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Simulation of a Moving Elastic Beam Using Hamilton's Weak Principle

Simulation of a Moving Elastic Beam Using Hamilton's Weak Principle

Paperback

Technology & EngineeringGeneral Education

ISBN10: 1249833124
ISBN13: 9781249833123
Publisher: Biblioscholar
Published: Oct 17 2012
Pages: 192
Weight: 0.61
Height: 0.41 Width: 6.14 Depth: 9.21
Language: English

Hamilton's Law is derived in weak form for slender beams with closed cross sections. The result is discretized with mixed space-time finite elements to yield a system of nonlinear, algebraic equations. An algorithm is proposed for solving these equations using unconstrained optimization techniques, obtaining steady-state and time accurate solutions for problems of structural dynamics. This technique provides accurate solutions for nonlinear static and steady-state problems including the cantilevered elastica and flatwise rotation of beams. Modal analysis of beams and rods is investigated to accurately determine fundamental frequencies of vibration, and the simulation of simple maneuvers is demonstrated.

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