Open AccessJournal Article
Size effect on the dynamic characteristic of a micro beam based on cosserat theory
TLDR
In this article, the Hamilton principle was used to derive the freely vibration equation of a micro beam in the absence of damping, and the dependence of the resonant frequency on its size was analyzed.Abstract:
Many micro experiments have shown that the mechanical properties of materials at micro scale are size dependent. The vibration characteristic (mainly the resonant frequency) of a micro beam has been analyzed theoretically using couple stress theory (Cosserat theory). Based on the couple stress elasticity theory the freely vibration equation of a micro beam in the absence of damping is derived using the Hamilton principle. The dependence of the resonant frequency of a micro beam on its size is analyzed, and the results show that the resonant frequency will increase markedly when the thickness of the beam decreases to a value which is comparable to the material length scale parameter.read more
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The size-dependent natural frequency of Bernoulli-Euler micro-beams
TL;DR: In this article, the dynamic problems of Bernoulli-Euler beams are solved analytically on the basis of modified couple stress theory and Hamilton's principle, and the difference between the natural frequencies predicted by the newly established model and classical beam model is very significant when the ratio of characteristic sizes to internal material length scale parameter is approximately equal to one, but is diminishing with the increase of the ratio.
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Static and dynamic analysis of micro beams based on strain gradient elasticity theory
TL;DR: In this paper, the static and dynamic problems of Bernoulli-Euler beams are solved analytically on the basis of strain gradient elasticity theory due to Lam et al.
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A micro scale Timoshenko beam model based on strain gradient elasticity theory
TL;DR: In this article, a micro scale Timoshenko beam model based on strain gradient elasticity theory was developed and the governing equations, initial conditions and boundary conditions were derived simultaneously by using Hamilton's principle.
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On the size-dependent behavior of functionally graded micro-beams
TL;DR: In this article, the size-dependent static and vibration behavior of micro-beams made of functionally graded materials (FGMs) is analyzed on the basis of the modified couple stress theory in the elastic range.
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Free vibration analysis of size-dependent shear deformable functionally graded cylindrical shell on the basis of modified couple stress theory
TL;DR: In this paper, size-dependent equations of motion for functionally graded cylindrical shell were developed using shear deformation model and rotation inertia, where material properties of the shell were assumed as continuously variable along thickness, consistent with the variation in the component's volume fraction based on power law distribution.