土木工程专业英语 教学课件 作者 陈瑛 1.3. Structural Dynamics.ppt

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1、1.3StructuralDynamicsEquationsofMotionforLinearSingle-Degree-of-FreedomSystemskisthespringconstantthatrelatesthelateralstoreydeflectionxtothestoreyshearforce层间剪力,andthedashpot阻尼器relatesthedamping阻尼forcetothevelocitybyadampingcoefficientcdampingcoefficientspringconstantma

2、ssvelocitystoreydeflectionstoreyacceleration[Ak7selE5reiFEn]time-varyingforceEquationsofMotionforLinearSingle-Degree-of-FreedomSystemsEquationofmotionduetothegroundaccelerationresonatenaturalfrequency固有共振频率sinusoidalmotion[9saInE`sRIdLl]正弦曲线[5rezEneit]谐[共]振Solutiongenera

3、lsolution通解Ifthesystemisdamped,oscillation[7Csi5leiFEn]振动correspondingtothegeneralsolutionwilldecaywithtimeparticularsolution特解particularsolutionforcedvibration强迫振动DisplacementWhenthedynamicforceisappliedatafrequencymuchlowerthanthenaturalfrequencyofthesystem,theresponse

4、isquasi-static,TheresponseisproportionaltothestiffnessofthestructureWhentheforceisappliedatafrequencymuchhigherthanthenaturalfrequency,theresponseisproportionaltothemassofthestructure.resonanceEquationsofMotionforLinearMultiple-Degree-of-FreedomSystemsThenodalequations结点

5、方程ofamultipledegreesystemconsistingofndegreesoffreedom[m]isasymmetricalnxnmatrix[5meitriks]矩阵ofmass[c]isasymmetricalnxnmatrixofdampingcoefficientF(t)istheforcevector向量whichiszerointhecaseoffreevibration.generalsolution:angularfrequencyphaseangleConstantstobedeterminedfro

6、mtheinitialboundaryconditionsofthemotionConsiderasystemunderfreevibrationwithoutdamping:Fornontrivial[5nCn5triviEl]solutionsTheexpansionofthedeterminant行列式yieldsapolynomial[7pCli5nEumjEl]多项式的ofndegreeasafunctionof,,非平凡解Theresultingmotionisasumofharmonic[hB:5mCnik]motions

7、简谐运动,eachgovernedbytherespectivenaturalfrequency,writtenas