4.2单质点结构被动调谐减震控制Vibrationcontrol of SDOF systemwithTMD主结构受外激励的情况分两种，一种是直接对主结构激励（例如风、海浪、机器振动等），另一种是通过地面激励（例如地震、环境振动等）。外激励又分为两类，一类是简谐激励（机器振动），另一类是随机激励（地震、风、海浪等）。The are two types of excitation on the structure. one is theexcitation directly on the main structure (such as wind, waves,machine vibration, etc.), and the other is ground excitation(such as earthquakes, environmental vibration, etc.)According to the frequency spectra, the external excitationscan be classified as the harmonic excitation (vibrationmachine), and the random excitation (earthquake, windwaves, etc.)
4.2 单质点结构被动调谐减震控制 Vibration control of SDOF system with TMD 主结构受外激励的情况分两种，一种是直接对主结构激励（例如风、 海浪、机器振动等），另一种是通过地面激励（例如地震、环境振动 等）。外激励又分为两类，一类是简谐激励（机器振动），另一类是 随机激励（地震、风、海浪等）。 The are two types of excitation on the structure. one is the excitation directly on the main structure (such as wind, waves, machine vibration, etc.), and the other is ground excitation (such as earthquakes, environmental vibration, etc.). According to the frequency spectra, the external excitations can be classified as the harmonic excitation (vibration machine), and the random excitation (earthquake, wind, waves, etc.)
4.2.1主结构直接受简谐激励的调谐减震控制Tuned vibration absorption system under directharmonic excitationPassive tuned vibration absorption isadopted when the machines in thestructure vibrate and directly act harmonicKexcitation on the main structure.Thedynamicmodelof SDOFsystemP(0)passive tuned vibration absorber isshowedinthepictures
Passive tuned vibration absorption is adopted when the machines in the structure vibrate and directly act harmonic excitation on the main structure. The dynamic model of SDOF system passive tuned vibration absorber is showed in the pictures 4.2.1 主结构直接受简谐激励的调谐减震控制 Tuned vibration absorption system under direct harmonic excitation
4.2.1主结构直接受简谐激励的调谐减震控制Tuned vibration absorption system under directharmonic excitationxdm1. K1, C, are the mass, stiffness, andXdamping of main structure respectivelyma. Kd. Ca are the mass, stiffness, andKddamping of the substructure respectivelyP(t) is the external harmonic excitationP(O)P(t)=PosinwtX, is the displacement of main structureXgis the displacement of substructure
m1， K1 ，C1 are the mass, stiffness, and damping of main structure respectively. md， Kd ，Cd are the mass, stiffness, and damping of the substructure respectively. P(t) is the external harmonic excitation, P(t)=P0sinωt x1 is the displacement of main structure xd is the displacement of substructure 4.2.1 主结构直接受简谐激励的调谐减震控制 Tuned vibration absorption system under direct harmonic excitation
无阻尼子结构的调谐减震控制Vibrationcontrolofundamped structure with undamped TMDmxi +(K +Ka)x - K_xa = P(t)maxa +Kβ(xa -x)= 0Calculatingbytheconversionfunctionmethod(转换函数法）Pof2h2r, =H(a)P,=Kiht=h[1+f2(1+μ)]+f?P.f2ra= Ha(w)P。=K,h4-hE1+f(1+μ)J+f2f?-h?A=h-h[1+f(1+m)]+ff2Ag= h-h[1+f(1+μm)]+f?
无阻尼子结构的调谐减震控制 Vibration control of undamped structure with undamped TMD 1 1 1 1 1 ( ) ( ) ( ) 0 d d d d d d d m x K K x K x P t m x K x x Calculating by the conversion function method(转换函数法) 2 2 1 4 2 2 2 2 4 2 2 2 , [1 (1 )] [1 (1 )] d f h A h h f f f A h h f f
f? - h?A=h-h[+p(+)+f", At=-[+f(1+m)+md00h :01mi0式中，h：外激励与主结构的频率比，从：子结构与主结构的质量比，f：子结构与主结构的固有频率比Where, h is the ratio of the frequency of external excitationto the naturalfrequency ofmainstructureuisthemassratioof substructureto mainstructuref is the natural frequency ratio of substructure to mainstructure
2 2 2 1 4 2 2 2 4 2 2 2 , [1 (1 )] [1 (1 )] d f h f A A h h f f h h f f 式中， h :外激励与主结构的频率比， μ :子结构与主结构的质 量比， f : 子结构与主结构的固有频率比 Where，h is the ratio of the frequency of external excitation to the natural frequency of main structure. μ is the mass ratio of substructure to main structure. f is the natural frequency ratio of substructure to main structure. 1 1 1 , , d d m f h m