Modeling the vibration of a thin bar using SimScape
Carter J. Childs, Stephen C. Thompson · The Journal of the Acoustical Society of America · 2019
The standard treatment of longitudinal and flexural vibrations of thin bars follow the methods described by Raleigh. The solution for longitudinal vibrations is completely analogous to electrical signals in electrical transmission lines. Thus, longitudinal mechanical vibrations can be modeled using lumped or distributed parameter analog circuits. The same is true of transverse vibrations of perfectly flexible strings. However, when bending stiffness is included for transverse vibrations, the simplicity of the transmission line analogies is not present. The authors are not aware of a lumped parameter model of the flexural vibration of a thin bar that includes the effects of bending stiffness. This paper presents a lumped parameter model for a thin bar that provides accuracy similar to that of a lumped parameter model of a flexible string. The differential length element of the bar is modeled in the same way as the differential element in the standard treatment of bra vibrations. The model will be demonstrated in the SimScape modeling software, though it can also be implemented in Modelica and possibly in some versions of SPICE.