Continuous SystemsContinuousSystems

IntroductionIntroduction

PDEsPDEs TransverseVibrationofatightlystretchedString/cable LongitudinalVibrationofabar Tortional vibrationofshaft/rod Lateralvibrationofbeams

b d i f i fi i i ll ll FreebodyDiagramofaninfinitesimallysmallelementofaparticularsystem NewtonsLaw

AssumingSHM Infinite#ofNaturalFrequencies/ModeShapes

Transverse Vibration of a String or CableTransverseVibrationofaStringorCable

Initial and Boundary ConditionsInitialandBoundaryConditions

ICs

IfStringisfixedatoneendg

If x=0 end is free and P is const

EndcannotSupportTransverseforce

Ifx 0endisfreeandPisconst

Free Vibrations of a StringFreeVibrationsofaString

FreeVibrationsofaStringwithBothd dEndsFixed

Longitudinal Vibration of a bar/rodLongitudinalVibrationofabar/rod

Lateral Vibration of BeamsLateralVibrationofBeams