Theory of Vibrations

3 units

Analytical methods in vibrations. Topics include: Duhamel's integral, Laplace and Fourier transforms, and Fourier series with applications to transient response, forced response, and vibration isolation, Lagrange's equations for linear systems, discrete systems, degrees of freedom, reducible coordinates, holonomic constraints, and virtual work, matrix methods and state variable approach with applications to frequencies and modes, stability, and dynamic response in terms of real and complex modal expansions, dynamic response of continuous systems by theory of partial differential equations, Rayleigh-Ritz and Galerkin energy methods, finite difference and finite element algorithms.