rayleigh_ritz_springs

rayleigh_ritz_springs - V A V B F A F B K A K B Solution W...

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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 : Consider the system of two springs as shown. Find the displacements, V A and V B of the two springs from the state when no forces are applied.

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Unformatted text preview: V A V B F A F B K A K B Solution W U − = Π ( ) 2 2 2 1 2 1 A B B A A V V K V K U − + = B B A A V F V F W − = ( ) B B A A A B B A A V F V F V V K V K − − − + = Π 2 2 2 1 2 1 = Π A dV d gives ( ) ) 1 ......... ( A A B B A A F V V K V K = − − = Π B dV d gives ( ) ) 2 ( .......... B A B B F V V K = − From (1) and (2), we get the displacements B B A A K F F V + = A B A B B B K F F K F V + =...
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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 - Tampa.

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rayleigh_ritz_springs - V A V B F A F B K A K B Solution W...

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