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Bending and wave propagation analysis of axially functionally graded beams based on a reformulated strain gradient elasticity theory
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作者 Shaopeng WANG Jun HONG +1 位作者 Dao WEI Gongye ZHANG 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI CSCD 2023年第10期1803-1820,共18页
A new size-dependent axially functionally graded(AFG) micro-beam model is established with the application of a reformulated strain gradient elasticity theory(RSGET). The new micro-beam model incorporates the strain g... A new size-dependent axially functionally graded(AFG) micro-beam model is established with the application of a reformulated strain gradient elasticity theory(RSGET). The new micro-beam model incorporates the strain gradient, velocity gradient,and couple stress effects, and accounts for the material variation along the axial direction of the two-component functionally graded beam. The governing equations and complete boundary conditions of the AFG beam are derived based on Hamilton's principle. The correctness of the current model is verified by comparing the static behavior results of the current model and the finite element model(FEM) at the micro-scale. The influence of material inhomogeneity and size effect on the static and dynamic responses of the AFG beam is studied. The numerical results show that the static and vibration responses predicted by the newly developed model are different from those based on the classical model at the micro-scale. The new model can be applied not only in the optimization of micro acoustic wave devices but also in the design of AFG micro-sensors and micro-actuators. 展开更多
关键词 Timoshenko beam theory reformulated strain gradient elastic theory(RSGET) axially functionally graded(AFG)material Hamilton's principle
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Vibration analysis of nano-structure multilayered graphene sheets using modified strain gradient theory
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作者 Amir ALLAHBAKHSHI Masih ALLAHBAKHSHI 《Frontiers of Mechanical Engineering》 SCIE CSCD 2015年第2期187-197,共11页
In this paper, for the first time, the modified strain gradient theory is used as a new size-dependent Kirchhoff micro-plate model to study the effect of interlayer van der Waals (vdW) force for the vibration analys... In this paper, for the first time, the modified strain gradient theory is used as a new size-dependent Kirchhoff micro-plate model to study the effect of interlayer van der Waals (vdW) force for the vibration analysis of multilayered graphene sheets (MLGSs). The model contains three material length scale parameters, which may effectively capture the size effect. The model can also degenerate into the modified couple stress plate model or the classical plate model, if two or all of the material length scale parameters are taken to be zero. After obtaining the governing equations based on modified strain gradient theory via principle of minimum potential energy, as only infinitesimal vibration is considered, the net pressure due to the vdW interaction is assumed to be linearly proportional to the deflection between two layers. To solve the goveming equation subjected to the boundary conditions, the Fourier series is assumed for w = w(x, y). To show the accuracy of the formulations, present results in specific cases are compared with available results in literature and a good agreement can be seen. The results indicate that the present model can predict prominent natural frequency with the reduction of structural size, especially when the plate thickness is on the same order of the material length scale parameter. 展开更多
关键词 GRAPHENE van der Waals (vdW) force modi- fied strain gradient elasticity theory size effect parameter
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Analysis of wave propagation in micro/nanobeam-like structures: A size-dependent model 被引量:3
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作者 Bing-Lei Wang Jun-Feng Zhao +1 位作者 Shen-Jie Zhou Xi Chen 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2012年第6期1659-1667,共9页
By incorporating the strain gradient elasticity into the classical Bernoulli-Euler beam and Timoshenko beam models, the size-dependent characteristics of wave propaga- tion in micro/nanobeams is studied. The formulati... By incorporating the strain gradient elasticity into the classical Bernoulli-Euler beam and Timoshenko beam models, the size-dependent characteristics of wave propaga- tion in micro/nanobeams is studied. The formulations of dis- persion relation are explicitly derived for both strain gradi- ent beam models, and presented for different material length scale parameters (MLSPs). For both phenomenological size- dependent beam models, the angular frequency, phase veloc- ity and group velocity increase with increasing wave num- ber. However, the velocity ratios approach different values for different beam models, indicating an interesting behavior of the asymptotic velocity ratio. The present theory is also compared with the nonlocal continuum beam models. 展开更多
关键词 strain gradient elasticity theory ~ Bernoulli-Euler beam theory. Timoshenko beam theory Wave propa-gation
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