mass_spr_rod

mass_spr_rod - Lamped-parameter and finite difference...

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Unformatted text preview: Lamped-parameter and finite difference models for a transversely vibrating beam Consider continues and discrete mass-spring-rod models of a cantilever beam shown below. Lumped parameter model with uniform elements length h Newtons second law applied to the mass i m gives 1 = i i i i V V u m & & . Taking moment about the left end of the left rod gives i i i i L M M V 1 1 + = . ( ) i i i i k M = + + + 1 1 1 1 m m 1 m 2 m 1 k 2 k n k n m 1 n m 2 n m 1 u L 1 L n L ( ) x E ( ) x ( ) x A ( ) x I L 1 2 n 1 n 2 n i L 1 + i L i m i V i V i V 1 i V 1 i V 1 i V 1 + i M 2 + i M 1 + i M i M 1 + i i i u 2 1 1 1 1 1 2 1 1 1 1 1 1 + + + + + + + + + + = = i i i i i i i i i i i i i i i M L M L L M L L M M L M M V V ( ) ( ) ( ) 2 1 2 1 1 2 1 1 1 1 1 1 2 1 2 1 1 1 1 1 1 1 1 1 1 1 + + + + + + + + + + + + + + +...
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This note was uploaded on 12/02/2011 for the course ME 7153 taught by Professor Ram,y during the Fall '08 term at LSU.

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mass_spr_rod - Lamped-parameter and finite difference...

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