本文選題：非線性地基 + 剛性路面板�。� 參考：《長(zhǎng)沙理工大學(xué)》2015年碩士論文

【摘要】：在公路面板、各式橋體構(gòu)件、建筑結(jié)構(gòu)等范疇中,剛性板均遍及運(yùn)用。剛性板、梁的力學(xué)性態(tài)、裂紋缺陷對(duì)結(jié)構(gòu)的影響,長(zhǎng)期以來(lái)都是學(xué)術(shù)界極為關(guān)注的焦點(diǎn)。但實(shí)際應(yīng)用中地基模型的繁雜程度、周邊約束的難處理性,使得至今仍未構(gòu)建出較為精確的力學(xué)模型來(lái)研究此課題�；诩扔械睦碚摽剂�,本文探求非線性地基上含裂紋剛性路面板的非線性靜、動(dòng)力特征,以非線性地基上周邊自由含Ⅰ型裂紋矩形薄板為探討對(duì)象,結(jié)合地基耦合效應(yīng)及體系承受外力變形,分析剛性板與板下基礎(chǔ)板體間的關(guān)系,探求其非線性力學(xué)的變化特性。首先,基于薄板理論、剛性板彎曲理論、裂紋板理論、Hamilton變分原理并考慮非線性因素,構(gòu)建非線性地基上含Ⅰ型裂紋剛性路面板非線性靜力控制方程組,對(duì)其去量綱化簡(jiǎn),擬定一符合全部面力、位移、裂紋連續(xù)性等邊界條件的試函數(shù),將含裂紋非線性無(wú)量綱微分方程組簡(jiǎn)化為含裂紋無(wú)量綱代數(shù)方程組,采用Galerkin對(duì)其數(shù)值近似求解,引入前人案例驗(yàn)證本文控制方程推演的正確性,得到板、裂紋、地基各個(gè)參數(shù)對(duì)含裂紋剛性路面板非線性靜力變形的變化規(guī)律。然后,基于非線性動(dòng)力學(xué)理論、裂紋板理論、Hamilton能量變分原理并結(jié)合非線性因素,構(gòu)建非線性地基上含Ⅰ型裂紋剛性路面板非線性自由振動(dòng)控制方程組,對(duì)其去量綱化簡(jiǎn),擬定一符合全部面力、位移、裂紋連續(xù)性等邊界條件的試函數(shù),采用伽遼金、諧波平衡法并運(yùn)用本征函數(shù)的正交性求非線性自由振動(dòng)無(wú)量綱控制方程組,利用案例數(shù)值研討其動(dòng)力響應(yīng),定量分析所求非線性地基上含Ⅰ型裂紋剛性路面板的非線性自由振動(dòng)頻率依據(jù)板、裂紋、地基各個(gè)參數(shù)變化所表現(xiàn)的非線性動(dòng)力學(xué)性態(tài)。最后,總結(jié)剛性路面板含裂紋缺陷工作時(shí),板結(jié)構(gòu)物理參數(shù)、地基板反應(yīng)模量、裂紋位置及深度的模擬取值對(duì)結(jié)構(gòu)非線性撓度變形、動(dòng)力響應(yīng)的變化規(guī)律,并探討對(duì)剛性裂紋板承載力、剛度、振動(dòng)頻率等產(chǎn)生的影響,為構(gòu)件的裂紋檢測(cè)、維修、路面板的保養(yǎng)提供了很好的理論參考依據(jù),當(dāng)結(jié)構(gòu)運(yùn)營(yíng)產(chǎn)生裂紋缺陷時(shí),結(jié)合本文結(jié)論,采取適當(dāng)措施防止裂紋的擴(kuò)展、匯集。
[Abstract]:Rigid slabs are widely used in highway panels, bridge components and building structures. The mechanical behavior of rigid plates and beams and the influence of crack defects on structures have long been the focus of academic attention. However, because of the complexity of the foundation model and the rationality of the peripheral constraints in practical application, more accurate mechanical models have not been constructed to study this subject. Based on the existing theoretical considerations, this paper investigates the nonlinear static and dynamic characteristics of the rigid pavement slab with cracks on the nonlinear foundation, and takes the free type I cracked rectangular thin plate on the nonlinear foundation as an object of study. Based on the coupling effect of the foundation and the deformation of the system subjected to external force, the relationship between the rigid plate and the plate under the plate is analyzed, and the nonlinear mechanical characteristics of the rigid plate are studied. Firstly, based on thin plate theory, rigid plate bending theory, crack plate theory and Hamilton variational principle and considering nonlinear factors, the nonlinear static governing equations of rigid pavement panel with mode I cracks on nonlinear foundation are constructed, and their dimensionality is reduced. A trial function with boundary conditions such as full surface force, displacement and crack continuity is proposed. The nonlinear dimensionless differential equations with cracks are simplified to algebraic equations with cracks, and the numerical solution is obtained by Galerkin. By introducing previous cases to verify the correctness of the governing equation in this paper, the nonlinear static deformation law of plate, crack and foundation parameters on the cracked rigid pavement slab is obtained. Then, based on nonlinear dynamics theory, crack plate theory and Hamilton energy variational principle, combined with nonlinear factors, nonlinear free vibration control equations of rigid pavement panel with mode I cracks on nonlinear foundation are constructed, and their dimensionality is reduced. A trial function with boundary conditions such as full surface force, displacement and crack continuity is drawn up. The Galerkin, harmonic balance method and the orthogonality of eigenfunction are used to solve the dimensionless governing equations of nonlinear free vibration. In this paper, the dynamic response is studied numerically by a case study, and the nonlinear dynamic behavior of the nonlinear free vibration frequency based on the plate, crack and foundation parameters of the rigid road slab with mode I cracks on the nonlinear foundation is quantitatively analyzed. Finally, the variation law of the physical parameters of the plate structure, the response modulus of the ground slab, the location and depth of the crack to the nonlinear deflection and the dynamic response of the rigid pavement slab with crack defects are summarized. The influence on the bearing capacity, stiffness and vibration frequency of the rigid cracked plate is discussed, which provides a good theoretical reference for the crack detection, repair and maintenance of the pavement slab. Combined with the conclusion of this paper, appropriate measures are taken to prevent the crack from spreading and collecting.
【學(xué)位授予單位】：長(zhǎng)沙理工大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2015
【分類(lèi)號(hào)】：U416.222

【參考文獻(xiàn)】

相關(guān)期刊論文 前10條

1 劉文光;嚴(yán)鋮;;考慮裂紋效應(yīng)的彈性板振動(dòng)分析模型[J];振動(dòng)與沖擊;2014年07期

2 于海;陳予恕;曹慶杰;;多自由度裂紋轉(zhuǎn)子系統(tǒng)非線性動(dòng)力學(xué)特性分析[J];振動(dòng)與沖擊;2014年07期

3 石路楊;余天堂;;多裂紋擴(kuò)展的擴(kuò)展有限元法分析[J];巖土力學(xué);2014年01期

4 鐘陽(yáng);高Z腪，

本文編號(hào)：2116845