Size-dependent bending, buckling and free vibration of functionally graded Timoshenko microbeams based on the most general strain gradient theory

Ansari, R.; Gholami, R.; Shojaei, M. Faghih; Mohammadi, V.; Sahmani, S.

doi:10.1016/j.compstruct.2012.12.048

Cited by 144 publications

(49 citation statements)

References 48 publications

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“…Many recent studies have contributed to the understanding large-scale functionally graded plates based on the classical continuum theory [29][30][31]. Recently several studies have been dealing with the size-dependent functionally graded micro/nano-beams [32][33][34][35][36] and two-dimensional micro/nano-plates. Natarjan et al [37] studied the nonlocal size dependent linear free vibration of functionally graded (FG) nanoplates based on the finite element method.…”

Section: Introductionmentioning

confidence: 99%

Natural frequency analysis of functionally graded rectangular nanoplates with different boundary conditions via an analytical method

2015

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In this paper, the natural frequencies of a functionally graded nanoplate are analyzed for different combinations of boundary conditions. Application of new materials and specially the functionally graded materials in the micro-and nano-scale devices and systems is increasingly spread. Therefore, the study of the natural frequencies of functionally graded materials for different boundary conditions seems to be necessary in the micro/nano-structures. The article presented here covers broad types of common boundary conditions for the free vibration of functionally graded rectangular nanoplates for the first time. The analytical solution method used here is new for this subject and solves the governing equations with no approximation. The size dependency is considered according to Eringen's differential form of nonlocal elasticity theory. The elasticity modulus and mass density of the plate are varied along the thickness of the plate according to a power-law distribution of the constituents' volume fractions. As the in-plane and out-of-plane displacement variables are coupled in the equations of motion, a new exact solution method is introduced to solve the displacement fields analytically. The method is capable of dealing with new combinations of boundary conditions which have not been studied before in the literature. The validity and accuracy of the present method is investigated by comparing some of the present results to their counterparts reported in the literature. The results presented here are new and discussed for the first time in this subject. As a novelty a detailed study is carried out to examine the effects of power-law distribution, the characteristic internal length, the plate aspect ratio and the mode number on the natural frequencies of functionally graded rectangular plates for different boundary conditions. It's shown that the type of boundary condition affects considerably on the values of natural frequency but the behavior of the frequency variations is in the same manner for different combinations of boundary conditions. These results can be used as benchmark for future studies.

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Section: Introductionmentioning

confidence: 99%

Natural frequency analysis of functionally graded rectangular nanoplates with different boundary conditions via an analytical method

2015

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“…He and Balachandran [24] examined the buckling and free oscillations of clamped-clamped composite microresonators. Ansari et al [25] contributed to the field by analyzing the size-dependent buckling behaviour of a functionally graded straight microbeam based on a strain gradient theory. The nonlinear analyses of the system were conducted, for example, by Xia et al [26] and Medina et al [27]; e.g.…”

Section: Introductionmentioning

confidence: 99%

On the nonlinear resonant dynamics of Timoshenko microbeams: effects of axial load and geometric imperfection

et al. 2015

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The nonlinear size-dependent dynamics of a geometrically imperfect Timoshenko microbeam subject to an axial load is investigated numerically based on the modified couple stress theory. Increasing the compressive axial load leads to an increase in the deflection (bending) amplitude of the microbeam. A distributed harmonic excitation load in the transverse direction is then applied to the microbeam and the nonlinear dynamics over the new deflection is analyzed. More specifically, the kinetic energy of the system, the size-dependent strain potential energy, and the works due to the external excitations and damping are constructed as functions of the displacement field. These expressions are then inserted in Hamilton's principle, a variational energy technique, in order to obtain the nonlinear partial differential equations of motion. The Galerkin scheme is then applied to the resultant equations, yielding a set of second-order nonlinear ordinary differential equations. These equations are solved numerically via a direct time integration method as well as a continuation technique. Results are plotted in the form of deflectionaxial load diagrams, frequency-responses, forceresponses, time traces, phase-plane portraits, and fast Fourier transforms. The importance of taking into account small-size effects, through use of the modified couple stress theory, is highlighted.

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“…In other words, the mechanical behavior of nanostructures is size-dependent. Since the classic continuum models cannot capture the size effect, some higher-order continuum theories such as the modified couple stress theory [6,7], the strain gradient theory [8,9], the surface stress theory [10][11][12][13], and the nonlocal elasticity theory [14][15][16][17] can be employed for the analysis of small-scale systems. In addition, Peddieson et al [18] indicated that the nonlocal elasticity theory can be appropriately applied to nanotechnology applications.…”

Section: Introductionmentioning

confidence: 99%

Nonlocal vibration analysis of circular double-layered graphene sheets resting on an elastic foundation subjected to thermal loading

Ansari

Torabi

2016

Acta Mech. Sin.

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Based on the nonlocal elasticity theory, the vibration behavior of circular double-layered graphene sheets (DLGSs) resting on the Winkler-and Pasternak-type elastic foundations in a thermal environment is investigated. The governing equation is derived on the basis of Eringen's nonlocal elasticity and the classical plate theory (CLPT). The initial thermal loading is assumed to be due to a uniform temperature rise throughout the thickness direction. Using the generalized differential quadrature (GDQ) method and periodic differential operators in radial and circumferential directions, respectively, the governing equation is discretized. DLGSs with clamped and simply-supported boundary conditions are studied and the influence of van der Waals (vdW) interaction forces is taken into account. In the numerical results, the effects of various parameters such as elastic medium coefficients, radius-to-thickness ratio, thermal loading and nonlocal parameter are examined on both in-phase and anti-phase natural frequencies. The results show that the thermal load and elastic foundation respectively decreases and increases the fundamental frequencies of DLGSs.

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Size-dependent bending, buckling and free vibration of functionally graded Timoshenko microbeams based on the most general strain gradient theory

Cited by 144 publications

References 48 publications

Natural frequency analysis of functionally graded rectangular nanoplates with different boundary conditions via an analytical method

Natural frequency analysis of functionally graded rectangular nanoplates with different boundary conditions via an analytical method

On the nonlinear resonant dynamics of Timoshenko microbeams: effects of axial load and geometric imperfection

Nonlocal vibration analysis of circular double-layered graphene sheets resting on an elastic foundation subjected to thermal loading

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