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Derivation of Equations: Variational Approach
Variational Approach
Vibration problems can be formulated using an equilibrium, a variational, or an integral equation approach. This chapter considers the variational approach in which the conditions of the extremization of a functional are used to derive the equations of motion. It presents basic concepts of calculus of variations since the variational methods make use of the principles of calculus of variations. The calculus of variations deals with the determination of extreme (minima, maxima, or stationary) values of functionals. In some cases, the extremization of a functional subject to a condition is desired. The best‐known case, called the isoperimetric problem, involves finding the closed curve of a given perimeter for which the enclosed area is a maximum. The principles of minimum potential energy, minimum complementary energy, and stationary Reissner energy can be used to formulate static problems.
Derivation of Equations: Variational Approach
Variational Approach
Vibration problems can be formulated using an equilibrium, a variational, or an integral equation approach. This chapter considers the variational approach in which the conditions of the extremization of a functional are used to derive the equations of motion. It presents basic concepts of calculus of variations since the variational methods make use of the principles of calculus of variations. The calculus of variations deals with the determination of extreme (minima, maxima, or stationary) values of functionals. In some cases, the extremization of a functional subject to a condition is desired. The best‐known case, called the isoperimetric problem, involves finding the closed curve of a given perimeter for which the enclosed area is a maximum. The principles of minimum potential energy, minimum complementary energy, and stationary Reissner energy can be used to formulate static problems.
Derivation of Equations: Variational Approach
Variational Approach
Rao, Singiresu S. (Autor:in)
Vibration of Continuous Systems ; 87-124
06.03.2019
38 pages
Aufsatz/Kapitel (Buch)
Elektronische Ressource
Englisch
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