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| Analysis of Circumferential Free Vibration of Functionally Graded Conical-cylindrical Joined Shells |
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Abstract In order to promote the application of functionally graded materials (FGMs) in the aerospace field, this paper presents an analysis of the circumferential free vibration of a functionally graded conical-cylindrical joined shell. The properties of the FGMs are described by the Voigt model and the four-parameter power function volume fraction. Based on the Donnell thin shell theory, the displacement and strain relations of the conical shell and the cylindrical shell are derived, and the energy expressions of the conical shell and the cylindrical shell are obtained. Artificial springs are introduced to simulate arbitrary boundaries and joined conditions, and the displacement function is constructed based on Chebyshev polynomials. Then, the modal frequencies of the FGMs conical-cylindrical joined shell are calculated using the Rayleigh-Ritz method, and the effects of gradient exponent, boundary conditions, and geometric parameters on modal frequencies are analyzed. Moreover, the main results of this paper include: for the circumferential wave number is less than 6, stronger boundary constraint conditions lead to a higher overall modal frequency of the structure, increasing the ceramic volume fraction can also effectively increase the modal frequency of the structure, the axial spring stiffness has a more significant impact on the modal frequency of the structure compared to the circumferential and radial spring stiffness; for the circumferential wave number is greater than 3, the modal frequency of the structure increases linearly with increasing shell thickness, while increasing the conical-cylindrical shell length ratio results in a lower modal frequency of the structure.
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Received: 10 April 2023
Published: 28 February 2024
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2024, Vol. 45 
