机械振动加州大学UniversityofCaliforniaChapterOscillatoryMotion

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1、Chapter1OscillatoryMotion·Mostengineeringmachinesandstructures:–Experiencevibrationtosomedegree–Allbodieswithmassandelasticitycapableofvibration·Oscillatorysystems:–Linearsystemswiththeprincipleofsuperpositionandthemathematicaltechniquesavailable–Techniqu

2、esfortheanalysisofnonlinearsystemsarelesswellknown,anddifficulttoapply.·Freevibrations:–Systemsoscillateundertheactionofforcesinherentinthesystemitself–Externalimpressedforcesareabsent–Vibrateatoneormoreofitsnaturalfrequencies·Forcedvibrations:–Whentheexc

3、itationisoscillatory,thesystemisforcedtovibrateattheexcitationfrequency.–Resonanceifthefrequencyofexcitationcoincideswithoneofthenaturalfrequencies–Thefailureofmajorstructuressuchasbridges,buildings,orairplanewingsisawesomepossibilityunderresonance.–Theca

4、lculationofthenaturalfrequenciesisofmajorimportanceinthestudyofvibration.·Damping:-Energydissipationbyfrictionandotherresistances-Importanceinlimitingtheamplitudeofoscillationatresonance·DegreesofFreedom(DOF):17/17-Thenumberofindependentcoordinatesrequire

5、dtodescribethemotionofasystem-ThreeDOFforaparticleandsixDOFforarigidbody-InfiniteDOFforacontinuouselasticbody-RigidbodyassumptionforfiniteDOF-Infact,asurprisinglylargenumberofvibrationproblemscanbetreatedwithsufficientaccuracybyreducingthesystemtoonehavin

6、gafewDOF.1.1HARMONICMOTION·PeriodicMotion:-Themotionisrepeatedinequalintervaloftime,t-tistheperiodoftheoscillation-ThefrequencyoftheoscillationÞ-Theperiodicmotioncanbeexpressedas·17/17HarmonicMotion:-Thesimplestformofperiodicmotion-Demonstratedbyasuspende

7、dmass(Fig.1.1.1)-Themotioncanbeexpressedas:(1.1.1)whereAistheamplitudeofoscillation,measuredfromtheequilibriumpositionofthemass,andtistheperiod.·Harmonicmotionisoftenrepresentedastheprojectiononastraightlineofapointthatismovingonacircleatconstantspeed.-Wi

8、ththeangularspeed(circularfrequency),(1.1.2)17/17-Becausethemotionrepeatsitselfin2pradians,(1.1.3)-Thevelocityandaccelerationofharmonicmotion(1.1.4)(1.1.5)-Thevelocityandaccelerationarealsoharmonicwiththesamefrequen