Mechanical Vibration: Where Do We Stand?
June 13, 2005 — June 17, 2005
Coordinator:
- Isaac Elishakoff (Florida Atlantic University, Boca Raton, Florida, USA)
Mechanical vibrations play a central role in several fields of engineering. Since the field undergoes extensive continuous development, it makes sense to pause from time to time and ponder on its important developments, needed to modern engineers, graduate students, and university educators. This course is dedicated to reviewing recent developments in several fields of vibration theory and practice along with providing basic skills in subjects that still did not become a required topic in engineering education. Emphasis will be placed on deep understanding of the mechanics side, rather than encyclopedic or cook- book type approaches.
The course presents basic equations for elastic continuous systems, conservation equations, Hamilton’s principle for continuous systems; recent achievements in three- dimensional analysis of structures, needed for rigorous analysis of thick structural elements; vibrations of smart structures representing unique opportunities to integrate sensing and actuation into structures and materials; equations of motion and response properties for structures combined with piezoceramic and piezopolymer materials, shape memory alloys and magnetorheological fluids will be presented; basic notions of random vibration theory will be reviewed for linear structures; vibrational mechanics, a new approach to the explanation and description of the nonlinear vibrational effects will be exposed; vibrorheology, transformation of the mechanical properties of the bodies under the action of vibration will be covered; most universal method of stochastic linearization for nonlinear structures will be extensively illuminated along with most recent developments; stochastic eigenvalue problems will be elucidated with expressions for probabilistic densities of eigenvalues; novel closed-form solution for inhomogeneous structures will be presented.
The course is addressed to graduate and PhD students, practicing engineers who want to pursue continuous education, as well as to university educators in the beginning or mid-careers. The course will be useful even if background escapes the memories of the participants.