Dynamic Stability and Response of a Beam Subject to a Deflection Dependent Moving Load

The dynamic stability and transverse vibration of a beam subject to a deflection dependent moving load is considered. The deflection dependent moving load is motivated by the cutting forces in machining operations. Galerkin’s method is used to obtain a set of ordinary differential equations with periodic coefficients. It is found that parametric instability can be expected for a continuous sequence of moving loads. The response under the moving deflection dependent load is also calculated.