โ Scribed by Bin Hu; Peter Eberhard
No coin nor oath required. For personal study only.
Wave propagation due to longitudinal impacts on thin rods is a classical problem of mechanics, but only few completely analytical results for longitudinal wave propagation are available in literature. In this paper, it is shown that even such complicated impact problems can nowadays be solved using symbolic computation. As an example, the wave propagation in a thin rod struck by a moving rigid body is discussed and analytical results describing the longitudinal wave propagation are given in detail so that these results may be used to validate some numerical programs for contact and impact analysis using the ยฎnite element methods or the boundary element methods, respectively. Further, from the obtained analytical results the duration of contact and the coecient of restitution can be computed much more easily. Some numerical results for these important quantities in impact analysis are also listed.
๐ SIMILAR VOLUMES
## In this paper, a direct and unified algorithm for constructing multiple travelling wave solutions of nonlinear partial differential equations (PDBs) is presented and implemented in a computer algebraic system. The key idea of this method is to take full advantage of a Riccati equation involving
Symbolic manipulation (REDUCE and SCHOONSCHIP) has been applied to the analytic evaluation of the coefficients in the Taylor series expansion of timecorrelation functions. These expressions are derived for cylindrically and biaxially symmetric particles reorienting in a uniaxial fluid. The possibili
The two-dimenslonal flow of a mass of cohesionless granular materiaI down a rough bed is studied by the use of the method of strMned coordinates. The work is relevant to the motion of rockfalls, ice avalanches and dense flowing snow avalanches. By appropriate non-dimensionalization, a small paramete