Abstract
We consider the influence of a plane gravitational wave on the following Newtonian system: a self-gravitating elastic sphere without rotation. We determine the equation governing the elastic oscillations within the framework of the general relativity. We include dissipative processes by using a simple relativistic model of viscoelasticity. If the wavelength is much larger than the dimension of the elastic sphere, we transform these equations into the form derived by Ashby and Dreitlein previously. We also determine the equations governing the elastic oscillations within the framework of the Brans-Dicke scalar-tensor theory of gravitation.
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