本文選題：Mindlin板理論 + 聲輻射��； 參考：《中北大學(xué)》2014年碩士論文

【摘要】：板式結(jié)構(gòu)作為一種基本結(jié)構(gòu)形式，在國防、民用等行業(yè)產(chǎn)品中廣泛應(yīng)用，它不僅在受到激勵(lì)作用下會向外輻射噪聲，，而且也可用于控制噪聲的傳播。因此，對板式結(jié)構(gòu)的振動(dòng)聲輻射研究不僅具有理論研究意義，也有較大的工程應(yīng)用價(jià)值。本文針對板式結(jié)構(gòu)的振動(dòng)聲輻射特性展開了研究，并對表面大量采用板式結(jié)構(gòu)的發(fā)動(dòng)機(jī)模型進(jìn)行了聲場求解分析。 本文的主要研究工作有： （1）基于彈性力學(xué)及有限元的相關(guān)理論,結(jié)合Mindlin板彎曲理論,探究了單元應(yīng)變位移關(guān)系、位移函數(shù)同應(yīng)變陣的關(guān)系以及應(yīng)力與應(yīng)變之間的關(guān)系。對板式結(jié)構(gòu)在不同載荷情況下的振動(dòng)響應(yīng)情況進(jìn)行了理論分析。基于振動(dòng)響應(yīng)結(jié)果，研究了板結(jié)構(gòu)振動(dòng)所激發(fā)的聲學(xué)響應(yīng)，推導(dǎo)得到了邊界積分方程的離散形式。 （2）介紹了以三次B樣條函數(shù)作為單元型函數(shù)的研究方法來分析薄板的彎曲、振動(dòng)問題。建立基于Helmholtz邊界方程的邊界元模型，采用基于三次B樣條函數(shù)的耦合有限元法-邊界元法對在空氣介質(zhì)中的矩形鋼板進(jìn)行了輻射聲功率的數(shù)值計(jì)算，同采用Matlab編制的Rayleigh積分公式計(jì)算矩形鋼板輻射聲功率的結(jié)果對比，由此來驗(yàn)證基于三次B樣條函數(shù)的耦合FEM-BEM方法在計(jì)算板式結(jié)構(gòu)輻射聲功率上的精度和準(zhǔn)確性。 （3）探討了以下板式結(jié)構(gòu)參數(shù)對其聲輻射特性的影響：1）平板、加肋板、梯形板、三角形板和梯形板這五種不同的板式結(jié)構(gòu)形狀；2）加肋板中肋條的布置方案；3）20種不同組合的邊界約束條件；4）在等厚板中不同的厚度值、在厚度值線性變化的變厚度中不同的傾斜角；5）不同的長寬比。 （4）針對邊界元法在計(jì)算大規(guī)模問題時(shí)耗時(shí)、耗計(jì)算空間甚至出現(xiàn)無法計(jì)算的問題，文章應(yīng)用快速多極邊界元算法，并以此為理論基礎(chǔ)對表面結(jié)構(gòu)大量采用板式結(jié)構(gòu)的某型發(fā)動(dòng)機(jī)模型進(jìn)行了聲輻射求解，并同采用常規(guī)邊界元算法進(jìn)行了對比，驗(yàn)證了快速多極邊界元法在計(jì)算大規(guī)模問題時(shí)的準(zhǔn)確性和高效性。
[Abstract]:Plate structure, as a basic structure form, is widely used in industries such as national defense, civil industry, etc. It not only radiates noise but also can be used to control the propagation of noise. Therefore, the study of vibration and acoustic radiation of plate structure is not only of theoretical significance, but also of great engineering application value. In this paper, the characteristics of vibration sound radiation of plate structure are studied, and the acoustic field of engine model with plate structure is analyzed. The main research work of this paper is as follows: 1) based on the theory of elastic mechanics and finite element, combined with Mindlin plate bending theory, the relationship between strain displacement, displacement function and strain matrix, and the relationship between stress and strain are discussed. The vibration response of plate structure under different loads is theoretically analyzed. Based on the results of vibration response, the acoustic response of plate structure excited by vibration is studied, and the discrete form of boundary integral equation is derived. In this paper, the method of using cubic B-spline function as element function to analyze the bending and vibration of thin plate is introduced. A boundary element model based on Helmholtz boundary equation is established. The coupled finite element method based on cubic B-spline function and the boundary element method are used to calculate the radiated sound power of rectangular steel plate in air media. The accuracy and accuracy of the coupled FEM-BEM method based on cubic B-spline function in calculating the radiated sound power of plate structures are verified by comparing the results of the calculation of the radiated sound power of rectangular steel plate with the Rayleigh integral formula compiled by Matlab, which proves that the coupled FEM-BEM method based on cubic B-spline function is accurate and accurate in calculating the radiated sound power of plate structure. The influence of the following structure parameters on the acoustic radiation characteristics of the plate is discussed. (1) flat plate, stiffened plate, trapezoidal plate, Triangular plate and trapezoidal plate are five different plate structural shapes. The arrangement of rib in ribbed plate is divided into 20 kinds of boundary constraint conditions. (4) different thickness values in equal thickness plate. In the variable thickness with linearly varying thickness, the slanting angle is 5) and the aspect ratio is different. In this paper, the fast multipole boundary element algorithm is applied to solve the problem that the boundary element method is time-consuming and even can not be calculated in the computation of large scale problems. On the basis of this theory, the acoustic radiation of a certain engine model with a large number of plate structures is solved and compared with the conventional boundary element algorithm. The accuracy and efficiency of the fast multipole boundary element method for large scale problems are verified.
【學(xué)位授予單位】：中北大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2014
【分類號】：TB53

【參考文獻(xiàn)】

相關(guān)期刊論文 前8條

1 孟文輝;;求解聲波散射問題的邊界元快速多極算法的一種新型樹結(jié)構(gòu)[J];西北大學(xué)學(xué)報(bào)(自然科學(xué)版);2009年06期

2 張敬東,何祚鏞;有限元+邊界元——修正的模態(tài)分解法預(yù)報(bào)水下旋轉(zhuǎn)薄殼的振動(dòng)和聲輻射[J];聲學(xué)學(xué)報(bào);1990年01期

3 黎勝,趙德有;用有限元/邊界元方法進(jìn)行結(jié)構(gòu)聲輻射的模態(tài)分析[J];聲學(xué)學(xué)報(bào);2001年02期

4 姚濤;段國林;蔡瑾;;圓鋸片噪聲與振動(dòng)特性及降噪技術(shù)研究綜述[J];振動(dòng)與沖擊;2008年06期

5 吳文偉,冷文浩,沈順根;具有等間距相同加強(qiáng)筋板的聲輻射[J];中國造船;1999年03期

6 寧德志;滕斌;勾瑩;;兩種格林函數(shù)的快速多極子求解方法[J];中國科技論文在線;2007年01期

7 張升明，潘旭初;板架結(jié)構(gòu)的振動(dòng)噪聲研究[J];噪聲與振動(dòng)控制;1995年05期

8 吳學(xué)鋒;張保成;劉宇航;王素琴;;基于LMS Virtual.Lab的油底殼輻射噪聲預(yù)測分析[J];現(xiàn)代車用動(dòng)力;2013年03期

本文編號：1906870