On the Bending and Vibration Analysis of Functionally Graded Magneto-Electro-Elastic Timoshenko Microbeams

In this paper, a new magneto-electro-elastic functionally graded Timoshenko microbeam model is developed by using the variational formulation. The new model incorporates the extended modified couple stress theory in order to describe the microstructure effect. The power-law variation through the thickness direction of the two-phase microbeams is considered. By the direct application of the derived general formulation, the static bending and free vibration behavior of the newly developed functionally graded material microbeams are analytically determined. Parametric studies qualitatively demonstrate the microstructural effect as well as the magneto-electro-elastic multi-field coupling effect. The proposed model and its classic counterpart produce significant differences for thin graded magneto-electro-elastic Timoshenko microbeams. The thinner the microbeam is, the larger the difference becomes.

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Structural instability of non-conservative functionally graded micro-beams tunable with piezoelectric layers

Journal of Intelligent Material Systems and Structures ◽

10.1177/1045389x18818769 ◽

2019 ◽

Vol 30 (4) ◽

pp. 593-605 ◽

Cited By ~ 3

Author(s):

Mohammad Hosseini ◽

Reza Bahaadini ◽

Zahra Khalili-Parizi

Keyword(s):

Functionally Graded Material ◽

Strain Gradient ◽

Couple Stress Theory ◽

Modified Couple Stress Theory ◽

Functionally Graded ◽

Strain Gradient Theory ◽

Gradient Theory ◽

Modified Strain Gradient Theory ◽

Stress Theory ◽

Graded Material

This investigation aims to explore the non-conservative instability of a functionally graded material micro-beam subjected to a subtangential force. The functionally graded material micro-beam is integrated with piezoelectric layers on the lower and upper surfaces. To take size effect into account, the mathematical derivations are expanded in terms of three length scale parameters using the modified strain gradient theory in conjunction with the Euler–Bernoulli beam model. However, the modified strain gradient theory includes modified couple stress theory and classical theory as special cases. Applying extended Hamilton’s principle and Galerkin method, the governing equation and corresponding boundary conditions are obtained and then solved numerically by the eigenvalue analysis, respectively. The results illustrated effects of non-conservative parameter, length scale parameter, different material gradient index, and various values of piezoelectric voltage on the natural frequencies, flutter and divergence instabilities of a cantilever functionally graded material micro-beam. It is found that both the material gradient index and applied piezoelectric voltage have significant influence on the vibrational behaviors, divergence and flutter instability regions. Furthermore, a comparison between the various micro-beam theories on the basis of modified couple stress theory, modified strain gradient theory, and classical theory are presented.

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