Transient Dynamic Response of a Semi-infinite Elastic Permeable Solid with Cylindrical Hole Subject to Laser Pulse Heating Under Different Theories of Generalized Thermoelasticity

Our current work is related to the study of vibrations induced by laser beams on the behalf of distinct theories of magneto-thermo-elastic diffusion problem in a semi-infinitely long, conducting isotropic elastic solid with cylindrical hole in a uniform magnetic field acting on the surface of the cylindrical hole of the solid in the direction of the axis of the cylindrical hole. The temporal scheme of laser beam is considered as non-Gaussian and is acted on the surface of the cylindrical hole. The problem is solved with the help of Laplace transform domain and finally illustrated graphically. Note: This article will be very useful in material science specially, in powder metallurgy during sintering, hot pressing, wire and rods annealing are examined from a unified physical point of view, in different branches of engineering physics like plasma physics, nuclear physics, geophysics and related topics and also in oil industry (Lyashenko and Hryhorova (2014), Long and Heng-Wei (2018), Fryxell and Aitken (1969), Nowinski (1978), Legros et al. (1998), Galliero et al. (2019) etc.).

Theory of Charged Gels: Swelling, Elasticity, and Dynamics

The fundamental attributes of charged hydrogels containing predominantly water and controllable amounts of low molar mass electrolytes are of tremendous significance in biological context and applications in healthcare. However, a rigorous theoretical formulation of gel behavior continues to be a challenge due to the presence of multiple length and time scales in the system which operate simultaneously. Furthermore, chain connectivity, the electrostatic interaction, and the hydrodynamic interaction all lead to long-range interactions. In spite of these complications, considerable progress has been achieved over the past several decades in generating theories of variable complexity. The present review presents an analytically tractable theory by accounting for correlations emerging from topological, electrostatic, and hydrodynamic interactions. Closed-form formulas are derived for charged hydrogels to describe their swelling equilibrium, elastic moduli, and the relationship between microscopic properties such as gel diffusion and macroscopic properties such as elasticity. In addition, electrostatic coupling between charged moieties and their ion clouds, which significantly modifies the elastic diffusion coefficient of gels, and various scaling laws are presented. The theoretical formulas summarized here are useful to adequately capture the essentials of the physics of charged gels and to design new hydrogels with specified elastic and dynamical properties.

Euler-Bernoulli cantilever beam bending considering the inner diffusion flows finite propagation speed

Исследуются нестационарные колебания балки Эйлера-Бернулли с учетом массопереноса. Используется модель упругой диффузии для многокомпонентных сред. Для получения решения задачи используются вариационный принцип Даламбера и метод эквивалентный граничных условий. Unsteady vibrations of the Euler-Bernoulli beam are studied taking into account mass transfer. The model of elastic diffusion for multicomponent media is used. To obtain a solution to the problem, the d’Alembert variational principle and the equivalent boundary conditions method are used.

Problem formulation of a rectangular orthotropic elastodiffusive Kirchhoff plate vibrations

Исследуются нестационарные упругодиффузионные колебания ортотропной пластины Кирхгофа с учетом релаксации диффузионных потоков. В общем случае пластина находится под действием растягивающих усилий, изгибающих и крутящих моментов и перерезывающих сил. Здесь же заданы плотности диффузионных потоков. Для постановки задачи используется модель нестационарного плоского изгиба упругодиффузионной пластины Кирхгофа, полученная с помощью вариационного принципа Даламбера. We study unsteady elastic diffusion vibrations of a rectangular ortotropic Kirchhoff plate in the presence of diffusion fluxes relaxation. In general formulation the plate is subjected to tensile and shear forces as well as bending moments and torque. The unsteady model of an elastodiffusive Kirchhoff plate is obtained using the d’Alembert variational principle.