A perturbation technique for the prediction of the displacement of a line-driven plate with discontinuities

摘要

A novel technique is presented for obtaining approximate analytic expressions for an inhomogeneous line-driven plate. The equation of motion for the inhomogeneous plate is transformed, and the transform of the total displacement is written as a sum of the solution for a homogeneous line-driven plate plus a term due to the inhomogeneity. The result is an integral equation for the transform of the inhomogeneous contribution. This expression may in general be solved numerically. However, by introducing a small parameter into the problem, it may be solved approximately using perturbation techniques. This series may not be convergent, but its convergence may be improved using Pade approximation. Results are presented for the case of a single mass discontinuity, and a distribution of mass discontinuities.