The steady state out-of-plane response of a Timoshenko curved beam with internal damping

The steady state out-of-plane response of a Timoshenko curved beam with internal damping to a sinusoidally varying point force or moment is determined by use of the transfer matrix approach. For this purpose, the equations of out-of-plane vibration of a curved beam are written as a coupled set of the first order differential equations by using the transfer matrix of the beam. Once the matrix has been determined by numerical integration of the equations, the steady state response of the beam is obtained. The method is applied to free-clamped non-uniform beams with circular, elliptical, catenary and parabolical neutral axes driven at the free end; the driving point impedance and force or moment transmissibility are calculated numerically and the effects of the slenderness ratio, varying cross-section and the function expressing the neutral axis on them are studied.