The linear equations of motion of a uniformly rotating, elastic and self-gravitating earth model are analyzed under minimal regularity assumptions. We present existence and uniqueness results for the system, energy estimates, convergence of Galerkin approximations, and propose a method based on a Volterra equation to deal with the nonlocal self-gravitation.

We present a dynamical theory of a two–dimensional martensitic transition in an elastic solid, connecting a high–temperature phase which is nondegenerate and has triangular symmetry, and a low– temperature phase which is triply degenerate and has oblique symmetry. A global mode–based Galerkin method is employed to integrate the deterministic equation of motion, the latter of which is derived by...

In this paper, an analysis of free vibration in functionally graded nanoplate is presented. Third-order shear deformation plate theory is used to reach more accuracy in results. Small-scale effects are investigated using Eringen`s nonlocal theory. The governing equations of motion are obtained by Hamilton`s principle. It is assumed that the properties of nanoplates vary through their thicknesse...

The following article investigates buckling of moderately thick circular Nano plates with an orthotropic property under uniform radial compressive in-plane mechanical load. Taking into account nonlocal elasticity theory (Eringen), principle of virtual work, first order shear deformation plate theory (FSDT) and nonlinear Von-Karman strains, the governing equations are obtained based on displacem...

In this paper, free longitudinal vibration of nanorods is investigated from the wave viewpoint. The Eringen’s nonlocal elasticity theory is used for nanorods modelling. Wave propagation in a medium has a similar formulation as vibrations and thus,  it can be used to describe the vibration behavior. Boundaries reflect the propagating waves after incident. Firstly, the governing quation of nanoro...

The crystal of benzoic acid is comprised of tautomeric centrosymmetric dimers linked through bistable hydrogen bonds. Statistical disorder of the bonding protons is excluded by neutron diffraction from 6 K to 293 K. In addition to diffraction data, vibrational spectra and relaxation rates measured with solid-state-NMR and quasi-elastic neutron scattering are consistent with wave-like, rather th...