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This course is designed for graduate
students. It is aimed to teach the
fundamental concepts how continuous
systems vibrate. Fundamental aspects of
vibrations for mathematical modeling,
derivation/solution of boundary value
problem, and subsequent system analysis
will be covered both using analytical and
approximate methods: 1) Advanced
principles of dynamics (Elasticity and strain
energy, generalized coordinates, Hamilton’s
principle) 2) General Formulation of Natural
Modes of Vibration in Continuous System
(Boundary value problem, eigenvalue
problem, orthogonality) 3) Natural Modes
of Vibration in Continuous Systems
(vibration of strings, longitudinal vibration
of beams, bending vibrations of beams,
vibration of membranes, expansion and
enclosure theorems, Rayleigh’s quotient) 4)
Natural Modes of Vibration in Continuous
Systems using Approximate Methods
(Rayleigh’s energy method, Rayleigh-Ritz
method, Assumed modes method,
Galerkin’s method) 5) Response of
Undamped Continuous Systems (modal
analysis, assumed modes method, Galerkin’s method)
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