# Eringen’s nonlocal and modified couple stress theories applied to vibrating rotating nanobeams with temperature effects

Published on Jun 22, 2021in Mechanics of Advanced Materials and Structures4.03

· DOI :10.1080/15376494.2021.1939468

Published on Jun 22, 2021in Mechanics of Advanced Materials and Structures4.03

· DOI :10.1080/15376494.2021.1939468

References66

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Nonlocal finite element model for the bending and buckling analysis of functionally graded nanobeams using a novel shear deformation theory

Abstract In this study, an efficient nonlocal finite element model is developed to investigate the bending and buckling behavior of functionally graded (FG) nanobeams. New two-node beam element with eight degrees of freedom is formulated based on the recently refined higher order shear deformation theory proposed by the authors. The present theory can provide an accurate parabolic distribution of transverse shear stress through the thickness direction satisfying the traction free boundary condit...

Numerical evaluation of strain gradients in classical elasticity through the Boundary Element Method

Abstract Strain gradient fields seem to play an important role on the functionality of flexoelectric and functionally graded materials, bones, biomembranes, new sensing equipment and micro, nano and thin structures. A numerical method for evaluating strains and stresses with high accuracy is the Boundary Element Method (BEM). Despite to many BEM papers appearing so far in the literature, there is not a BEM reference dealing with the evaluation of strain gradients in classical elastic materials. ...

Abstract In structural dynamics, different damping models are used; however, due to modal decomposition, those models typically result in the use of the damping ratio as the modal damping parameter. If proportional viscous damping is used, the damping ratio can be related to the mass and stiffness parameters of a particular dynamic system, i.e. the damping is structure-specific. Lord Rayleigh introduced the idea of proportional damping based on the global kinetic and potential energies of a dyna...

The vibration of two-dimensional imperfect functionally graded (2D-FG) porous rotating nanobeams based on general nonlocal theory

Abstract A comprehensive vibrational analysis of bi-directional functionally graded (2D-FG) rotating nanobeams with porosities is studied for the first time. The beam is modeled based on general nonlocal theory (GNT) where the beam governing equations are derived depending on two different nonlocal parameters. Unlike Eringen’s conventional form of nonlocal theory, the general nonlocal theory can reveal both hardening and softening behaviors of the material. Here, the attenuation functions are al...

On dynamic-vibration analysis of temperature-dependent Timoshenko microbeam possessing mutable nonclassical length scale parameter

AbstractIn this research paper, lateral vibration analysis of simply-supported microbeam under thermal stress is investigated. Microbeam model is presented based on the modified couple stress theory and Timoshenko beam theory. Thermo-mechanical properties of the microbeam are assumed variable by temperature shifts. This means that any shift in the temperature leads to different thermo-mechanical properties. Thermal stress is induced to the system due to the temperature difference between the lat...

A new isogeometric Timoshenko beam model is developed using a modified couple stress theory (MCST) and a surface elasticity theory. The MCST is wildly used to capture microstructure effects that in...

On wave propagation in two-dimensional functionally graded porous rotating nano-beams using a general nonlocal higher-order beam model

Abstract This paper studies the wave propagation of two-dimensional functionally graded (2D-FG) porous rotating nano-beams for the first time. The rotating nano-beams are made of two different materials, and the material properties of the nano-beams alter both in the thickness and length directions. The general nonlocal theory (GNT) in conjunction with Reddy's beam model are employed to formulate the size-dependent model. The GNT efficiently models the dispersions of acoustic waves when two inde...

A novel analysis method for damping characteristic of a type of double-beam systems with viscoelastic layer

Abstract The double-beam system with a viscoelastic layer is a classical mechanical model for many beam-type composite structures. However, few studies have been able to optimize the structure from the perspective of structural damping characteristics. To fully understand the damping characteristics of the viscoelastic double-beam system, an analysis method based on dynamic stiffness method and Wittrick-Williams algorithm is presented in this paper. Through numerical case studies, five typical p...

Anisotropic solid-like shells modeled with NURBS-based isogeometric approach: Vibration, buckling, and divergence analyses

Abstract We proposed an IGA formulation for free vibration, buckling and divergence analyses of generally anisotropic solid-like composite shells. Recently developed Rayleigh–Ritz based methods are not accurate enough for curved shells since they are not able to capture twisting mode shapes. Here, we use the advantages of isogeometric analysis (IGA) and develop a three-dimensional higher-order continuous solid-like shell (SLS) model. Since the continuity of material orientation is crucial in num...

An integral nonlocal model for the free vibration analysis of Mindlin nanoplates using the VDQ method

Eringen’s nonlocal theory (ENT) provides an efficient tool to consider the size dependency for the structural analysis of small-scale structures. Recently, it has been indicated that in some cases, inconsistent results may be obtained using the Eringen differential model (EDM) and Eringen integral model (EIM) should be employed. In this regard, the vibration of nanoplates resting on the elastic medium is investigated on the basis of the EIM using variational differential quadrature (VDQ) method....

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Thermoelastic responses in rotating nanobeams with variable physical properties due to periodic pulse heating

Abstract null null Recently, many researchers have been interested in the so-called theories of nonlocal elasticity (NET) and modified couple stress (MCS). The effect of size and dependence on the micron scale was predicted using this theory. A new set of equations was created that governs this theory including the equation for a couple of moments and the use of the concept of couple stress elasticity. Also, the generalized thermoelastic model with phase lag is used. The present work concentrate...