Free Vibration Analysis of Curved Beam with Variable Curvature (Elliptic Line) Based on Semi-analytical Method of Structural Mechanics.

Objective: To study the free vibration problem of a variable curvature beam different from the conventional circular model. Methods: Based on the principle of virtual work, an analytical expression of in-plane displacement of a beam with variable curvature fixed at both ends under concentrated load is established in this paper. The flexibility matrix and stiffness matrix of curved beam are obtained by Moore integral calculation, and the mass matrix of variable curvature beam is obtained by lumped mass method. The stiffness matrix and mass matrix are transformed by static condensation method, and the natural vibration frequency of the beam with variable curvature is obtained. The finite element simulation model of the actual curved bridge and the laboratory curved arch model are established, and the simulation analysis results and laboratory measurement results are compared with the results in this paper. Conclusion: It is proved that the theory presented in this study has good engineering application and can be used as the theoretical basis for the structural research and design of the variable curvature bridge. [ABSTRACT FROM AUTHOR]