Generalized SDOF Systems

Generalized SDOF Systems - CE 573 Structural Dynamics...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: CE 573: Structural Dynamics Generalized SDOF Systems • Theory Assume dynamic equilibrium for displacement ( , ): ( ) ( ) ( ) ( ) 0, with each force dependent on ( , ) except for the external forces. I D S E beam beam beam beam v x t F t F t F t F t v x t ⇒ + + + = ∑ ∑ ∑ ∑ E.g.: inertial forces – 2 2 2 2 2 2 ( ) ( ) ( , ) ( , ); ( ) ( ) ( , ) ( , ); ( ) ( ) ( , ) ( , ) ( ) ( , ) ; ( ) ( , ) ( , ). L L I a a D beam a beam d L L L S c c E beam c beam b v v v v d d b b F t m x x t dx m x t F t c x x t dx c x t t t t t v F t k x v x t dx k v x t EI x x t dx F t f x t dx F x t x ∂ ∂ ∂ ∂ ∴ = − − = − − ∂ ∂ ∂ ∂ ∂ = − − − = + ∂ ∑ ∑ ∑ ∑ ∫ ∫ ∑ ∑ ∑ ∫ ∫ ∫ ∑ If we now give the beam a virtual displacement ( , ) v x t δ from dynamic equilibrium, we see that * ( ) ( ) ( ) ( ) *0 ( ) ( ) ( ) ( ) 0. I D S E beam beam beam beam I D S E beam beam beam beam total v F t F t F t F t v W t W t W t W t W δ δ δ δ δ δ δ ⎛ ⎞ + +...
View Full Document

This note was uploaded on 05/09/2008 for the course CE 573 taught by Professor Whalen during the Fall '05 term at Purdue.

Page1 / 3

Generalized SDOF Systems - CE 573 Structural Dynamics...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online