A Closed Form Solution of a Longitudinal Beam With a Viscous Boundary Condition
Technical progress rept.,
NAVAL UNDERSEA WARFARE CENTER NEWPORT DIV NEW LONDON CT NEW LONDON DETACHMENT
Pagination or Media Count:
This paper develops a closed form solution of a longitudinal beam with a viscous boundary condition subjected to point loading. A new inner product 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, 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.