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Abstract Curved beam has the advantages of beautiful appearance and good mechanical performance, so it has been widely used in engineering. A moving-least squares (MLS) meshless method is proposed in this paper to solve the free vibration and forced vibration problems of Timoshenko curved beams, and the first-order shear deformation theory (FSDT) is adopted. Firstly, a series of discrete points is used to establish the meshless model of the curved beam. Then, the potential energy and kinetic energy equations of the curved beam are derived. The equations governing the free vibration and forced vibration of the curved beam are given according to the Hamiltonian principle, and the full transformation method is employed to deal with the essential boundary conditions because the boundary conditions cannot be directly applied by the meshless method. Lastly, the natural frequencies and vibration modes are obtained by solving the corresponding equations. At the end of this paper, the effectiveness of the meshless method is verified by numerical examples, and the results show that the proposed method has good convergence characteristics. In addition, the effects of various boundary conditions, span height ratios, variable sections and curvatures on the free vibration and forced vibration of curved beams are discussed. The calculated results are compared with the literature solution or ABAQUS solution, which shows that the meshless method has high accuracy and is suitable for actual engineering projects.
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Received: 17 January 2022
Published: 28 October 2022
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2022, Vol. 43 
