【摘要】：邊界條件是影響耦合結(jié)構(gòu)振動的重要因素,研究邊界條件對耦合結(jié)構(gòu)動態(tài)特性的影響,有利于探索邊界條件在耦合結(jié)構(gòu)減振降噪方面的潛力,為結(jié)構(gòu)減振降噪提供新的思路。本文圍繞彈性約束邊界條件下耦合結(jié)構(gòu)振動問題,針對常見的耦合結(jié)構(gòu)開展了如下研究工作:提出了一種彈性約束邊界條件下多段耦合梁橫向彎曲振動問題的解析方法。與傳統(tǒng)的“傅里葉余弦級數(shù)+輔助多項式”梁位移表達式相比,本文提出使用三角函數(shù)作為梁位移表達式的輔助函數(shù),簡化了公式推導(dǎo)過程。利用耦合邊界的位移連續(xù)和力平衡條件建立了多段耦合梁的邊界方程,聯(lián)立梁振動方程,將梁振動求解轉(zhuǎn)變?yōu)橐粋�標準的矩陣特征值問題,獲得了彈性邊界條件下多段耦合梁的模態(tài)以及振動響應(yīng),并使用數(shù)值仿真和實驗方法驗證了本文多段耦合梁彈性邊界理論。本文進一步在加筋耦合結(jié)構(gòu)變形協(xié)調(diào)條件模型基礎(chǔ)上加入了彈性約束邊界條件,建立了具有彈性約束邊界條件加筋板振動理論模型。利用改進的二維傅里葉級數(shù)作為加筋板位移假設(shè)函數(shù),使得加筋板振動控制方程離散為可求解的線性方程組,利用矩陣運算實現(xiàn)了彈性約束邊界條件下加筋板自由振動以及穩(wěn)態(tài)聲振響應(yīng)的求解。通過與已有文獻和有限元結(jié)果對比,驗證了本文方法的穩(wěn)定性和有效性。通過引入Rayleigh阻尼,求解獲得了彈性約束邊界條件下帶阻尼加筋板穩(wěn)態(tài)振動響應(yīng)。將彈性邊界理論由單個平板結(jié)構(gòu)推廣到了多平接板耦合振動系統(tǒng)。利用耦合板耦合部位的平衡條件和連續(xù)性條件,推導(dǎo)了田字型耦合平板邊界耦合方程,使用改進的傅里葉級數(shù)作為每個子板的彎曲位移函數(shù),離散邊界耦合方程和各子板的振動方程為求解方便的線性方程組。通過數(shù)值仿真和實驗方法驗證了本文所建立理論模型的正確性。利用本文建立的理論模型,分析了耦合邊界阻尼對耦合板聲振響應(yīng)的影響,結(jié)果表明:耦合邊界阻尼可以在一定程度上削弱聲振響應(yīng)共振峰,而且其抑振效果受耦合邊界剛度影響。進一步仿真研究了耦合板結(jié)構(gòu)內(nèi)的振動功率流傳遞特性,結(jié)果表明:增大橫向彈性邊界剛度能有效抑制功率流在邊界處的流動;當外激勵頻率為低階共振頻率時,功率流更容易流向與受激板相同材質(zhì)的接受板。本文利用耦合部位的平衡條件和連續(xù)性條件,完整地考慮了面內(nèi)剪切力、面內(nèi)縱向力、彎矩和橫向剪切力的耦合效應(yīng),建立了多段耦合圓柱殼結(jié)構(gòu)的耦合邊界方程,解決了彈性邊界條件下邊界耦合方程不易表達的難題,將彈性邊界理論從單段圓柱殼推廣到多段耦合圓柱殼。使用本文改進的傅里葉級數(shù)作為圓柱殼位移表達式,使得微分形式的邊界耦合方程和各個殼體的振動方程離散為求解方便的線性方程組。使用有限元方法和實驗方法驗證了多段耦合圓柱殼理論模型的有效性,并分析了邊界約束剛度對多段耦合圓柱殼結(jié)構(gòu)振動響應(yīng)的影響,結(jié)果表明:相比軸向和旋轉(zhuǎn)邊界剛度,環(huán)向和徑向邊界剛度對耦合圓柱殼結(jié)構(gòu)振動響應(yīng)影響更大。將發(fā)展的彈性邊界計算方法應(yīng)用于水下敷瓦加筋圓柱殼振動響應(yīng)與傳遞分析。分別利用等效單層理論和正交各向異性理論,建立了彈性邊界條件下敷瓦圓柱殼和加筋圓柱殼振動理論模型。結(jié)合彈性邊界理論,引入了水流體負載的影響,得到了彈性邊界條件下水下敷瓦加筋圓柱殼的振動響應(yīng)計算方法。開展了加筋圓柱殼和敷瓦加筋圓柱殼實驗研究。獲得了加筋圓柱殼以及水下敷瓦加筋圓柱殼的振動響應(yīng),測試結(jié)果與理論結(jié)果一致性良好。
[Abstract]:The boundary condition is an important factor affecting the vibration of coupled structures. The study of the influence of boundary conditions on the dynamic characteristics of coupled structures is beneficial to the exploration of the potential of boundary conditions in the vibration and noise reduction of coupled structures, and provides a new idea for the vibration and noise reduction of the structure. The coupling structure has carried out the following research work: an analytical method for the lateral bending vibration of multi segment beams under the elastic confinement boundary condition is proposed. Compared with the traditional "Fourier cosine series + auxiliary polynomial" beam displacement expression, this paper proposes a triangular function as the auxiliary function of the beam displacement expression. By using the displacement continuity and force balance conditions of the coupled boundary, the boundary equation of the multi segment coupling beam is established and the vibration equation of the joint beam is established. The solution of the beam vibration is transformed into a standard matrix eigenvalue problem. The modal and vibration response of the multi segment beam under the elastic boundary condition are obtained, and the numerical simulation and experimental side are used. In this paper, the elastic boundary theory of the multi segment coupling beam is verified. In this paper, the elastic constrained boundary condition is added to the deformation coordination condition model of the stiffened coupling structure, and the theoretical model of the stiffened plate with elastic constraint boundary condition is established. The improved two-dimensional Fu Liye series is used as the displacement hypothesis function of the stiffened plate. The vibration control equation of the stiffened plate is discrete to the solution of the linear equations. The matrix calculation is used to solve the free vibration of the stiffened plate and the steady sound vibration response under the elastic constrained boundary condition. The stability and effectiveness of the proposed method are verified by the comparison with the existing literature and finite element results. The solution is solved by introducing the Rayleigh damping. The steady vibration response of a stiffened stiffened plate with elastic constraint boundary conditions is obtained. The elastic boundary theory is extended from a single plate structure to a multi flat plate coupled vibration system. The coupling equation of the field type coupling plate boundary boundary is derived by using the balance condition and the continuity condition of the coupling plate. The improved Fourier series is used. As the flexural displacement function of each sub plate, the discrete boundary coupling equation and the vibration equation of each sub plate are the convenient linear equations. The correctness of the theoretical model is verified by numerical simulation and experimental method. The acoustic vibration response of coupling plate with coupled boundary damping is analyzed by using the theoretical model established in this paper. The results show that the coupling boundary damping can weaken the resonant peak of the acoustic vibration response to a certain extent, and its vibration suppression effect is affected by the coupling boundary stiffness. The vibration power flow transmission characteristics in the coupling plate structure are further simulated and studied. The results show that the increase of the lateral elastic boundary stiffness can effectively restrain the flow of power flow at the boundary. When the external excitation frequency is low order resonance frequency, the power flow is easier to flow to the plate with the same material as the excited plate. In this paper, the coupling effect of the in-plane shear force, the longitudinal force, the bending moment and the transverse shear force of the plane is considered, and the coupling of the multi section coupled cylindrical shell structure is established by using the equilibrium condition and the continuity condition of the coupling. The boundary equation solves the problem that the boundary coupling equation is not easy to express under the elastic boundary condition. The elastic boundary theory is extended from a single cylindrical shell to a multi section cylindrical shell. The Fourier series is used as the displacement expression of the cylindrical shell, which makes the boundary coupling equation of differential form and the vibration equation of each shell discrete into the equation. The finite element method and experimental method are used to verify the validity of the multi section coupled cylindrical shell theory model and the influence of the boundary constraint stiffness on the vibration response of the multi section coupled cylindrical shell structure. The results show that the stiffness of the circumferential and radial boundary and the stiffness of the circumferential and radial boundary on the coupled cylindrical shell junction are compared. The elastic boundary calculation method is applied to the vibration response and transfer analysis of the stiffened cylindrical shells under water. By using the equivalent monolayer theory and the orthotropic theory, the vibration theory model of the cylindrical shell and stiffened cylindrical shell under the elastic boundary condition is established, and the elastic boundary theory is introduced. The effect of water load on the vibration response of a cylindrical shell with elastic reinforcement under the elastic boundary condition is obtained. The experimental study on the stiffened cylindrical shell and the stiffened cylindrical shell is carried out. The vibration response of the stiffened cylindrical shell and the stiffened cylindrical shell under water is obtained. The results of the test are in good agreement with the theoretical results.
【學(xué)位授予單位】：西北工業(yè)大學(xué)
【學(xué)位級別】：博士
【學(xué)位授予年份】：2015
【分類號】：U661.44
，

本文編號：2137081