Mathematics – Analysis of PDEs
Scientific paper
2011-08-12
Mathematics
Analysis of PDEs
Scientific paper
This paper presents the generalized Fourier series solution for the longitudinal vibrations of a bar subjected to viscous boundary conditions at each end. The model of the system produces a non-self-adjoint eigenvalue-like problem which does not yield orthogonal eigenfunctions. Therefore, these functions cannot be used to calculate the coefficients of expansion in the Fourier series. Furthermore, the eigenfunctions and eigenvalues are complex valued. Nevertheless, the eigenfunctions can be utilized if the space of the wave operator is extended and a suitable inner product is defined. It is further demonstrated that the series solution contains the solutions for free-free, fixed-damper and fixed-free bar cases. The presented procedure is applicable in general to other problems of this type. As an illustration of the theoretical discussion, the results from numerical simulations are presented.
No associations
LandOfFree
A Fourier series solution for the longitudinal vibrations of a bar with viscous boundary conditions at each end does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with A Fourier series solution for the longitudinal vibrations of a bar with viscous boundary conditions at each end, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A Fourier series solution for the longitudinal vibrations of a bar with viscous boundary conditions at each end will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-635626