第一讲 结构的阻尼.pdf

第一讲,结构的阻尼结构动力学基本方程:MXCXKX0(P(t))1阻尼的分类(Categoryofdamping)2确定粘弹性阻尼的试验方法粘弹性阻尼(与速度成正比反向)的测量方法vmm,其中,ln(n)1,自由振动衰减法mv2m(/D)2mnm2,共振峰处放大系数法1ust0p0,ust02u0k3,半功率带宽法n4,等效阻尼法3粘弹性阻尼的物理意义粘弹性阻尼(SDOF)稳态振动情况下:mxcxkxf(t)p0sin(ωt)xx0sin(ωtφ)粘弹性阻尼一周耗散的能量:TDEDfd(x)dxfd(x)dx0TD2(cx)xdtπcωx00外力输入的能量:TDEIp(t)dx(p0sin(ωt))xdt0TD(p0sin(ωt))(ωx0cos(ωtφ))dt02πp0x0sin(φ)πcωx04粘弹性阻尼的物理意义mxcxkxf(t)p0sin(ωt)xx0sin(ωtφ)势能(应变能:strainenergy):TDESfs(x)dx(kx)xdt02πωk(x0sin(ωtφ))(ωx0cos(ωtφ))dt00动能(icenergy):TDEKdTdt(mx)xdt005粘弹性阻尼耗散的能量mxcxkxf(t)p0sin(ωt)xx0sin(ωtφ)fd(x)cxcωx0cos(ωtφ)222cωx0x0sin(ωtφ)22cωx0x(t)22xf1x0cωx02Aπcωx06粘弹性阻尼耗散的能量mxcxkxf(t)p0sin(ωt)xx0sin(ωtφ)2试验中测量的总抗力:Aπcωx0fs(x)fd(x)kxcx222kxcωx0x0sin(ωtφ)22kxcωx0x(t)22xfkx1x0cωx0讨论:ω0,A0有塑性变形,plasticdeformation7弹性阶段为何?试验方法-等效阻尼法等效阻尼法为最普通的确定结构阻尼的方法,它利用一个循环内的力和位移曲线(滞回曲线)。f滞回曲线所围的面积为结构耗散D的能量:2/2/2EDfDdu(cu)udtcudtu0002/222c[u0cos(t)]dtcu02ku00n1应变能(Strainenergy):Eku2s02011ED1EDED4eq.n4/nEs04Es08粘滞阻尼(Hystereticdamping,rate-independentdamping试验发现:1,周期加载耗散能量不与频率相关;2,结构各阶阻尼比相当,差别不大。2EDπcωx0ηkfxDωηkEHπωx2Dω02πηkx02πηES09结构外阻尼产生的原因(EXTERNALMECHANISMSOFDAMPING),wherebythevibrationalresponsecoupleswiththesurroundingfluidmedium,,inwhichthevibrationofstructuresurfacesforcesthefluidmediumwithinwhichthestructureisimmersedtopasscyclicallythroughnarrowpathsorleaksbetweendifferentzonesofthesystemorbetweenthesystemandtheexterior,,inwhichadjacenttouchingpartsofthemachineorstructureslidecyclicallyrelativetooneanother,onamacroscopicoramicroscopicscale,dissipatingenergy,