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MAE 340 – VibrationsImage from FDR Libraryand MuseumImage from HunterEngineering Co.Image from Giant Bicycle Inc.Image from dub-connectionIntroduction to MechanicalVibrationsImage from A-TechInstruments Ltd.Image from Sound by SingerImage from E. Klingelé
MAE 340 – Vibrations2Vibration Vibration is the study of:the repetitive motion of objects relative to a stationaryframe of reference or nominal position (e.g., the equilibriumposition) Vibration is an important factor in many designs: Products that break if they vibrate too much: Buildings and bridges
MAE 340 – Vibrations3Vibration Products that can’t be used if they vibrate toomuch: Power/machine tools Robots Products that customers don’t like to vibrate toomuch: Seat for automobile/tractor/airplane Products that have to vibrate in a specific way:
MAE 340 – VibrationsFree vs. Forced Vibration Free Vibration vs. Forced Vibration Free VibrationAll interfaces of the body with theenvironment are static.Forced VibrationAt least one point of the body issubjected to periodic forces ordisplacements.4
MAE 340 – VibrationsSDOF vs. MDOF Systems In a Single-Degree-of-Freedom (SDOF)System we study the motion of a rigid bodyin one direction.The motion may be rectilinear or rotational.Image from D Inman, Engineering Vibration.5
MAE 340 – Vibrations6SDOF vs. MDOF Systems In a Multi-Degree-of-Freedom (MDOF)System we study the independent motionsof multiple rigid bodies or one rigid bodyin multiple directions.x4x1x2k1k2Fcos ωtm4x3m1m2k4m3x2k3m2x1k2kckm1ck1
MAE 340 – VibrationsDiscrete vs. Continuous Systems A discrete system has rigid (lumped)masses connected by massless, flexiblemembers (e.g., massless springs and dampers)xkmckckc7
MAE 340 – Vibrations8Discrete vs. Continuous Systems A continuous system has flexiblemembers whose distributed mass issignificant to the vibrationsImage from www.jeffkemp.comImage from Dlubal Software GmbH
MAE 340 – VibrationsSpring-Mass System9
MAE 340 – VibrationsSpring-Mass System Solving differential equation10
MAE 340 – VibrationsSpring-Mass System How do we find A and φ?11
MAE 340 – VibrationsGraphing x (t )12
MAE 340 – VibrationsWorking with Vibration Amplitudes If we have any two of: Natural frequency Displacement amplitude Velocity amplitude Acceleration amplitude then we can get the other two.13
MAE 340 – VibrationsVibration Nomograph Use it to specifylimits on vibration: FrequencyDisplacementamplitudeVelocity amplitudeAccelerationamplitude14
MAE 340 –Vibrations 2 Vibration Vibration is the study of: the repetitive motion of objects relative to a stationary frameof reference or nominal position (e.g., the equilibrium position) Vibration is an important factor in ma
