本文選題：分?jǐn)?shù)階微積分 + 基礎(chǔ)激勵(lì)��； 參考：《物理學(xué)報(bào)》2016年08期

【摘要】：本文研究了基礎(chǔ)激勵(lì)下含分?jǐn)?shù)階阻尼的線性系統(tǒng)的響應(yīng)特性.當(dāng)基礎(chǔ)激勵(lì)為簡諧激勵(lì)時(shí),通過待定系數(shù)方法求得系統(tǒng)的動(dòng)力傳遞系數(shù);當(dāng)基礎(chǔ)激勵(lì)為非簡諧周期激勵(lì)時(shí),首先將激勵(lì)展開成傅里葉級數(shù),然后根據(jù)線性系統(tǒng)的疊加原理求得激勵(lì)中各階頻率成分所引起的動(dòng)力傳遞系數(shù),并根據(jù)展開的傅里葉級數(shù)解決了數(shù)值運(yùn)算中的不可導(dǎo)問題.用數(shù)值仿真的方法對解析結(jié)果進(jìn)行了驗(yàn)證,兩者符合良好,證明了解析分析的正確性.研究表明,基礎(chǔ)激勵(lì)引起的動(dòng)力傳遞系數(shù)依賴于分?jǐn)?shù)階阻尼階數(shù)的值,通過調(diào)節(jié)阻尼階數(shù)可以控制動(dòng)力傳遞系數(shù)的大小.對于基礎(chǔ)激勵(lì)為非簡諧的周期激勵(lì)情況,當(dāng)激勵(lì)頻率一定時(shí),激勵(lì)中的高階頻率成分引起的動(dòng)力傳遞系數(shù)可能大于激勵(lì)中的低階頻率成分引起的動(dòng)力傳遞系數(shù).因此,激勵(lì)中的高階頻率成分所起的作用是不可忽略的.
[Abstract]:In this paper, the response characteristics of linear systems with fractional damping under fundamental excitation are studied. When the foundation excitation is harmonic excitation, the dynamic transfer coefficient of the system is obtained by the undetermined coefficient method, and when the foundation excitation is anharmonic periodic excitation, the excitation is first expanded into Fourier series. Then according to the superposition principle of the linear system, the dynamic transfer coefficients caused by the frequency components in the excitation are obtained, and the non-differentiable problem in the numerical calculation is solved according to the expanded Fourier series. The numerical simulation method is used to verify the analytical results, which are in good agreement with each other, and the correctness of the analytical analysis is proved. The results show that the dynamic transfer coefficient caused by the foundation excitation depends on the value of the fractional damping order and the magnitude of the dynamic transfer coefficient can be controlled by adjusting the damping order. When the excitation frequency is fixed, the dynamic transfer coefficient caused by the high-order frequency component may be larger than that caused by the low-order frequency component. Therefore, the role of high-order frequency components in excitation can not be ignored.
【作者單位】： 中國礦業(yè)大學(xué)機(jī)電工程學(xué)院;上海交通大學(xué)機(jī)械與動(dòng)力工程學(xué)院;中國礦業(yè)大學(xué)江蘇省礦山機(jī)電裝備重點(diǎn)實(shí)驗(yàn)室;
【基金】：國家自然科學(xué)基金(批準(zhǔn)號:51305441) 江蘇省高校優(yōu)勢學(xué)科建設(shè)工程資助的課題~~
【分類號】：O32

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