A CLOSED-FORM SOLUTION OF A LONGITUDINAL BAR WITH A VISCOUS BOUNDARY-CONDITION

A closed form solution of a longitudinal bar with a viscous boundary condition subjected to point loading is developed in this paper. A new series solution is formulated that allows the time and space modes of the beam to decouple. This expansion yields explicit eigenvalues and eigenvectors. A frequency domain example is presented, and the results are compared with finite element solutions of the same problem. It is shown that the closed form solution is computationally more efficient than a finite element solution. Additionally, the truncation error at lower frequencies is shown to be extremely small. The method is easily implemented, and can provide time and frequency domain solutions to this class of problems. © 1994 Academic Press Limited.