259355946-2009-CT-4140-Book-of-Slides.8

259355946-2009-CT-4140-Book-of-Slides.8 - 8 The General...

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25 The General Solution in Real Form and Free Vibrations of 1 DOFS without Damping CT 4140 Structural Mechanics Faculty of Civil Engineering and Geosciences 2009 Delft, The Netherlands The General Solution: ( ) ( ) ( ) ( ) ( ) 1 2 exp i exp i cos sin n n n n x t X t X t A t B t ω ω ω ω = + = + ( ) ( ) ( ) ( ) ( ) 0 0 0 0 2 2 0 0 0 1 0 0 0 cos sin cos amplitude tan initial phase n n n n n n v x t x t t A t A x v v x ω ω ω ϕ ω ω ϕ ω = + = = + = Begin Important Formula Free Vibration: ( ) ( ) ( ) exp i cos isin n n n t t t ω ω ω = + End Important Formula t x x 0 A 0 2 π / ω n v 0 Lecture 1 Recollection of knowledge regarding undamped 1 DOF systems 26 Contents of Lecture 2 Lecture 2 CT 4140 Structural Mechanics Faculty of Civil Engineering and Geosciences 2009 Delft, The Netherlands 1. Recollection of knowledge regarding undamped 1 DOF systems vibrations under harmonic force, amplitude-frequency and phase- frequency characteristics, resonance, vibrations under general disturbing force 2. Dirac delta-function and derivation of Duhamel’s integral 3.
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  • Fall '09
  • Andrei V. Metrikine
  • Dynamics Of Structures, SDOF, MDOF, Vibration, Civil Engineering and Geosciences, DOF Systems

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