Eigen-oscillations of contrasting non-homogeneous elastic bodies: asymptotic and uniform estimates for eigenvalues

Abstract

Estimates of convergence rates for the eigenvalues of spectral stiff elasticity problems are obtained. The bounds in the estimates are expressed in terms of the stiffness ratio h and characteristic properties of the limit spectrum for low and middle frequency ranges. These estimates allow us to distinguish between individual and collective asymptotics of the eigenvalues and eigenvectors and to determine precisely the intervals for the small parameter h where the mathematical model considered provides a suitable approach and accuracy. The results in this paper hold for different boundary conditions, two- and three-dimensional models and scalar problems.


Key Words: eigenfrequencies; linear elasticity; spectral analysis; stiff problems