ME 5200Mechanical Vibrations

Catalog

The course provides fundamentals for vibration analysis of linear discrete and continuous dynamic systems, A vibrating system is first modeled mathematically as an initial value problem (IVP) or a boundary-initial value problem (BIVP) by the Newton-D’Alembert method and/or the Lagrange energy approach and then solved for various types of system. Explicit solutions for dynamic response of a linear single-degree-of-freedom (SDOF) system, both damped and undamped, is derived for free-vibration caused by the initial conditions and forced vibration caused by different excitations. Modal analysis is presented to solve for vibration response of both multi-degreeof-freedom (MDOF) systems and continuous systems with distributed parameters. As the basis of modal analysis, the natural frequencies and vibration modes of a linear dynamic system are obtained in advance by solving an associated generalized eigenvalue problem and the orthogonal properties of the vibration modes with respect to the stiffness and mass matrices are strictly proved. Computational methods for vibration analysis are introduced. Applications include but are not limited to cushion design of falling packages, vehicles traveling on a rough surface, multi-story building subjected to seismic and wind loading, and vibration analysis of bridges subjected to traffic loading. Students cannot receive credit for this course if they have taken the Special Topics (ME 593V) version of the same course or ME522.