Fedotov, IFedotova, TShatalov, MTenkam, HM2010-01-222010-01-222009-07Fedotov, 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 5978-988-18210-1-0http://hdl.handle.net/10204/3915World Congress on Engineering 2009, London, U.K., 1-3 July 2009The 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.enGreen's functionBishop theoryOrthogonalityWave equationVibrationEigenfunction orthogonalitiesConference PresentationFedotov, I., Fedotova, T., Shatalov, M., & Tenkam, H. (2009). Application of eigenfunction orthogonalities to vibration problems. http://hdl.handle.net/10204/3915Fedotov, I, T Fedotova, M Shatalov, and HM Tenkam. "Application of eigenfunction orthogonalities to vibration problems." (2009): http://hdl.handle.net/10204/3915Fedotov I, Fedotova T, Shatalov M, Tenkam H, Application of eigenfunction orthogonalities to vibration problems; 2009. http://hdl.handle.net/10204/3915 .TY - Conference Presentation AU - Fedotov, I AU - Fedotova, T AU - Shatalov, M AU - Tenkam, HM AB - 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. DA - 2009-07 DB - ResearchSpace DP - CSIR KW - Green's function KW - Bishop theory KW - Orthogonality KW - Wave equation KW - Vibration KW - Eigenfunction orthogonalities LK - https://researchspace.csir.co.za PY - 2009 SM - 978-988-18210-1-0 T1 - Application of eigenfunction orthogonalities to vibration problems TI - Application of eigenfunction orthogonalities to vibration problems UR - http://hdl.handle.net/10204/3915 ER -