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Linear theory of non-local viscoelasticity
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In this article, the theory of non-local viscoelastic media is studied and the constitutive equation of strain and strain rate dependent, stress and stress rate dependent as well as continuous memory dependent are derived and discussed.Abstract:
The theory of non-local viscoelastic media is studied. The constitutive equation of strain and strain rate dependent, stress and stress rate dependent as well as continuous memory dependent are derived and discussed. The thermodynamical restrictions are also studied.read more
Citations
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A Galerkin method for distributed systems with non-local damping
TL;DR: In this paper, a non-local damping model including time and spatial hysteresis effects is used for the dynamic analysis of structures consisting of Euler-Bernoulli beams and Kirchoff plates.
Journal ArticleDOI
Vibration analysis of beams with non‐local foundations using the finite element method
TL;DR: In this paper, a non-local viscoelastic foundation model is proposed and used to analyse the dynamics of beams with different boundary conditions using the finite element method, where the reaction of the nonlocal model is obtained as a weighted average of state variables over a spatial domain via convolution integrals with spatial kernel functions that depend on a distance measure.
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Non-local finite element analysis of damped beams
TL;DR: In this article, a non-local viscoelastic beam model with different boundary conditions using the finite element method is used to analyse the dynamics of beams with various boundary conditions.
Journal ArticleDOI
On the stability of a microbeam conveying fluid considering modified couple stress theory
TL;DR: In this article, the size-dependent vibrational behavior of a microbeam conveying fluid was investigated using the modified couple stress theory and the Galerkin-based reduced order model and the effects of material length-scale parameter on its natural frequencies were evaluated.
Journal ArticleDOI
Stability via nonlocal continuum mechanics
TL;DR: In this article, a nonlocal elasticity theory and nonlocal damping is used to describe the motion of the Euler-Bernoulli beam, and the dynamic stability problem is solved for the beam made from micro and nano-materials.
References
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Journal ArticleDOI
On nonlocal elasticity
TL;DR: In this article, a theory of non-local elasticity is presented via the vehicles of global balance laws and the second law of thermodynamics via the use of a localized Clausius-Duhem inequality and a variational statement of Gibbsian global thermodynamics.
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Nonlocal polar elastic continua
TL;DR: In this article, a continuum theory of non-local polar bodies is developed for nonlinear micromorphic elastic solids, and the balance laws and jump conditions are given.
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Linear theory of nonlocal elasticity and dispersion of plane waves
TL;DR: In this article, the dispersion relations for one dimensional plane waves were obtained by fitting the nonlocal material moduli to exactly the acoustical branch of elastic waves within one Brillouin zone in periodic one dimensional lattices.
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Elasticity theory of materials with long range cohesive forces
TL;DR: In this paper, the authors derived a linear model for the elastic long-range strain energy of a deformed material with spatial interaction, which can be expressed in a differential (multipolar) form or in a non-local form.
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Linear theory of micropolar viscoelasticity
TL;DR: Viscoelasticity for micropolar solids, obtaining constitutive equations of strain and microrotation rate dependent materials, were obtained in this article, where the authors considered the case of micropolecular solids.