Coupled out-of-plane bending and torsion vibration characteristics of variable stiffness circular curved beam under elastic constraints

Coupled vibration characteristics of the variable stiffness circular curved beam subjected to elastic constraints is investigated in this paper. A linear spring and two rotation springs are used to simulate elastic constraints, and a mechanical model of variable stiffness circular curved beams under elastic constraints is established. Based on force analysis of infinitesimal elements, three governing equations with varying coefficients are derived for circular curved beams. As a highly efficient numerical method, the differential quadrature method (DQM) is utilized for determining the modal properties of the curved beam. The effects of axial force, warping stiffness, opening angle, and other factors on the modal characteristics of the circular curved beams are investigated. Many numerical results demonstrate how various parameters affect the modal characteristics of curved beams. The axial tension increases the natural frequencies of the circular curved beam; however, opposite conclusions are drawn with certain factors such as the opening angle. The frequency steering phenomenon caused by the cross-section variation coefficient is also discussed.