In this paper, we extend the classical Lie symmetry analysis from partial differential equations to integro-differential equations with functional derivatives. We continue the work of Oberlack and Wacławczyk (2006, Arch. Mech. 58, 597), (2013, J. Math. Phys. 54, 072901), where the extended Lie symmetry analysis is performed in the Fourier space. Here, we introduce a method to perform the extend...

We propose a geometrical approach to the mechanics of continuous media equipped with inner structures and give basic (Navier–Stokes, mass conservation energy conservation) equations their motion.

this paper presents the thermal vibration analysis of double-layer graphene sheet embedded in polymer elastic medium, using the plate theory and nonlocal continuum mechanics for small scale effects. the graphene is modeled based on continuum plate theory and the axial stress caused by the thermal effects is also considered. nonlocal governing equations of motion for this double-layer graphene s...

The existing measuremenJs of the viscosity of gaseous systems can be extended if use is made of statistical mechanics. In this work, we confine ourselves to the measurements of the viscosity of multicomponent mixtures of low-density gases. The method is applied to one sample of natural gas.

In the first part of this work, the shear wave phenomena in an elastic 3D continuum are investigated and an analogy to Maxwellian electrodynamics is shown. In the present part, the model is extended assuming the continuum to be a momentum-supporting hypersurface in 4D space (a hypershell). The transverse (flexural) deformations of the shell are governed by a Generalized Nonlinear Dispersive Wav...

It is an important and difficult inverse problem to construct variational principles from complex models directly, because their formulations are theoretical bases for many methods solve or analyze the non-linear problems. At first, this paper extends two kinds of geophysical KdV equations in continuum mechanics fractional partners fractal porous media with irregular boundaries. Then, by design...