Non-uniform rational B-spline based free vibration analysis of axially functionally graded tapered Timoshenko curved beams

更新时间:2023-05-28

【摘要】The free vibration of axially functionally graded(FG) tapered Timoshenko curved beams is studied with the numerical approach. By using the non-uniform rational B-spline(NURBS) basis functions, the exact geometry and the generalized displacement?eld are formulated. Variable geometric parameters and material properties, including the curvature, cross-sectional area, area moment of inertia, mass density, and Young’s modulus, are expanded as functions of the coordinate in a parametric domain. Based on Hamilton’s principle, the weak formulation is derived by applying a re?ned constitutive relation which considers the thickness e?ect. Natural frequencies and mode shapes are obtained from the eigenvalue equation. Circular, elliptic, and parabolic curved beams are considered in numerical examples. The obtained results are in good agreement with those in the existing studies and those calculated by the ?nite element software ANSYS.Moreover, the e?ects of the material gradient, taper ratio, slenderness ratio, and heightspan ratio on vibration behaviors are discussed.

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