rayleigh_ritz_beam_tapered_beam

rayleigh_ritz_beam_tapered_beam - Principle of Stationery...

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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
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() 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
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rayleigh_ritz_beam_tapered_beam - Principle of Stationery...

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