Analytical Methods in Vibrations

This course presents the principles relevant to understanding and modelling of vibrating systems. The systems may either be continuous, or discrete with multiple degrees of freedom. The following topics of a general nature are first covered: principles of dynamics, strain energy, virtual work, the variational principle, and Lagrange's equation. Discrete-system topics covered are eigenvalue problems, modal analysis, natural modes of vibration, solution of the characteristic determinant, and approximate methods of solution, (e.g., using finite element methods). Continuous-system topics covered are formulation of the boundary value problem, vibration of rods and membranes, Rayleigh's integral method, the Rayleigh-Ritz method, and Galerkin's method. The course work includes computer algebra, computer simulation, and experiments in the laboratory.