Some Spectral Problems of Mechanics

Abstract

We obtain a spectral problem by formally considering a solution u of the form

$$u({\bf x},t)=e^{i\omega t}v{({\bf x})}$$

for a dynamic equation

$$B(u({\bf x}, t)) = \rho \frac{\partial^2 u(\bf x), t}{\partial t^2}$$

where B is a differential operator having coefficients independent of t, defined by the model of an elastic body, and ρ is the density of the body.