Research on Vibration Characteristics of Functionally Graded Stepped Cylindrical Shells with Arbitrary Boundary Conditions
Research on vibration characteristics of functionally graded materials(FGMs)in the aero-space field is a hot topic of current research.In this paper,the vibration characteristics of metal-ceramic functionally graded(FG)stepped cylindrical shells under arbitrary boundary conditions are studied.To conduct this research,a mechanical model of a metal-ceramic FG stepped cylindrical shell based on the axi-al segmentation concept is developed.First,the properties of metal-ceramic FGMs are obtained using the Voigt model and power function volume fraction.Second,the artificial spring technique is introduced to simulate continuous coupling conditions of shell segments and arbitrary boundary conditions at the ends of the shell.The energy expression for the cylindrical shell is then derived based on the first-order shear de-formation theory.Finally,the admissible function is constructed via the Chebyshev polynomial,and the dynamic differential equations of the metal-ceramic FG stepped cylindrical shell under arbitrary boundary conditions are calculated using the Rayleigh-Ritz method.The validity and convergence of the method are verified through comparison with existing literature,and the effects of boundary conditions,volume frac-tion,geometric parameters,and spring stiffness on modal frequencies are analyzed.It is found that the natural frequency of the FG stepped cylindrical shell initially decreases and then increases with increased number of circumferential waves under classical boundary conditions,and it increases with the number of circumferential waves under both elastic boundary conditions.The natural frequency of the shell increases exponentially with volume fraction.The effects of length-to-radius ratio and thickness-to-radius ratio on the vibration characteristics of the shell differ,with the natural frequency of the shell decreasing with in-creased length-to-radius ratio and increasing with thickness-to-radius ratio.Additionally,the stiffness of translational springs significantly influences the vibration characteristics of the shell compared to rotational springs.
functionally graded materialsstepped cylindrical shellsarbitrary boundary conditionsvibration characteristicsartificial spring technology
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