ENGR 5242G - Advanced Vibrations

This course builds upon the knowledge students have gained in a first vibration course to cover more advanced vibrating systems. Topics covered include Lagrange’s equations of motion, generalized coordinates and force, virtual work, linearization of equations for small oscillations, multi-degree of freedom linear systems, mass matrix, flexibility and stiffness matrix, natural frequencies and mode shapes, orthogonality of the mode shapes, modal matrix and decoupling procedure, harmonic force and series solution for arbitrary excitation. Linear continuous systems, free vibration of strings, rods and shafts, lateral vibration of Euler-Bernoulli beams, effect of rotary inertia and shear on the vibration of beams, orthogonality of the mode shapes, harmonic excitation of beams, mode summation method in the case of arbitrary excitation. Approximate methods for free vibration analysis: Rayleigh, Dunkerly, Rayleigh-Ritz, Holzer, Myklestud and matrix iteration methods. Vibration of plates, free vibration analysis using analytical methods, Rayleigh and Rayleigh- Ritz methods, harmonic excitation and Galerkin’s method in forced vibration analysis of plates.
Credit hours: 3