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相對(duì)振型轉(zhuǎn)換法求解分段線性邊界條件連續(xù)體振動(dòng)響應(yīng)的優(yōu)點(diǎn)

The relative mode transfer method for solving the vibration problems of continuous system with piecewise-linear boundary conditions

  • 摘要: 為了研究航天領(lǐng)域關(guān)注的非線性連接結(jié)構(gòu)對(duì)整體結(jié)構(gòu)振動(dòng)響應(yīng)的影響，文章利用變分原理，重新推導(dǎo)了基于振型轉(zhuǎn)換的求解具有任意分段線性及可以轉(zhuǎn)換為分段線性邊界條件的連續(xù)體振動(dòng)響應(yīng)的方法——相對(duì)振型轉(zhuǎn)換法，并與文獻(xiàn)10中的混合方法的推導(dǎo)過程進(jìn)行了對(duì)比，印證了相對(duì)振型轉(zhuǎn)換法的正確性及其優(yōu)點(diǎn)。針對(duì)一個(gè)施加均布載荷的端點(diǎn)單側(cè)帶阻擋的懸臂梁算例，分別應(yīng)用相對(duì)振型轉(zhuǎn)換法及力積分法進(jìn)行了求解，通過懸臂梁端點(diǎn)的分岔響應(yīng)研究了系統(tǒng)的非線性響應(yīng)，討論了兩種方法得到的結(jié)果。

     

    Abstract: Based on the variational principle, the Relative Mode Transfer Method (RMTM), that we previously proposed, is deduced again in the present paper, for solving the vibration problems of continuous systems with arbitrary piece-linear boundary conditions and nonlinear boundary conditions that can be transformed into piece-linear boundary conditions. The derivations in this paper and reference 10 are compared in order to verify the validity of the RMTM and its advantages are discussed. A cantilever with a stop at the end and excited by a uniform distributed force is considered and the responses are obtained both by the RMTM and the Force Integration Method(FIM). The nonlinear vibration of the typical system is studied through the bifurcation response and the time history at the end, and the results are discussed.

     

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