ME 545: Elastodynamics and Vibrations

Class Description:

Review of theory of multi-degree-of-freedom systems; problems in the free and forced vibration of continuous linear elastic structures, rods, beams, membranes, plates, and three-dimensional solid and fluid bodies; Lagrangian densities, Sturm Liouville problems, time and frequency domains, damping, Green's functions, and elastic waves; propagation and modal analysis; modeling of damping in structures; and response of complex structures Same as TAM 514. Prerequisite: TAM 412, TAM 542, and TAM 551; or equivalents. 4 hours.

Textbook:

Principles and Techniques of Vibration Analysis, Leonard Meirovitch, Prentice Hall Publishers

Topics:

Review of the classical theory of discrete linear multi-degree-of-freedom systems (6 hr)

Classical vibrations of finite continuous systems (12 hr)
Free responses and initial value problems: equations of motion, boundary-value problems, Sturm-Liouville eigenvalue problems, self-adjoint operators, Lagrangian densities; variational reformulation, orthogonality and expansion theorem, integral equation reformulation, perturbation methods, applications to finite strings, rods, bars, plates, membranes, 3-D fluid and elastic bodies; symmetries

Forced responses (10 hr)
Green|#39;s functions, Fourier transforms, time and frequency domains, causality, eigenfunction expansions of Green|#39;s function, internal and boundary loads

Damping (6 hr)
Mechanics and physics of internal friction in solids; viscoelastic models, structural damping and dry friction, mathematical treatment of multi- and continuous-degree-of-freedom systems with damping

Elastic waves (14 hr)
Vibrations and infinitely extended homogeneous elastic bodies; spatial Fourier transforms and Hankel transforms; dispersion relations, phase and group velocity; rods, Euler-Bernoulli and Timoshenko beams, plates; and in three dimensions, plane waves: longitudinal and shear waves in isotropic solids; anisotropic effects; Green|#39;s dyadic in unbounded isotropic solids; wave-mode duality in finite and infinite bodies

Optional material to be chosen by the instructor (10 hr)
Such topics as: system identification and modal analysis, review of frequency and time-domain methods, complete and incomplete models; experimental aspects: data acquisition, measurement devices, post-processing of data, applications to practical engineering problems; large, complex and disordered structures: modal density, statistical energy analysis, substructuring, ray chaos, mode veering, eigenstatistics

Examinations (2 hr)
TOTAL HOURS: 60

All Courses

ME

TAM