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چکیده
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Based on the Strain gradian theory (SGT), free vibration of variable section Functionally graded (FG) microbeams and Functionally graded (FG) Non-Rectangular microplates in thermal environment are investigated. beam carry a concentrated mass at the beam end and another concentrated mass at an intermediate point. Non-rectangular plates refers to the plates skew, triangular, trapezoidal and its circle. Temperature-dependent material properties are assumed to be constant changes in the thickness direction, Which are intended for power distribution. The governing equations using the principle of Hamilton and based on theory first-order shear have been obtained. In this thesis by Ritz and sentences Chebyshev polynomial functions as displacement, natural frequencies, these structures have been obtained. To prove the effectiveness of the methodology used and the accuracy of the results, a study in conjunction with the answers convergence rate and how is done. To prove the authenticity of the results formulation and the method used, the results with the results available in the scientific literature that theories such as classical theory, first-order shear theory, the theory of higher shear theory of three-dimensional elasticity and also have used comparative case has been accepted. In this thesis, a parametric study to evaluate the effect of different parameters such as boundary conditions, different theories, material properties index distribution, the temperature distribution, the aspect ratio structures, the angle between the sides, width and thickness on the natural frequencies of the micro beam Micro plates are taken. Here it should be noted that so far, the answer to the vibration of these structures made of Functionally graded (FG) and temperature-dependent under the thermal environment and based on the theory of first-order shear is not available. So a series of new results for the free vibration of these structures will be provided with different boundary conditio
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