Modern Analytical Methods Applied to Mechanical Engineering Systems
In the following lectures modern analytical methods are applied to several industrial systems. The first application is the use of singular perturbation analysis in the eigenvalue problem of a vibrating string with a small bending stiffness. This models the behavior of overhead transmission lines. A more complicated system is the eigenvalue problem of a cylinder vibrating in an cylindrical duct, which is filled with a viscous fluid.
The next lecture shows the use of analytical methods in the modelling of ultrasonic motors. Of special interest is the coupling between the electric and the mechanical field in the piezoelectric patches. Here Hamilton’s principle for electromechanical systems is of great importance. It allows to find approximate solutions fulfilling additional constraint equations.
In overhead transmission lines also wind excited vibrations are important as they may lead to fatigue. Models for the corresponding mechanism are given as well as the analysis of special vibration absorbers designed by modern methods of vibration theory.
The last lecture deals with three problems of nonholonomic systems and of stability and instability theorems. The first problem shows that the augmented Lagrangian is not stationary for nonholonomic systems. The second gives a simple exercise in Liapunov stability. The last deals with the Lagrange-Dirichlet theorem and its inverses.
KeywordsNonholonomic System Bonding Layer Outer Solution Ultrasonic Motor Singular Perturbation Theory
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