Short wavelength approximation of a boundary integral operator for homogeneous and isotropic elastic bodies.
نویسندگان
چکیده
A short wavelength approximation of a boundary integral operator for two-dimensional isotropic and homogeneous elastic bodies is derived from first principles starting from the Navier-Cauchy equation. Trace formulas for elastodynamics are deduced connecting the eigenfrequency spectrum of an elastic body to the set of periodic rays where mode conversion enters as a dynamical feature.
منابع مشابه
Asymptotic Distribution of Eigenfunctions and Eigenvalues of the Basic Boundary-contact Oscillation Problems of the Classical Theory of Elasticity
The basic boundary-contact oscillation problems are considered for a three-dimensional piecewise-homogeneous isotropic elastic medium bounded by several closed surfaces. Using Carleman’s method, the asymptotic formulas for the distribution of eigenfunctions and eigenvalues are obtained. 1. After the remarkable papers of T. Carleman [1–2] the method based on the asymptotic investigation of the r...
متن کاملDamped Vibrations of Parabolic Tapered Non-homogeneous Infinite Rectangular Plate Resting on Elastic Foundation (RESEARCH NOTE)
In the present paper damped vibrations of non-homogeneous infinite rectangular plate of parabolically varying thickness resting on elastic foundation has been studied. Following Lévy approach, the equation of motion of plate of varying thickness in one direction is solved by quintic spline method. The effect of damping, elastic foundation and taperness is discussed with permissible range of pa...
متن کاملControllability of isotropic viscoelastic bodies of Maxwell-Boltzmann type
Abstract: In this paper we consider a viscoelastic three dimensional body (of Maxwell-Boltzmann type) controlled on (part of) the boundary. We assume that the material is isotropic and homogeneous. If the body is elastic (i.e. no dissipation due to past memory), controllability has been studied by several authors. We prove that the viscoelastic body inherits the controllability properties of th...
متن کاملShear Waves Through Non Planar Interface Between Anisotropic Inhomogeneous and Visco-Elastic Half-Spaces
A problem of reflection and transmission of a plane shear wave incident at a corrugated interface between transversely isotropic inhomogeneous and visco-elastic half-spaces is investigated. Applying appropriate boundary conditions and using Rayleigh’s method of approximation expressions for reflection and transmission coefficients are obtained for the first and second order approximation of the...
متن کاملRocking Rotation of a Rigid Disk Embedded in a Transversely Isotropic Half-Space
The asymmetric problem of rocking rotation of a circular rigid disk embedded in a finite depth of a transversely isotropic half-space is analytically addressed. The rigid disk is assumed to be in frictionless contact with the elastic half-space. By virtue of appropriate Green's functions, the mixed boundary value problem is written as a dual integral equation. Employing further mathematical tec...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Physical review. E, Statistical, nonlinear, and soft matter physics
دوره 75 3 Pt 2 شماره
صفحات -
تاریخ انتشار 2007