rayleigh_ritz_beam_tapered_beam

# rayleigh_ritz_beam_tapered_beam - Principle of Stationery...

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

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 : A tapered bar as shown in the figure is subject to an axial load ‘P’. The area of the tapered bar varies linearly from y = 0 to y = L, from, to o A 2 o A . Assuming an admissible displacement of v find the displacement of y = L using the principle of stationary potential energy. () , 2 0 y c y b y o + = Side View Front View Top View 2 o A y L P o A Assume an expression for the area ‘A’ as c my A + = then () c m A o + = 0 () c L m A o + = 2 0 A c = L A m o 2 = o o A y L A A + = 2

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

View Full Document
() y L L A o 2 2 = = V y y dV U σ 2 1 Ε = V y y dV 2 1 dV dy dv dy dv V Ε
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 / 4

rayleigh_ritz_beam_tapered_beam - Principle of Stationery...

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

View Full Document
Ask a homework question - tutors are online