Wuhan University of TechnologyChapter8Generalized SDOFsystems8-1
8-1 Wuhan University of Technology Chapter 8 Generalized SDOF systems
Wuhan University of TechnologyContents8.1General comments on SDOFsystems8.2 Generalized properties: assemblages of rigid bodies8.3Generalizedproperties:distributedflexibility8.4Expressionsforgeneralizedsystemproperties8.5 Vibration analysis by Rayleigh's method8.6 Selection of the Rayleigh vibration shape8-2
8-2 Wuhan University of Technology 8.1 General comments on SDOF systems 8.2 Generalized properties: assemblages of rigid bodies 8.3 Generalized properties: distributed flexibility 8.4 Expressions for generalized system properties 8.5 Vibration analysis by Rayleigh's method 8.6 Selection of the Rayleigh vibration shape Contents
Wuhan Universityof Technology8.1 General comments on SDOF systemsInthischapterwewilldiscussthesegeneralizedSDOFsystems,andinformulatingtheir equationsof motion it is convenient to dividethem intotwocategories:(1) Assemblages of rigid bodies in which elastic deformations are limited tolocalizedweightlessspringelementsand(2)Systemshavingdistributedflexibilityinwhichthedeformationscanbecontinuousthroughoutthestructure,orwithinsomeofitscomponents.Inbothcategories,thestructureisforcedtobehavelikeaSDOFsystembythefactthatdisplacementsofonlyasingleformorshapearepermitted,andtheassumedsingledegreeoffreedomexpressestheamplitudeofthispermissibledisplacementconfiguration.8-3
8-3 Wuhan University of Technology 8.1 General comments on SDOF systems In this chapter we will discuss these generalized SDOF systems, and in formulating their equations of motion it is convenient to divide them into two categories: (1) Assemblages of rigid bodies in which elastic deformations are limited to localized weightless spring elements and (2) Systems having distributed flexibility in which the deformations can be continuous throughout the structure, or within some of its components. In both categories, the structure is forced to behave like a SDOF system by the fact that displacements of only a single form or shape are permitted, and the assumed single degree of freedom expresses the amplitude of this permissible displacement configuration
Wuhan Universityof Technology8.2 Generalized properties: assemblages ofrigid bodiesThetotal mass and the2212centroidalmassmomentm=mYa622ofinertiaofauniformmasmkngthrod and of uniformmassareaplatesofvarious shapes23aresummarized inFig.81.8-4
8-4 Wuhan University of Technology 8.2 Generalized properties: assemblages of rigid bodies The total mass and the centroidal mass moment of inertia of a uniform rod and of uniform plates of various shapes are summarized in Fig. 81
Wuhan UniversityofTechnology8.2 Generalized properties: assemblages ofrigid bodiesp(x,t)=p≤f(t)HingeWeightless, rigid bar EHm2,j2HNGEBDskak,C2aa2aFIGUREE8-1Example of arigid-body-assemblageSDOFsystem8-5
8-5 Wuhan University of Technology 8.2 Generalized properties: assemblages of rigid bodies FIGURE E8-1 Example of a rigid-body-assemblage SDOF system