corresponding with that given by others using potential theory. Particularly, when the punch has elliptic cross-section, and the pressure and electric displacement are given by some certain forms of polynomial functions, then the displacement and electric potential are prescribed by polynomial functions in the contact area. The parameters contained in it satisfy a set of linear algebraic equations, whose coefficients involve contour integrals. The problem of indentation by a smooth flat punch is examined for special orthotropic piezoelectric media, and some results obtained can be degenerated to the case of transversely isotropic piezoelectric media.     

Calculation of the effectiveness of plate cooling with coolant ejection at an angle to the main flow with allowance for the stagnant zone

A method is presented for calculating the efficiency of cooling of a flat surface with large ejection angles. The gaseous wall screen is calculated from formulas for tangential ejection.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 48, No. 5, pp. 715–719, May, 1985.     

Exact solution for free in-plane vibration analysis of an eccentric elliptical plate

A two-dimensional analytical model is formulated for free extensional vibrations of a thin elastic plate of elliptic planform with an arbitrarily located elliptical cutout, based on Navier’s displacement equation of motion for the state of plane stress. The analytic solution is obtained by invoking Helmholtz’s decomposition theorem and utilizing the method of separation of variables in elliptical coordinates in conjunction with the translational addition theorems for Mathieu functions. The first three panel in-plane natural frequencies are tabulated in a systematic fashion for selected panel/cutout aspect ratios, and cutout location/orientation parameters, under different combinations of classical (clamped/free) edge conditions. Also, selected two-dimensional vibration mode shapes are represented in vivid graphical form. The accuracy of the solutions is ensured through proper convergence studies, and the validity of results is demonstrated with the aid of a commercial finite element package as well as by comparison with the existing data. The herein reported data are believed to be the first rigorous attempt on the in-plane free vibrational characteristics of thin eccentric circular/elliptical plates for a wide range of geometric parameters.     

New solutions of the II. Stokes problem for an oscillating flat plate

Summary We generalize the fluid flow problem of an oscillating flat plate (II. Stokes problem) in two directions. We discuss first the oscillating porous flat plate with superimposed blowing or suction. The second generalization is concerned with an increasing or decreasing velocity amplitude of the oscillating flat plate. Finally we show that a combination of both effects is possible as well.Dedicated to Prof. Dr. Dr. h. c. F. Ziegler on the occasion of his 60th birthday     

Solution of one mixed problem of plate bending for a domain with partially unknown boundary

The paper addresses the problem of finding a full-strength contour in the problem of plate bending for a cycle-symmetric doubly connected domain. An isotropic elastic plate, bounded by a regular polygon, is weakened by a required full-strength hole whose symmetry axes are the regular polygon diagonals. Rigid bars are attached to each component of the broken line of the outer boundary of the plate. The plate bends under the action of concentrated moments applied to the middle points of the bars. An unknown part of the boundary is free from external forces. Using the methods of complex analysis, the analytical image of Kolosov?CMuskhelishvili??s complex potentials (characterising an elastic equilibrium of the body) and of an unknown full-strength contour are determined. A numerical analysis is performed and the corresponding plots are obtained by means of the Mathcad system.     

Thin plate bending of dissimilar half-planes with interface debonding emanating from an elliptical hole

The problem of thin plate bending of two bonded dissimilar half-planes containing an elliptical hole on the interface with debonding emanating on both sides is presented. The external load is a uniformly distributed bending moment applied at infinity perpendicular to the interface. An analytical solution is obtained using the complex stress function approach and the rational mapping function technique. Stress distributions on the interface, the boundaries of the hole and in the vicinity of the debonded tips are obtained. The stress intensity of debonding is obtained for aribitrary lengths of debonding, all possible hole dimensions and rigidity ratios.     

Numeric modeling of the strength and longevity of structures with allowance for scale effect. Report 1. Substantiation of strength and longevity criteria

The nonlocal criterion of the static strength of structurally inhomogeneous construction materials, whose basic mechanical properties depend heavily on the loaded volume in a complex stress-strain state, is developed. A statistical interpretation of the proposed criterion is given. The case where the criterion is used for an isotropic material with volume-dependent ultimate tensile, compressive, and torsional strengths is analyzed as an example. A longevity criterion, which makes it possible to account for the different character of the material's rupture strength as the form of the stress state changes, in addition to the scale effect, is proposed for structural components that operate under asymmetric low-cycle loading. This criterion is in accord with the static criterion and is obtained on the assumption of the invariance of the limiting-stress diagrams, which apply to the ultimate strength relative to the form of stress state.Translated from Problemy Prochnosti, No. 5, pp. 37–43, May, 1991.     

Heating of a micropolar liquid due to viscous energy dissipation in channels. 1. Poiseuille flow

An analytical study is made of the effect of the internal microstructure of a liquid on its heating due to viscous energy dissipation.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 46, No. 2, pp. 202–208, February, 1984.     

Stress intensity factors for an embedded elliptical crack in a plate of finite thickness

Summary This paper deals with the three-dimensional analysis of the stress distribution in a plate of finite thickness containing an embedded elliptical crack subjected to a constant pressure. By using the douboe Fourier transform, the problem is reduced to the solution of the integro-differential equation which is solved iteratively. A numerical solution of the integro-differential equation is also obtained. These solutions are compared with the results in the published accounts.     

Solution to certain contact problems without axial symmetry in the case of a punch with an elliptical cross section

A solution is obtained to two new contact problems in the class of problems considered earlier [3]. The analytically established relations are suitable for use in several mechanical and engineering applications as, for instance, in the problem of heat and electric current conduction through a contact between solid deformable bodies. The most essential parameters have been computed and the results are shown here in the form of graphs.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 24, No. 2, pp. 334–342, February, 1973.     

Experiments with a strategic oscillation algorithm for the pallet loading problem

This paper concerns the use of strategic oscillation (SO) for packing problems. The SO algorithm spends a certain time exploring infeasible solutions rather than restricting the search to feasible solutions only. The main features of the algorithm are explained and suggestions on different implementations are given. The pallet-loading problem is probably the simplest form of packing problem and is thus suitable for initial experiments with SO. The results obtained suggest that SO is successful for this problem and that it will probably be fruitful to extend the use of SO to other, harder, packing problems.