Dynamic model of a porous gradient medium and classification of wave processes
Аuthors
*, **Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia
*e-mail: egorovams@mai.ru
**e-mail: tushavinaov@mai.ru
Abstract
This paper presents a generalized dynamic model of a porous gradient medium, constructed using a variational approach. A Lagrangian incorporating kinetic and potential energies is formulated using the variational principle. Equations of motion and a porosity equation are derived, containing eleven physical constants. Seven of these describe static properties (classical and gradient elastic moduli, porosity parameters, and their interactions), while four describe the inertial characteristics of the matrix and pores, as well as dynamic interactions.
Asymptotic dependences of frequency on wavenumber in the long- and short-wavelength regions are established, and the conditions for wave existence and the ranges of "locking" (opacity) of the medium are identified. It is shown that, in general, the medium exhibits complex dispersion behavior with alternating zones of transparency and opacity, which is fundamental for predicting the behavior of porous materials under dynamic loads.
Keywords:
porous medium; gradient theory of elasticity; dynamic model; porosity waves; wave dispersion; equations of motion; variational principle; classification of wave processes; "locking" effect; microstructure.References
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