rayleigh_ritz_beam_uniform

rayleigh_ritz_beam_uniform - Principle of Stationery...

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

View Full Document Right Arrow Icon
Principle of Stationery Potential Energy Among all admissible displaced configurations of a conservative system those that satisfy equations of equilibrium make the potential energy stationery with respect to small admissible variations of displacement. If the stationery condition is a relative minimum, the equilibrium state is stable. Example : For the beam shown, using an admissible displacement function ( )( ) x L x a x v = 1 , use the principle of stationery potential energy to find the maximum deflection of the beam. P x y,v Solution: The potential energy of the system is given by W - U = Π The strain energy in the beam is dV 2 1 U x x V = σ Since I My x = and correspondingly EI My x = , = V dV EI My I My 2 1 = V dV EI y M 2 2 2 2 1 Now given, 2 2 dx v d I E M =
Background image of page 1

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

View Full DocumentRight Arrow Icon
= V dV dx v d EI y I E U 2 2 2 2 2 2 2 2 1 V dV y dx v d E 2 2 2 2 2 1 = dx dA y dx
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 11/22/2011 for the course EML 6653 taught by Professor Law during the Fall '09 term at University of South Florida.

Page1 / 3

rayleigh_ritz_beam_uniform - Principle of Stationery...

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