【摘要】：運(yùn)用了參數(shù)變易法對(duì)Timoshenko、Rayleigh和Shear梁的橫向自由振動(dòng)模型進(jìn)行了推導(dǎo),分析了鉸支座、集中質(zhì)量、轉(zhuǎn)動(dòng)慣性、拉壓彈簧和扭轉(zhuǎn)彈簧的復(fù)雜邊界條件的情形,進(jìn)而給出了帶有多個(gè)復(fù)雜邊界條件的三種梁的自由振動(dòng)模型。在其簡(jiǎn)化的Euler梁下對(duì)三個(gè)有一定工程實(shí)踐意義的模型進(jìn)行了推導(dǎo),分別是雙跨梁、雙跨梁帶有任意個(gè)集中質(zhì)量和單跨梁帶有任意個(gè)拉壓彈簧的自由振動(dòng)模型,三個(gè)模型的頻率方程的結(jié)果與已有文獻(xiàn)的結(jié)果相比具有很好的一致性。并運(yùn)用Nastran將雙跨梁進(jìn)行了算例分析,該方法提出的公式計(jì)算的一階頻率與有限元方法得出的一階頻率之差小于5%,表明提出的模型是合理可用的。
[Abstract]:The transverse free vibration model of Timoshenko,Rayleigh and Shear beams is derived by parameter variation method. The complex boundary conditions of hinged bearing, concentrated mass, rotational inertia, tension spring and torsional spring are analyzed. Furthermore, the free vibration models of three kinds of beams with complex boundary conditions are given. Under its simplified Euler beam, three models of engineering practice are deduced, which are two span beam, two span beam with any concentrated mass and one span beam with any tension and compression spring. The results of the frequency equations of the three models are in good agreement with those obtained in the literature. The difference between the first order frequency and the first order frequency obtained by finite element method is less than 5, which shows that the proposed model is reasonable and usable.
【作者單位】： 南京航空航天大學(xué)機(jī)械結(jié)構(gòu)力學(xué)及控制國(guó)家重點(diǎn)實(shí)驗(yàn)室;
【基金】：國(guó)家自然科學(xué)基金(51105197;51075203) 江蘇高校優(yōu)勢(shì)學(xué)科建設(shè)工程資助項(xiàng)目
【分類(lèi)號(hào)】：V214

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本文編號(hào)：2317086