非线性地基上含裂纹刚性路面板的非线性力学特性分析

发布时间：2018-07-12 10:22

本文选题：非线性地基 + 刚性路面板　；参考：《长沙理工大学》2015年硕士论文

【摘要】：在公路面板、各式桥体构件、建筑结构等范畴中,刚性板均遍及运用。刚性板、梁的力学性态、裂纹缺陷对结构的影响,长期以来都是学术界极为关注的焦点。但实际应用中地基模型的繁杂程度、周边约束的难处理性,使得至今仍未构建出较为精确的力学模型来研究此课题。基于既有的理论考量,本文探求非线性地基上含裂纹刚性路面板的非线性静、动力特征,以非线性地基上周边自由含Ⅰ型裂纹矩形薄板为探讨对象,结合地基耦合效应及体系承受外力变形,分析刚性板与板下基础板体间的关系,探求其非线性力学的变化特性。首先,基于薄板理论、刚性板弯曲理论、裂纹板理论、Hamilton变分原理并考虑非线性因素,构建非线性地基上含Ⅰ型裂纹刚性路面板非线性静力控制方程组,对其去量纲化简,拟定一符合全部面力、位移、裂纹连续性等边界条件的试函数,将含裂纹非线性无量纲微分方程组简化为含裂纹无量纲代数方程组,采用Galerkin对其数值近似求解,引入前人案例验证本文控制方程推演的正确性,得到板、裂纹、地基各个参数对含裂纹刚性路面板非线性静力变形的变化规律。然后,基于非线性动力学理论、裂纹板理论、Hamilton能量变分原理并结合非线性因素,构建非线性地基上含Ⅰ型裂纹刚性路面板非线性自由振动控制方程组,对其去量纲化简,拟定一符合全部面力、位移、裂纹连续性等边界条件的试函数,采用伽辽金、谐波平衡法并运用本征函数的正交性求非线性自由振动无量纲控制方程组,利用案例数值研讨其动力响应,定量分析所求非线性地基上含Ⅰ型裂纹刚性路面板的非线性自由振动频率依据板、裂纹、地基各个参数变化所表现的非线性动力学性态。最后,总结刚性路面板含裂纹缺陷工作时,板结构物理参数、地基板反应模量、裂纹位置及深度的模拟取值对结构非线性挠度变形、动力响应的变化规律,并探讨对刚性裂纹板承载力、刚度、振动频率等产生的影响,为构件的裂纹检测、维修、路面板的保养提供了很好的理论参考依据,当结构运营产生裂纹缺陷时,结合本文结论,采取适当措施防止裂纹的扩展、汇集。
[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.
【学位授予单位】：长沙理工大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：U416.222

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