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.
Dynamic Stability and Response of a Beam Subject to a Deflection Dependent Moving Load
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Katz, R., Lee, C. W., Ulsoy, A. G., and Scott, R. A. (October 1, 1987). "Dynamic Stability and Response of a Beam Subject to a Deflection Dependent Moving Load." ASME. J. Vib., Acoust., Stress, and Reliab. October 1987; 109(4): 361–365. https://doi.org/10.1115/1.3269454
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