-coupling mechanisms are sufficient to obtain exponential decay in strain gradient elasticity
نویسندگان
چکیده
Abstract In this paper, we consider the time decay of solutions to some problems arising in strain gradient thermoelasticity. We restrict two-dimensional case, and assume that two dissipative mechanisms are introduced, temperature mass dissipation. First, show problem is well-posed proving operator defining it generates a contractive semigroup linear operators. Then, assuming function involving coupling terms elliptic, exponential concluded as well analyticity solutions. Finally, describe how obtain stability case hyperbolic
منابع مشابه
Static analysis of rectangular nanoplates using exponential shear deformation theory based on strain gradient elasticity theory
In this research, the bending analysis of rectangular nanoplates subjected to mechanical loading is investigated. For this purpose, the strain gradient elasticity theory with one gradient parameter is presented to study the nanoplates. From the best knowledge of authors, it is the first time that the exponential shear deformation formulation based on strain gradient elasticity theory is carried...
متن کاملstatic analysis of rectangular nanoplates using exponential shear deformation theory based on strain gradient elasticity theory
in this research, the bending analysis of rectangular nanoplates subjected to mechanical loading is investigated. for this purpose, the strain gradient elasticity theory with one gradient parameter is presented to study the nanoplates. from the best knowledge of authors, it is the first time that the exponential shear deformation formulation based on strain gradient elasticity theory is carried...
متن کاملComputational Evaluation of Strain Gradient Elasticity Constants
Classical effective descriptions of heterogeneous materials fail to capture the influence of the spatial scale of the heterogeneity on the overall response of components. This influence may become important when the scale at which the effective continuum fields vary approaches that of the microstructure of the material and may then give rise to size effects and other deviations from the classic...
متن کاملExponential decay in one-dimensional porous-thermo-elasticity
This paper concerns the one dimensional problem of the porous-thermo-elasticity. Two kinds of dissipation process are considered: the viscosity type in the porous structure and the thermal dissipation. It is known that when only thermal damping is considered or when only porous damping is considered we have the slow decay of the solutions. Here we prove that when both kinds of dissipation terms...
متن کاملFree Vibration Analysis of Microtubules as Orthotropic Elastic Shells Using Stress and Strain Gradient Elasticity Theory
In this paper, vibration of the protein microtubule, one of the most important intracellular elements serving as one of the common components among nanotechnology, biotechnology and mechanics, is investigated using stress and strain gradient elasticity theory and orthotropic elastic shells model. Microtubules in the cell are influenced by internal and external stimulation and play a part in con...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: European Journal of Applied Mathematics
سال: 2023
ISSN: ['0956-7925', '1469-4425']
DOI: https://doi.org/10.1017/s0956792523000086