Transcription of Lecture 8: Mechanical Vibration
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Lecture 8: Mechanical Vibration
1 ENE 5400 ( ) ( ) ( ) ( ) , Spring 20041 Lecture 8: Mechanical Vibration Discrete systems Energy method Lumped-parameter analysis 1 (Eigenvalue analysis) Continuous systems Direct solving of partial differential equations Rayleigh s method (the energy approach) Example: a laterally-driven folded-flexure comb-drive resonatorReference: Singiresu S. Rao, Mechanical Vibrations, 2nd Ed., Addison-W esleyPublishing Company, Inc., 1990 ENE 5400 ( ) ( ) ( ) ( ) , Spring 20042 Energy Method Conservation of energy; the maximum kinetic energy is equal to the maximum potential energy: Tmax= Vmax Also known as Rayleigh s energy method Example: Effect of spring mass ms on the resonant frequency n=sdTmydylkKinetic energy of spring length dy:=TTotal kinetic energy:x(t)2 ENE 5400 ( ) ( ) ( ) ( ) , Spring 20043 Cont d The total potential energy: By assuming a harmonic motion x(t) = X cos nt, By equating Tmax= Vmax,221kxU====2max22max21)3(21kXUXmmTns ====++++==== 3/snmmk++++====
1 ENE 5400 , Spring 2004 1 Lecture 8: Mechanical Vibration Discrete systems Energy method Lumped-parameter analysis »1 d.o.f. »Multi-d.o.f. (Eigenvalue analysis)
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