ANALYTICAL SOLUTIONS FOR FORCED VIBRATIONS OF TIMOSHENKO CURVED BEAM BY MEANS OF GREEN’S FUNCTIONS

This paper derives analytical solutions for the forced vibrations of Timoshenko curved beams and establishes the vibration equation of Timoshenko curved beams by analyzing the equilibrium equation for the intersection of curved beams. Green’s functions of Timoshenko curved beams are solved for different boundary conditions using the separation of variables and Laplace transform. Two characteristic parameters are introduced to measure damping effects on beam vibrations. Numerical calculations are conducted to validate analytical solutions, and the effects of various related physical parameters are investigated. The results show that by setting the radius R to infinity, it can be simplified to the Timoshenko straight beam vibration model, and on this basis, if the shear correction factor κ is set to infinity, it can be reduced to the Prescott straight beam vibration model. Finally, the moment of inertia γ is set to 0, which can be reduced to the Bernoulli-Euler straight beam vibration model. Numerical calculations are performed to validate the solutions.