The modelling of vibration problems is of great importance in engineering. A popular method of analysing such problems is the variational method. The simplest vibration model is represented using the example of a long rod. Two kinds of eigenfunctions orthogonality are proved and the corresponding norms are used to derive Green's function that gives rise to an analytical solution of the problem. The method can be easily generalized to a broad class of hyperbolic problems.
Reference:
Fedotov, I, Fedotova, T et al. 2009. Application of eigenfunction orthogonalities to vibration problems. World Congress on Engineering 2009, London, U.K., 1-3 July 2009, pp 5
Fedotov, I., Fedotova, T., Shatalov, M., & Tenkam, H. (2009). Application of eigenfunction orthogonalities to vibration problems. http://hdl.handle.net/10204/3915
Fedotov, I, T Fedotova, M Shatalov, and HM Tenkam. "Application of eigenfunction orthogonalities to vibration problems." (2009): http://hdl.handle.net/10204/3915
Fedotov I, Fedotova T, Shatalov M, Tenkam H, Application of eigenfunction orthogonalities to vibration problems; 2009. http://hdl.handle.net/10204/3915 .
