FREE VIBRATION OF THIN FUNCTIONALLY GRADED PLATES BY EXACT FINITE STRIP METHOD

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SOLTANI M.; HATAMI S.; AZHARI M.

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Journal: JOURNAL OF COMPUTATIONAL METHODS IN ENGINEERING (ESTEGHLAL) Year:2014 | Volume:32 | Issue:2 Page(s): 33-54

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Title

FREE VIBRATION OF THIN FUNCTIONALLY GRADED PLATES BY EXACT FINITE STRIP METHOD

Author(s)

SOLTANI M. | HATAMI S. | AZHARI M. | Issue Writer Certificate

Keywords

FUNCTIONALLY GRADED MATERIAL (FGM)Q2

FREE VIBRATIONQ2

EXACT FINITE STRIPQ2

CLASSICAL PLATE THEORY (CPT)Q2

THIN FGM PLATEQ2

IN-PLANE FORCESQ2

Abstract

In this article, an EXACT FINITE STRIP method is developed for FREE VIBRATION of rectangular thin functionally graded plates subjected to in-plan forces. First, a reference surface, instead of mid-plane of the plate, is used to extract the equation of motion based on classical plate theory so that there is no coupling between in-plane and out-of-plane equations of functionally graded plates. Then, an EXACT FINITE STRIP method is developed for the uncoupled differential equation of motion by keeping two parallel edges of the plate as simply supported. In the method, the multi-span plate is divided into a small number of strips. The shape function of each strip is sinusoidal in the direction perpendicular to the simple edges; and in the other direction, the shape function is the analytical solution of the differential equation governing FREE VIBRATION of the functionally graded plate. Thus, the elements of exact stiffness matrix for any finite strip are a function of natural frequencies, IN-PLANE FORCES, and material and geometry properties of the plate. As the standard eigenvalue algorithms cannot solve the FREE VIBRATION problem, an efficient algorithm is developed to extract the natural frequencies from determinant of the stiffness matrix.Comparison studies are performed to verify the validity of the present results. Also, some examples are presented in an attempt to illustrate the ability of the EXACT FINITE STRIP method to solve various problems with different parameters such as boundary conditions, internal supports, IN-PLANE FORCES, aspect ratio, and power of volume fraction. As expected, the natural frequency increases when the stiffness of supports and IN-PLANE FORCES increase. The exact vibration solutions obtained for such plates can serve as important benchmark solutions for checking the accuracy of numerical methods for the analysis of FG plates. But, the classical plate theory used in this study is valid for thin plates; thus in comparison to shear deformation plate theories, the accuracy of results decreases when the plate thickness increases.

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APA: Copy

SOLTANI, M., HATAMI, S., & AZHARI, M.. (2014). FREE VIBRATION OF THIN FUNCTIONALLY GRADED PLATES BY EXACT FINITE STRIP METHOD. JOURNAL OF COMPUTATIONAL METHODS IN ENGINEERING (ESTEGHLAL), 32(2), 33-54. SID. https://sid.ir/paper/173604/en

Vancouver: Copy

SOLTANI M., HATAMI S., AZHARI M.. FREE VIBRATION OF THIN FUNCTIONALLY GRADED PLATES BY EXACT FINITE STRIP METHOD. JOURNAL OF COMPUTATIONAL METHODS IN ENGINEERING (ESTEGHLAL)[Internet]. 2014;32(2):33-54. Available from: https://sid.ir/paper/173604/en

IEEE: Copy

M. SOLTANI, S. HATAMI, and M. AZHARI, “FREE VIBRATION OF THIN FUNCTIONALLY GRADED PLATES BY EXACT FINITE STRIP METHOD,” JOURNAL OF COMPUTATIONAL METHODS IN ENGINEERING (ESTEGHLAL), vol. 32, no. 2, pp. 33–54, 2014, [Online]. Available: https://sid.ir/paper/173604/en

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