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On the Characteristics of Non-Material Boundary Conditions Using the Example of a Vibrating String

Franze A., Zastrau B. W.

Machine Dynamics Research

2011

Vol. 35, No. 4

11-31

In this paper the possibilities and limits of solving equations of motion with non-material boundary conditions are investigated. Therefore the system of equations for the nonstationary motion of a three-dimensional body is derived. To overcome the time dependency of the boundary conditions an Arbitrary Lagrangean Eulerian (ALE) kinematics is used. In combination with the introduced operator notation a very clear formulation of the system of the equations of motion is derived. The model of a perfect flexible and inextensible string is used as an illustration. In this case analytical solutions are given in a closed form for an example with one non-material boundary condition. This allows studying the characteristics of such boundary conditions.