本文選題：懸垂索 + 主共振��； 參考：《應(yīng)用力學(xué)學(xué)報(bào)》2017年02期

【摘要】：當(dāng)面外橫向振動(dòng)和面內(nèi)橫向振動(dòng)頻率的比接近1:2時(shí),懸索會(huì)出現(xiàn)面內(nèi)和面外耦合共振現(xiàn)象。為了研究懸索這種復(fù)雜獨(dú)特的非線性特性,利用多尺度法對(duì)諧波激勵(lì)的懸索動(dòng)力學(xué)方程進(jìn)行求解,得到對(duì)應(yīng)于不同階小量的偏微分方程組,其中二階小量偏微分方程中的久期項(xiàng)不為0;采用提出的小參數(shù)法可以得到由久期項(xiàng)引起的懸索振動(dòng)形態(tài),解決久期項(xiàng)頻率與系統(tǒng)頻率相同但不能直接求解的問題;為了證明小參數(shù)法的準(zhǔn)確性,采用Galerkin方法離散懸垂索的運(yùn)動(dòng)方程,然后利用多尺度法求解離散的運(yùn)動(dòng)方程,得到采用基函數(shù)描述的由久期項(xiàng)引起的連續(xù)系統(tǒng)的振動(dòng)形態(tài),與小參數(shù)法結(jié)論一致。
[Abstract]:When the frequency ratio of external transverse vibration and in-plane transverse vibration is close to 1:2, the in-plane and out-of-plane coupling resonance will occur in the suspension cable. In order to study the complex and unique nonlinear characteristics of the suspension cable, the dynamic equations of the suspension cable excited by harmonics are solved by using the multi-scale method, and the partial differential equations corresponding to different order small quantities are obtained. The duration term in the second order partial differential equation is not zero, the vibration form of suspension cable caused by the duration term can be obtained by using the proposed small parameter method, and the problem that the frequency of duration term is the same as that of the system can not be solved directly. In order to prove the accuracy of the small parameter method, the Galerkin method is used to discretize the equations of motion of the suspended cables, and then the discrete equations of motion are solved by using the multi-scale method, and the vibration shape of the continuous system caused by the duration term described by the basis function is obtained. It is consistent with the conclusion of small parameter method.
【作者單位】： 重慶交通大學(xué)力學(xué)系;重慶大學(xué)力學(xué)系;
【基金】：國(guó)家自然科學(xué)基金(51308570;51277186) 重慶市教委科學(xué)技術(shù)研究項(xiàng)目(KJ1400302) 博士點(diǎn)聯(lián)合基金(20125522120003)
【分類號(hào)】：O32

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本文編號(hào)：2091983