摘要:

The problems of acoustic waves diffraction by elastic plates or shells with edges, conjunctions, cracks, inclusions and stiffeners attract wide interest caused by the needs of shipbuilding, acoustics of the ocean and other sciences. Much attention in paid to problems that can be solved exactly. Then the analysis of physical effects is the most simple. Up to present practically all the explicit solutions have been already examined. To analyse new physical effects one needs to use more and more cumbrous approaches with large computer resources needed for realization.

ISSN:0003-6811    

DOI:10.1080/00036819808840619

出版商:Gordon and Breach Science Publishers    

年代:1998

数据来源: Taylor

摘要:

We show herein the uniform stability of a thermoelastic plate model with no added dissipative mechanism on the boundary(uniform stability of a thermoelastic plate with added boundary dissipation was shown in [3], as was that of the analytic case where rotational forces are negleted in [9]); both the analytic and nonanalytic cases are treated here. The proof is constructive in the sense that we make use of a multiplier with respect to the coupled system involved so as to generate afortiorithe desired estimates; this multiplier is of an operator theoretic nature, as opposed to the more standard differential quantities used for such work. Moreover, the particular choice of multiplier becomes clear only after recasting the pde model into an associated abstract evolution equation. With this direct technique, we also obtain an exponential stability estimate pertaining to the limit case in which rotational inertia is neglected, and which leads to an associated analytic semigroup.

ISSN:0003-6811    

DOI:10.1080/00036819808840620

出版商:Gordon and Breach Science Publishers    

年代:1998

数据来源: Taylor

摘要:

Boundary value contact problems are the problems of mathematical physics, whose statement contains some conditions at particular points or lines of the boundary. The purpose of this paper is to discuss some mathematical aspects of the BVCP, such as the correct functional classes and Fredholm type equations for the solution, the completeness of eigenfunctions, the connection between the BVCP and supersymmetric quantum mechanic, paritial radiation conditions, limiting absorption principle, existence of eigenfunctions in infinite domains, uniqueness of the solution, “optical” theorem, and so on.

ISSN:0003-6811    

DOI:10.1080/00036819808840621

出版商:Gordon and Breach Science Publishers    

年代:1998

数据来源: Taylor

摘要:

An algorithm is described for finding the parameters of a one-layer elastic seabed which is based upon the Nelder-Mead simplex method for minimizing a function. The effectiveness of the algorithm is demonstrated by testing it on a set of twelve sediments encompassing a wide range of values of the seabed parameters.

ISSN:0003-6811    

DOI:10.1080/00036819808840622

出版商:Gordon and Breach Science Publishers    

年代:1998

数据来源: Taylor

摘要:

In this paper, the problem of constructing the acoustic pressure field excited by a time-harmonic point source in a shallow ocean over an elastic seabed is considered. This is a transmission boundary value problem for a system of prtial differential equations. Two different expansions for thepropagating solutionsare derived. The first expansion is obtained by using Hankel transformation. We symbolically compute the Hankel transform of the propagating solution and then perform inversion usingMittag-Lefflerdecomposition and other spectral analysis techniques. The second expansion is normal mode expansion. We find an appropriate inner product in a suitable function space, which permits us to compute thegeneralized Fouriercoefficients. Numerical computations are presented to verify the orthogonality of the set of eigenfunctions with rewpect to this inner product, and to verify the equivalence of the two expansions.

ISSN:0003-6811    

DOI:10.1080/00036819808840623

出版商:Gordon and Breach Science Publishers    

年代:1998

数据来源: Taylor

摘要:

Consider the abstract Cauchy problems

ISSN:0003-6811    

DOI:10.1080/00036819808840624

出版商:Gordon and Breach Science Publishers    

年代:1998

数据来源: Taylor

摘要:

Full on Karman suystem describing nonlinear oscilations in dynamic elasticity is considered. The system is equipped with nonlinear boundary conditions prescribing moments and shears subject to a nonlinear, monotone damping. The main result of the paper is the wellposedness theory (existence and uniqueness) for weak, regular and “intermediate” solutions to this problem. in particular, this paper provides an affirmative asnwer to a long-standing open problem in the literature related to the uniqueness of weak (finite energy) solutions in dynamic nonlinear elasticity.

ISSN:0003-6811    

DOI:10.1080/00036819808840625

出版商:Gordon and Breach Science Publishers    

年代:1998

数据来源: Taylor

摘要:

A three-dimensional mathematical model is developed for handling environmental interactions in the ocean between a fluid medium and an elastic bottom. The model is a combination of three-dimensional wave propagaion models in both the fluid and the elastic media, together with the incorporation of a set of fluid-elastic interface conditons. A complete theory with regard to the mathematical formulation of the fluid and elastic models is discussed, along with an error analyiss, and a description of the derivation of the fluid-elactic interface equations is given. A ordinary differential equation (ODE) method in conjunction with a finite difference marching scheme to obtain the numerical solution of the complete representative system of coupled fluid-elastic wave equations is outlined; moreover, the theory with regard to the stability and consistency of the marching scheme is discussed. The major development of this paper is the combination of the fluid equations, the elastic equations and the set of fluid-elastic interface conditions into a single unified three-dimensional model capable of applications to realistic fluid-elastic interactions in the ocean environment.

ISSN:0003-6811    

DOI:10.1080/00036819808840626

出版商:Gordon and Breach Science Publishers    

年代:1998

数据来源: Taylor

摘要:

We seek to optimally control a reflection boundary coefficient for an acoustic wave equation. The goal-quantified by an objective functional- is to drive the solution close to a target by adjusting this coefficient, which acts as a control. The problem is solved by finding the optimal control, which minimizes the objective functional. Then the optimal control is used as a an approximation for an inverse “ identification” problem.

ISSN:0003-6811    

DOI:10.1080/00036819808840627

出版商:Gordon and Breach Science Publishers    

年代:1998

数据来源: Taylor

ISSN:0003-6811    

DOI:10.1080/00036819808840618

出版商:Gordon and Breach Science Publishers    

年代:1998

数据来源: Taylor