新型準(zhǔn)零剛度隔振器的設(shè)計(jì)和特性研究
本文選題:碟形彈簧 + 準(zhǔn)零剛度 ; 參考:《中國(guó)人民解放軍軍事醫(yī)學(xué)科學(xué)院》2015年博士論文
【摘要】:本文在總結(jié)國(guó)內(nèi)外準(zhǔn)零剛度隔振器理論研究和結(jié)構(gòu)設(shè)計(jì)的基礎(chǔ)上,針對(duì)車載精密儀器對(duì)其隔振器低頻隔振性能的要求和占用空間尺寸的限制,創(chuàng)新設(shè)計(jì)了兩種新型準(zhǔn)零剛度隔振器。綜合運(yùn)用非線性振動(dòng)的近似解析方法和數(shù)值方法,對(duì)所設(shè)計(jì)準(zhǔn)零剛度隔振器的靜力學(xué)特性,及其構(gòu)成的準(zhǔn)零剛度隔振系統(tǒng)的動(dòng)力學(xué)特性和隔振性能進(jìn)行了系統(tǒng)的研究,探索了兩自由度準(zhǔn)零剛度隔振系統(tǒng)的力傳遞率特性,設(shè)計(jì)裝配了準(zhǔn)零剛度隔振器原理樣機(jī),完成了靜力實(shí)驗(yàn)和振動(dòng)實(shí)驗(yàn)。主要工作和結(jié)論如下:(1)基于正負(fù)剛度并聯(lián)隔振原理,采用等厚度碟形彈簧作為負(fù)剛度元件與線性正剛度螺旋彈簧并聯(lián),設(shè)計(jì)了一種準(zhǔn)零剛度隔振器。首先通過(guò)靜力學(xué)特性研究,分別建立了等厚度碟形彈簧和準(zhǔn)零剛度隔振器的回復(fù)力和剛度特性表達(dá)式;并分別求取了等厚度碟形彈簧具有負(fù)剛度,以及隔振器在平衡位置附近具有準(zhǔn)零剛度特性的參數(shù)條件。研究結(jié)果表明,等厚度碟形彈簧在處于壓平狀態(tài)時(shí)具有剛度最小值,其最小負(fù)剛度值和負(fù)剛度區(qū)域范圍與等效高厚比和支點(diǎn)距離比兩個(gè)參數(shù)有關(guān)。通過(guò)增大等效高厚比和減小支點(diǎn)距離比,可以使等厚度碟形彈簧的最小負(fù)剛度值減小和負(fù)剛度區(qū)域范圍增大。對(duì)于準(zhǔn)零剛度隔振器,等效高厚比、支點(diǎn)距離比以及等厚度碟形彈簧與線性螺旋彈簧之間的剛度比是影響其準(zhǔn)零剛度特性的三個(gè)參數(shù)。當(dāng)?shù)刃Ц吆癖仍龃蠛椭c(diǎn)距離比減小時(shí),需要更小的剛度比來(lái)保證其在平衡位置處的零剛度。且通過(guò)增大等效高厚比和減小支點(diǎn)距離比,可以使準(zhǔn)零剛度隔振器在平衡位置附近具有更小的剛度和更大的較小剛度范圍,從而具有更大的準(zhǔn)零剛度特性位移范圍。然后通過(guò)動(dòng)力學(xué)特性研究,分別建立了諧波力激勵(lì)和諧波位移激勵(lì)條件下準(zhǔn)零剛度隔振系統(tǒng)的非線性運(yùn)動(dòng)微分方程;采用平均法求解了系統(tǒng)的穩(wěn)態(tài)響應(yīng),研究了系統(tǒng)參數(shù)和激勵(lì)幅值對(duì)系統(tǒng)頻響曲線和隔振性能的影響,并與其等效線性系統(tǒng)進(jìn)行了比較;采用馬蒂厄方程判別法得到了系統(tǒng)穩(wěn)態(tài)響應(yīng)解的穩(wěn)定性判定邊界條件。研究結(jié)果表明,兩種諧波激勵(lì)條件下準(zhǔn)零剛度隔振系統(tǒng)的運(yùn)動(dòng)微分方程為對(duì)稱激勵(lì)條件下的杜芬方程。準(zhǔn)零剛度隔振系統(tǒng)為剛度漸硬的非線性系統(tǒng),且存在不穩(wěn)定區(qū)域和跳躍現(xiàn)象。適當(dāng)?shù)販p小激勵(lì)幅值和增大阻尼比可以減小系統(tǒng)的不穩(wěn)定區(qū)域和隔振起始頻率,且能夠使諧波位移激勵(lì)條件下的系統(tǒng)穩(wěn)態(tài)響應(yīng)解避免出現(xiàn)無(wú)限大值。除此之外,在控制激勵(lì)幅值的基礎(chǔ)上,適當(dāng)?shù)卦龃笞枘岜?或通過(guò)增大等效高厚比和減小支點(diǎn)距離比來(lái)減小系統(tǒng)的非線性項(xiàng),均可以使準(zhǔn)零剛度隔振系統(tǒng)相對(duì)于其等效線性系統(tǒng)具有更好的低頻隔振性能。(2)由于等厚度碟形彈簧的變形量較小,將其作為負(fù)剛度元件構(gòu)建的隔振器具有準(zhǔn)零剛度特性的位移范圍也相對(duì)較小。針對(duì)此問(wèn)題,采用厚度沿徑向線性變化的變厚度碟形彈簧作為新的負(fù)剛度元件,設(shè)計(jì)了一種新的準(zhǔn)零剛度隔振器。首先通過(guò)靜力學(xué)特性研究,分別建立了變厚度碟形彈簧和準(zhǔn)零剛度隔振器的回復(fù)力和剛度特性表達(dá)式;并分別求取了變厚度碟形彈簧具有負(fù)剛度,以及隔振器在平衡位置附近具有準(zhǔn)零剛度特性的參數(shù)條件;對(duì)于分別具有等厚度和變厚度碟形彈簧的兩種隔振器,比較分析了相同參數(shù)條件下兩者的準(zhǔn)零剛度特性位移范圍;并對(duì)具有變厚度碟形彈簧的準(zhǔn)零剛度隔振器構(gòu)造參數(shù)進(jìn)行了優(yōu)化,得到了其具有最大準(zhǔn)零剛度特性位移范圍的最優(yōu)參數(shù)取值。研究結(jié)果表明,變厚度碟形彈簧和準(zhǔn)零剛度隔振器均在變厚度碟形彈簧處于壓平狀態(tài)時(shí)具有剛度最小值。相對(duì)于采用等厚度碟形彈簧,變厚度碟形彈簧可以使隔振器在相同位移處的剛度減小,且偏離平衡位置的位移和厚度變化規(guī)律參數(shù)?值越大,剛度減小的越大。因此,具有變厚度碟形彈簧的準(zhǔn)零剛度隔振器在平衡位置附近具有更小的剛度和更大的較小剛度范圍,從而具有更大的準(zhǔn)零剛度特性位移范圍。然后考慮實(shí)際應(yīng)用中系統(tǒng)極易出現(xiàn)的過(guò)載和欠載情況,通過(guò)動(dòng)力學(xué)特性研究,分別建立了諧波力激勵(lì)和諧波位移激勵(lì)下過(guò)載和欠載系統(tǒng)的非線性運(yùn)動(dòng)微分方程;采用諧波平衡法得到了過(guò)載系統(tǒng)的穩(wěn)態(tài)響應(yīng)近似解,并采用四階龍格庫(kù)塔法對(duì)其進(jìn)行了數(shù)值仿真驗(yàn)證;基于弗洛凱理論,得到了過(guò)載系統(tǒng)穩(wěn)態(tài)響應(yīng)解的穩(wěn)定性判定邊界條件;研究了偏移位移和激勵(lì)幅值對(duì)過(guò)載系統(tǒng)頻響曲線和隔振性能的影響,并與理想系統(tǒng)和等效線性系統(tǒng)進(jìn)行了比較;最后探討了阻尼比對(duì)三個(gè)系統(tǒng)隔振性能的影響。研究結(jié)果表明,兩種諧波激勵(lì)條件下過(guò)載和欠載系統(tǒng)的運(yùn)動(dòng)微分方程均為霍爾姆茲-杜芬方程,其可以轉(zhuǎn)化為非對(duì)稱激勵(lì)條件下的杜芬方程。采用諧波平衡法和四階龍格庫(kù)塔法得到的過(guò)載系統(tǒng)穩(wěn)態(tài)響應(yīng)基本吻合,證明了采用諧波平衡法求解的穩(wěn)態(tài)響應(yīng)近似解具有較強(qiáng)的精確性。不同偏移位移和激勵(lì)幅值條件下,過(guò)載系統(tǒng)的最多穩(wěn)態(tài)響應(yīng)解數(shù)量會(huì)出現(xiàn)1個(gè)、3個(gè)和5個(gè)的情況。隨著激勵(lì)幅值的增大,過(guò)載系統(tǒng)的剛度特性不斷變化,依次表現(xiàn)為線性、漸軟、先漸軟后漸硬、漸硬。偏移位移和激勵(lì)幅值越小,過(guò)載系統(tǒng)的隔振起始頻率越小,隔振頻率范圍越大。增大阻尼比,可以消除過(guò)載系統(tǒng)和理想系統(tǒng)的跳躍現(xiàn)象和不穩(wěn)定區(qū)域,提高其低頻隔振性能,但是會(huì)影響其在高頻段的隔振性能。而當(dāng)激勵(lì)幅值較大時(shí),適量的過(guò)載可以提高準(zhǔn)零剛度隔振系統(tǒng)的隔振性能。但總的來(lái)說(shuō),減小過(guò)載質(zhì)量、控制激勵(lì)幅值和適當(dāng)增大阻尼比,可以使準(zhǔn)零剛度隔振系統(tǒng)隔離更低頻的振動(dòng),具有更好的低頻隔振性能。(3)在無(wú)阻尼或阻尼較小的情況下,兩自由度線性隔振系統(tǒng)第二階共振頻率對(duì)應(yīng)的力傳遞率最大值較大,導(dǎo)致其在第二階共振頻率附近范圍內(nèi)不能隔振。針對(duì)此問(wèn)題,基于所設(shè)計(jì)優(yōu)化的準(zhǔn)零剛度隔振器,構(gòu)建了兩自由度準(zhǔn)零剛度隔振系統(tǒng)。首先完成了兩自由度準(zhǔn)零剛度隔振系統(tǒng)及其兩自由度等效線性系統(tǒng)的動(dòng)力學(xué)建模,然后采用平均法推導(dǎo)了諧波力激勵(lì)條件下兩個(gè)系統(tǒng)的力傳遞率,最后研究了激勵(lì)幅值、質(zhì)量比和阻尼比對(duì)其力傳遞率的影響,并比較分析了兩個(gè)系統(tǒng)的隔振性能。研究結(jié)果表明,兩自由度準(zhǔn)零剛度隔振系統(tǒng)第二階共振頻率對(duì)應(yīng)的力傳遞率最大值小于1,意味著其在第二階共振頻率附近范圍內(nèi)仍具有隔振效果,從而克服了其兩自由度等效線性系統(tǒng)的缺點(diǎn)。相較于兩自由度等效線性系統(tǒng),兩自由度準(zhǔn)零剛度隔振系統(tǒng)的隔振起始頻率更小,隔振頻率范圍更大,從而具有更好的低頻隔振性能。且激勵(lì)幅值越小,其低頻隔振性能優(yōu)勢(shì)越明顯。兩自由度準(zhǔn)零剛度隔振系統(tǒng)在高頻段也具有更好的隔振性能。但隨著質(zhì)量比和阻尼比的增大,其在高頻段內(nèi)的隔振性能優(yōu)勢(shì)減小。除此之外,通過(guò)適當(dāng)?shù)卦龃筚|(zhì)量比和阻尼比,可以減小兩自由度準(zhǔn)零剛度隔振系統(tǒng)的隔振起始頻率,增大隔振頻率范圍,提高其低頻隔振性能。(4)設(shè)計(jì)裝配了準(zhǔn)零剛度隔振器的原理樣機(jī),分別搭建實(shí)驗(yàn)平臺(tái)完成了靜力實(shí)驗(yàn)和振動(dòng)實(shí)驗(yàn)。首先通過(guò)靜力實(shí)驗(yàn),研究了碟形彈簧、線性螺旋彈簧和準(zhǔn)零剛度隔振器的靜力學(xué)特性;然后通過(guò)振動(dòng)實(shí)驗(yàn),研究了激勵(lì)幅值對(duì)過(guò)載系統(tǒng)隔振性能的影響,并與其等效線性系統(tǒng)進(jìn)行了比較。實(shí)驗(yàn)結(jié)果表明,所設(shè)計(jì)碟形彈簧和線性螺旋彈簧的實(shí)際與理論力-位移曲線基本吻合。但是由于材料和加工等影響因素的存在,碟形彈簧和線性螺旋彈簧的實(shí)際曲線與理論曲線仍存在一定的誤差。且實(shí)際裝配過(guò)程中產(chǎn)生的預(yù)緊力導(dǎo)致準(zhǔn)零剛度隔振器在其碟形彈簧處于壓平狀態(tài)時(shí)的回復(fù)力大于相同位置處碟形彈簧和線性螺旋彈簧的回復(fù)力之和。隨著激勵(lì)幅值的增大,過(guò)載系統(tǒng)的共振頻率及其對(duì)應(yīng)的傳遞率最大值均先減小后增大,與理論分析結(jié)論相符。但由于原理樣機(jī)和實(shí)驗(yàn)平臺(tái)存在較大的阻尼,實(shí)驗(yàn)獲得的實(shí)際傳遞率曲線均表現(xiàn)為線性,并沒(méi)有出現(xiàn)非線性現(xiàn)象。總的來(lái)說(shuō),碟形彈簧的負(fù)剛度能夠抵消線性螺旋彈簧的正剛度,從而有效降低準(zhǔn)零剛度隔振器的動(dòng)態(tài)剛度。相對(duì)于等效線性系統(tǒng),過(guò)載系統(tǒng)具有更小的隔振起始頻率和更大的隔振頻率范圍,從而具有更好的低頻隔振性能。但為了保證過(guò)載系統(tǒng)在高頻段的隔振性能優(yōu)勢(shì),系統(tǒng)的阻尼不能過(guò)大。本文對(duì)所設(shè)計(jì)準(zhǔn)零剛度隔振器的理論和實(shí)驗(yàn)研究結(jié)論,為將來(lái)應(yīng)用于車載精密儀器隔振,保證車載精密儀器的安全性和可靠性具有重要的意義。
[Abstract]:On the basis of summarizing the theoretical research and structural design of the quasi zero stiffness isolator at home and abroad, two new quasi zero stiffness isolators are designed and designed in this paper, aiming at the requirements for the low frequency vibration isolation performance of the vehicle precision instruments and the limitation of the space size of the vibration isolators. The static characteristics of the quasi zero stiffness isolator are designed and the dynamic characteristics and vibration isolation performance of the quasi zero stiffness isolation system are systematically studied. The force transfer rate characteristics of the two degree of freedom quasi zero stiffness isolation system are explored. The prototype of the quasi zero stiffness isolator is designed and assembled, and the static experiment and vibration experiment are completed. The main work and conclusions are as follows: (1) based on the principle of positive and negative stiffness parallel vibration isolation, a quasi zero stiffness isolator is designed with the equal thickness disc spring being parallel to the linear positive stiffness spiral spring as a negative stiffness element. First, the restoring force of the equal thickness disc spring and the quasi zero stiffness isolator is established by the static characteristics. The stiffness characteristic expression and the parameter conditions of the equal thickness disc spring with the negative stiffness and the quasi zero stiffness characteristic near the equilibrium position are obtained respectively. The results show that the minimum stiffness value of the equal thickness disc spring in the flat state, the minimum negative stiffness value and the negative stiffness region range and the equivalent thickness are obtained. The distance between the fulcrum and the fulcrum is related to the two parameters. By increasing the equivalent thickness ratio and reducing the distance ratio of the fulcrum, the minimum negative stiffness value of the equal thickness disc spring and the area of the negative stiffness can be increased. For the quasi zero stiffness isolator, the equivalent height to thickness ratio, the distance ratio of the pivot point and the stiffness between the equal thickness disc spring and the linear spiral spring are the same. The degree ratio is the three parameter that affects its quasi zero stiffness characteristics. When the ratio of the equivalent height to thickness increases and the distance between the pivot points is reduced, a smaller stiffness ratio is needed to ensure the zero stiffness at the equilibrium position. And the quasi zero stiffness isolator can have smaller stiffness near the equilibrium position by increasing the equivalent thickness ratio and reducing the distance ratio of the pivot point. And a larger smaller stiffness range has a larger quasi zero stiffness characteristic displacement range. Then through the study of the dynamic characteristics, the nonlinear differential equations of the quasi zero stiffness isolation system under the harmonic force excitation and the harmonic displacement excitation are established respectively. The steady-state response of the system is solved by means of the mean method, and the system parameters are studied. The effect of the excitation amplitude on the frequency response curve and vibration isolation performance of the system is compared with that of the equivalent linear system. The stability determination boundary condition of the steady-state response solution of the system is obtained by using the Mathieu equation method. The results show that the differential equation of the motion of the quasi zero stiffness isolation system under the two harmonic excitation conditions is symmetric excitation. The quasi zero stiffness isolation system is a nonlinear system with stiffness gradually hardening, and there is an unstable region and jumping phenomenon. Reducing the excitation amplitude and increasing the damping ratio can reduce the unstable region and vibration initiation frequency of the system, and can avoid the steady-state response solution of the system under the harmonic displacement excitation. In addition, on the basis of controlling the excitation amplitude, the damping ratio is properly increased, or the nonlinear term of the system is reduced by increasing the equivalent height to thickness ratio and the distance ratio of the fulcrum, all the quasi zero stiffness isolation system can have better low frequency vibration isolation performance relative to its equivalent linear system. (2) because of the equal thickness disc. The deformation of the shape spring is small, and the displacement range of the isolator, which is constructed by the negative stiffness element, is relatively small. A new quasi zero stiffness isolator is designed by using the variable thickness disc spring with the thickness along the radial line as a new negative stiffness element. The expressions of the restoring force and stiffness characteristic of variable thickness disc spring and quasi zero stiffness isolator are established respectively, and the parameters of the variable thickness disc spring with negative stiffness and the quasi zero stiffness characteristics near the equilibrium position are obtained respectively, and two kinds of separate plates with equal thickness and variable thickness are separated respectively. The displacement range of the quasi zero stiffness characteristic under the same parameters is compared and analyzed, and the structural parameters of the quasi zero stiffness isolator with variable thickness disc spring are optimized and the optimum parameters of the displacement range with the maximum quasi zero stiffness characteristic are obtained. The results show that the variable thickness disc spring and the quasi zero stiffness are obtained. The isolator has the minimum stiffness when the variable thickness disc spring is in the flat state. Compared with the same thickness disc spring, the variable thickness disc spring can reduce the stiffness of the isolator at the same displacement, and deviate from the equilibrium position and the variation of the thickness. The greater the value, the larger the stiffness decreases. Therefore, the thicker is thicker. Therefore, the thicker is thicker. Thus, the thicker is thicker. The quasi zero stiffness isolator of the degree disc spring has a smaller stiffness and a larger smaller stiffness range near the equilibrium position, thus having a larger quasi zero stiffness characteristic displacement range. Then considering the overloading and under load conditions that are very easy to appear in the practical application, the harmonic force excitation harmony is established through the study of the dynamic characteristics. The nonlinear motion differential equations of overload and under load system are excited by wave displacement, and the approximate solution of the steady-state response of the overload system is obtained by using the harmonic balance method. The four order Runge Kutta method is used to verify the numerical simulation. Based on the Floke theory, the stability determination boundary condition of the stability response solution of the overload system is obtained. The effect of displacement and excitation amplitude on the frequency response curve and vibration isolation performance of the overload system, and compared with the ideal system and the equivalent linear system. Finally, the influence of the damping ratio on the vibration isolation performance of the three systems is discussed. The results show that the differential equations of motion of the overload and under load systems under the two harmonic excitation conditions are all Holm This equation can be converted to the duffen equation under asymmetric excitation. The steady-state response of the overload system obtained by the harmonic balance method and the four order Runge Kutta method is basically consistent. It is proved that the approximate solution of the steady-state response by the harmonic balance method is more accurate. With the increase of the excitation amplitude, the stiffness characteristics of the overload system are constantly changing with the increase of the excitation amplitude. In turn, the stiffness characteristics of the overload system are constantly changing, which in turn shows linear, gradually softening, gradually softening and hardening. The smaller the offset displacement and excitation amplitude are, the smaller the starting frequency of the overload system is, the greater the frequency range of the vibration isolation is. The large damping ratio can eliminate the jumping and unstable region of the overload system and the ideal system, and improve its low frequency vibration isolation performance, but it will affect its vibration isolation performance at the high frequency section. When the excitation amplitude is large, a proper amount of overload can improve the vibration isolation performance of the quasi zero stiffness isolation system. But in general, the overload quality and control excitation are reduced. The excitation amplitude and the appropriate increase of damping ratio can make the quasi zero stiffness isolation system isolate the vibration of more low frequency, and have better low frequency vibration isolation performance. (3) the maximum value of the force transfer rate corresponding to the second order resonance frequency of the two degree of freedom linear isolation system is larger in the case of the less damped or less damped, which leads to its vicinity of the second order resonance frequency. In order to solve this problem, a quasi zero stiffness isolation system with two degrees of freedom is constructed based on the quasi zero stiffness isolator designed and optimized. The dynamic modeling of the two degree of freedom quasi zero stiffness isolation system and its two degree of freedom equivalent linear system is completed, and then two systems under the harmonic force excitation are derived by the flat mean method. The effect of the excitation amplitude, mass ratio and damping ratio on the force transfer rate is studied, and the vibration isolation performance of the two systems is compared and analyzed. The results show that the maximum value of the force transfer rate corresponding to the second order resonance frequency of the two degree of freedom quasi zero stiffness isolation system is less than 1, which means that it is near the second order resonance frequency. There is still a vibration isolation effect in the enclosure, thus overcoming the disadvantage of its two degree of freedom equivalent linear system. Compared with the equivalent linear system of two degrees of freedom, the two DOF quasi zero stiffness isolation system has a smaller vibration isolation starting frequency and a larger vibration isolation range, and thus has a better low frequency isolation performance. And the lower the excitation amplitude, the lower the vibration isolation performance. The more obvious advantage. The two degree of freedom quasi zero stiffness isolation system also has better vibration isolation performance at high frequency section. But with the increase of mass ratio and damping ratio, the advantage of vibration isolation performance decreases in the high frequency section. In addition, the vibration isolation of the quasi zero stiffness isolation system of two degrees of freedom can be reduced by increasing the mass ratio and damping ratio appropriately. First frequency, increase the frequency range of vibration isolation and improve its low frequency vibration isolation performance. (4) the prototype of quasi zero stiffness isolator is designed and assembled, and the static experiment and vibration experiment are completed respectively. First, the static characteristics of disc spring, linear spiral spring spring and quasi zero stiffness isolator are studied by static test. The effect of the excitation amplitude on the vibration isolation performance of the overload system is investigated and compared with the equivalent linear system. The experimental results show that the actual force displacement curves of the designed disc spring and the linear spiral spring are basically consistent with the theoretical force displacement curves. But the disc spring and linear screw are the influence factors of the material and processing. There is still some error between the actual curve and the theoretical curve of the rotating spring. And the pre tightening force produced in the actual assembly process leads to the sum of the restoring force of the quasi zero stiffness isolator in the plate spring at which the disk spring and the linear spiral spring are at the same position. With the increase of the excitation amplitude, the overload system is increased. The resonance frequency and its corresponding maximum transfer rate first decrease and then increase, which coincide with the theoretical analysis. However, because of the large damping of the prototype and the experimental platform, the actual transfer rate curves obtained by the experiment are linear and have no nonlinear phenomenon. In general, the negative stiffness of the disc spring can offset the linearity. The positive stiffness of the helical spring can effectively reduce the dynamic stiffness of the quasi zero stiffness isolator. Compared with the equivalent linear system, the overload system has smaller vibration isolation starting frequency and larger vibration isolation frequency range, thus having better low frequency vibration isolation performance. The theoretical and experimental conclusions of the quasi zero stiffness isolator designed in this paper are of great significance for the future application of the vehicle precision instruments to vibration isolation, and to ensure the safety and reliability of the vehicle precision instruments.
【學(xué)位授予單位】:中國(guó)人民解放軍軍事醫(yī)學(xué)科學(xué)院
【學(xué)位級(jí)別】:博士
【學(xué)位授予年份】:2015
【分類號(hào)】:TB535.1
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