發(fā)布時(shí)間：2018-05-27 04:36

  本文選題：阻抗 + 柔性隔振�。� 參考：《山東大學(xué)》2014年碩士論文

【摘要】：基礎(chǔ)的非剛性,隔振器的分布參數(shù)特性以及機(jī)器在高頻下所表現(xiàn)出的彈性特性造成了經(jīng)典隔振理論與實(shí)際隔振效果的高頻段差異。柔性隔振理論克服了經(jīng)典隔振理論的不足,將隔振系統(tǒng)中某子系統(tǒng)以適當(dāng)彈性模型代替,分析了子系統(tǒng)彈性阻抗特性對(duì)高頻隔振效果的影響。在隔振系統(tǒng)中,基礎(chǔ)的非剛性是造成經(jīng)典隔振理論差異的主要因素。此外,隔振器是具有一定質(zhì)量的分布參數(shù)系統(tǒng),當(dāng)激振頻率達(dá)到隔振器中彈性波半波長(zhǎng)的整數(shù)倍時(shí),就有可能在隔振器中產(chǎn)生駐波效應(yīng),這是導(dǎo)致高頻隔振效果下降的又一因素。除了基礎(chǔ)與隔振器所表現(xiàn)出的彈性.特性對(duì)隔振效果有影響外,系統(tǒng)中較為薄弱的部件或縱跨比較大的結(jié)構(gòu)在高頻下也可能因剛性不足而導(dǎo)致彈性模態(tài)被激發(fā)。如對(duì)于橫向尺寸較小的被隔振設(shè)備一般剛性較大,可以考慮成絕對(duì)剛體,但被隔振設(shè)備與隔振器間需通過(guò)支撐機(jī)腳、支撐框架等連接,這些部件在高頻下可能因剛性不足而表現(xiàn)出彈性特性；在雙層隔振或浮筏隔振系統(tǒng)中,中間質(zhì)量彈性模態(tài)在高頻下也有可能被激發(fā),在高頻下其有限阻抗特性都不能被忽略。若不考慮以上部件彈性阻抗特性,也會(huì)導(dǎo)致理論預(yù)估出現(xiàn)較大偏差。本學(xué)位論文著重對(duì)系統(tǒng)阻抗特性進(jìn)行探討,以功率流為評(píng)價(jià)指標(biāo)對(duì)系統(tǒng)中部件的彈性特性進(jìn)行研究,以期為工程實(shí)際提供理論指導(dǎo)。 為了探討柔性隔振系統(tǒng)中各子系統(tǒng)彈性特性的影響,建立了Euler-Bernoulli梁、Timoshenko梁、薄板和厚板等模型彎曲振動(dòng)微分方程,給出了不同邊界條件下的振型函數(shù),結(jié)合杜哈美積分與正交條件導(dǎo)出了不同模型的導(dǎo)納函數(shù)并通過(guò)實(shí)例仿真對(duì)導(dǎo)納函數(shù)進(jìn)行了對(duì)比。 針對(duì)單一垂向單層隔振系統(tǒng),分別以Euler-Bernoulli梁、Timoshenko梁、薄板以及厚板模型為基礎(chǔ),對(duì)比探討了兩種梁、板理論模型下的功率流譜。研究表明,在低頻下,兩種梁、板模型之間無(wú)明顯差異。但隨著激振頻的升高或梁長(zhǎng)細(xì)比減小、板厚度增大,Euler-Bernoulli梁和Timoshenko梁模型之間、薄板和厚板模型之間的差異逐漸增大；隔振器在基礎(chǔ)上的安裝方式會(huì)影響基礎(chǔ)模態(tài)的激發(fā)。對(duì)于兩端固定梁基礎(chǔ),隔振器對(duì)稱(chēng)布置僅激發(fā)其奇數(shù)階模態(tài),非對(duì)稱(chēng)布置時(shí)全部模態(tài)都被激發(fā)；對(duì)于四邊簡(jiǎn)支板基礎(chǔ),隔振器相對(duì)x、y軸全部對(duì)稱(chēng)布置時(shí),m、n均為奇數(shù)的模態(tài)被激發(fā),僅相對(duì)于x軸(y軸)方向?qū)ΨQ(chēng)時(shí),m為奇數(shù)(n為奇數(shù))的模態(tài)被激發(fā),若相對(duì)與x、y軸都不對(duì)稱(chēng),則所有模態(tài)都被激發(fā)；為了考察設(shè)備有限阻抗特性的影響,在單一垂向柔性隔振系統(tǒng)中,將被隔振設(shè)備分為剛性機(jī)器與彈性設(shè)備支撐兩部分。結(jié)合Euler-Bernoulli梁、薄板理論,將設(shè)備的支撐框架或支撐結(jié)構(gòu)考慮成兩端自由Euler-Bernoulli梁或四邊自由薄板,為了對(duì)設(shè)的彈性特性進(jìn)行探討,故忽略剛性機(jī)器的影響,將其視為振源且輸出一常力作用在設(shè)備支撐上,以導(dǎo)納功率流法著重探討了設(shè)備支撐彈性、振源激勵(lì)點(diǎn)位置以及隔振器安裝位置對(duì)隔振效果的影響。研究發(fā)現(xiàn),設(shè)備中作為振源的機(jī)器部分與隔振器都應(yīng)盡量對(duì)稱(chēng)布置,以避免低頻段系統(tǒng)橫搖模態(tài)的出現(xiàn),此時(shí)高頻段設(shè)備支撐與基礎(chǔ)會(huì)發(fā)生模態(tài)丟失現(xiàn)象,由此避免了峰值密集而導(dǎo)致隔振效果變差。考慮設(shè)備支撐彈性后功率流譜中會(huì)出現(xiàn)向下尖峰模態(tài),這種模態(tài)主要由設(shè)備支撐的彈性振動(dòng)引起,其出現(xiàn)頻率取決于設(shè)備支撐的物理參數(shù)與其上激勵(lì)點(diǎn)位置,與基礎(chǔ)及其耦合作用無(wú)關(guān)。 基于Euler-Bernoulli梁理論建立了三向復(fù)合激勵(lì)下的雙層主\被動(dòng)控制系統(tǒng)動(dòng)力學(xué)模型,分析了系統(tǒng)剛體模態(tài),隔振器駐波效應(yīng)以及基礎(chǔ)彈性模態(tài)對(duì)隔振效果的影響,分析了中間質(zhì)量有限阻抗特性的影響。對(duì)基礎(chǔ)功率流最小控制策略進(jìn)行了詳細(xì)研究。通過(guò)分析得出,在系統(tǒng)對(duì)稱(chēng)布置情況下,單一垂向激勵(lì)會(huì)激發(fā)系統(tǒng)兩階垂向剛體模態(tài),引起隔振器縱向駐波,使基礎(chǔ)奇數(shù)階彎曲振動(dòng)模態(tài)激發(fā)。單一橫搖力矩會(huì)激發(fā)系統(tǒng)兩階橫搖剛體模態(tài)并耦合兩階橫向剛體模態(tài),引起隔振器縱向駐波,使基礎(chǔ)偶數(shù)階彎曲振動(dòng)模態(tài)激發(fā)。單一橫向激勵(lì)會(huì)激發(fā)兩階橫向剛體模態(tài)并耦合兩階橫搖剛體模態(tài),引起隔振器彎曲駐波,使基礎(chǔ)偶數(shù)階彎曲振動(dòng)模態(tài)以及縱向振動(dòng)模態(tài)激發(fā)；在中間質(zhì)量基頻以后頻段范圍其剛體模型不再適用,中間質(zhì)量彈性模態(tài)被激發(fā)導(dǎo)致高頻隔振效果變差且可能在功率流譜中出現(xiàn)“反共振”峰；對(duì)于上層控制雙層隔振系統(tǒng),采用基礎(chǔ)功率流最小控制策略后,無(wú)約束主動(dòng)控制力使系統(tǒng)垂向、橫搖剛體模態(tài)消失,基礎(chǔ)彎曲振動(dòng)模態(tài)消失,同時(shí)隔振器縱向駐波消失,僅橫向剛體模態(tài)、隔振器彎曲振動(dòng)模態(tài)和基礎(chǔ)縱向振動(dòng)模態(tài)被激發(fā),但二次作動(dòng)力與一次力相比較大。施加控制約束后整體隔振效果較無(wú)約束時(shí)有所下降,但在低頻段對(duì)剛體模態(tài)峰值具有很好的衰減,且作動(dòng)力遠(yuǎn)小于無(wú)約束時(shí)作動(dòng)力,與一次力量級(jí)相同,因此約束主動(dòng)控制更符合工程實(shí)際要求。
[Abstract]:In addition , the vibration isolator is a distributed parameter system with a certain mass . In addition , the vibration isolator is a distributed parameter system with a certain mass . In addition , the vibration isolator is a distributed parameter system with a certain mass . In addition , the vibration isolator is an absolute rigid body when the excitation frequency reaches an integral multiple of the half wavelength of the elastic wave in the vibration isolator .
In the double - layer vibration isolation or floating raft vibration isolation system , the intermediate mass elastic mode can be excited at high frequency and its finite impedance characteristic cannot be ignored under high frequency . If the elastic impedance characteristic of the above components is not considered , the theoretical prediction can be greatly deviated . The paper mainly discusses the impedance characteristic of the system , and studies the elastic characteristics of the components in the system with the power flow as the evaluation index , so as to provide theoretical guidance for engineering practice .

In order to discuss the influence of the elastic properties of each subsystem in the flexible vibration isolation system , a differential equation of bending vibration of the model is established , such as Euler - Bernoulli beam , beam , thin plate and thick plate , and the vibration type function under different boundary conditions is given . The admittance function of different models is derived by combining the integration and the orthogonal conditions of Duhamel and the admittance function is compared by example simulation .

For a single vertical single - layer vibration isolation system , the power flow spectrum under the theoretical model of two beams and plates is compared with the Euler - Bernoulli beam , the beam , the thin plate and the slab model .
The vibration isolator is mounted on the foundation , which affects the excitation of the fundamental mode . For the fixed beam foundation at both ends , the symmetric arrangement of the vibration isolator only excites its odd order mode , and all modes are excited when the asymmetric arrangement is arranged .
When the vibration isolator is symmetrically arranged with respect to the x and y axes on the basis of the four - sided simple - supported plate , m and n are all symmetrically arranged with respect to the x - axis and the y - axis . When the vibration isolator is symmetrical only with respect to the x - axis ( y - axis ) direction , m is an odd number ( n is an odd number ) , and if both the x and y axes are not symmetrical , all modes are excited ;
In order to investigate the influence of the finite impedance characteristics of the equipment , the vibration isolation equipment is divided into two parts : a rigid machine and an elastic device in a single vertical flexible vibration isolation system . According to the Euler - Bernoulli beam and the thin plate theory , the supporting frame or the supporting structure of the equipment is considered as a free Euler - Bernoulli beam or a four - sided free thin plate .

Based on the Euler - Bernoulli beam theory , the dynamic model of the double - layer main passive control system under three - directional composite excitation is established , the influence of the rigid mode of the system , the standing wave effect of the vibration isolator and the fundamental elastic mode on the vibration isolation effect are analyzed .
in that frequency band aft the fundamental frequency of the intermediate quality , the rigid body model of the frequency band is no longer applicable , and the elastic mode of the intermediate mass is excite to cause the high - frequency vibration isolation effect to be degraded and the " anti - resonance " peak may appear in the power flow spectrum ;
For the upper - layer control double - layer vibration isolation system , after the minimum control strategy of the basic power flow is adopted , the system vertical , roll rigid body mode disappears , the vibration mode of the basic bending vibration disappears , the longitudinal standing wave of the vibration isolator disappears , and only the transverse rigid body mode , the vibration isolator bending vibration mode and the basic longitudinal vibration mode are excited .
【學(xué)位授予單位】：山東大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2014
【分類(lèi)號(hào)】：TB535.1

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