On porous-elastic system with localized damping

On deformation of porous plates

“…Thus, considering all unknown functions are only of the x 1 coordinate, Eqs. (16) and (17) for the problem stated have the form (the hatch corresponds to the derivative of x 1 ): Boundary conditions for the right edge x 1 = l:…”

“…Assuming all unknown functions are only of the x 1 coordinate, Eqs. (16) and (17) for the problem stated have the form:…”

“…To specify such problem the foundation of stiffness of k is introduced. Thus, according to (16), the stresses on the bottom surface of a plate should be specified, and for the case described this normal stress has the form p − 3 = −kw. Therefore, the system for the description of bending problem for a porous plate, lying on an elastic foundation, could be represented as:…”

“…For some objects it is not necessary to solve full 3D equations for the media deformation and is possible to confine ourselves with the application of corresponding simplified model. Thus, in [16] authors consider the one-dimensional equations of a homogeneous and isotropic porous elastic solid with Kelvin-Voigt damping, in [3] there described the mechanical behavior of porous rods. These are examples of dealing with 1D objects, an another approach is the model of plate that allows to describe effectively a deformation of bodies with the one size much less than two others.…”

On the decay rates for a one-dimensional porous elasticity system with past history

“…Recently, the present author and his co-author, Feng and Yin [11], extended the result to the case of the non-equal wave speeds, and the result also holds for b < 0. For more results concerning the stability to porous elastic solids, one can refer to [12,23,26,29,30,31] and so on.…”