【作者】 何姗；

【导师】 应祖光；

【作者基本信息】 浙江大学 ， 一般力学与力学基础， 2008， 硕士

【摘要】 玻纤增强环氧树脂材料已广泛应用于很多重要领域,但其复合结构非线性参激稳定性的研究极少。本文研究了复合梁的模态分析结合实验建模方法,及其静力与动力稳定性问题。利用玻纤增强环氧树脂材料和不锈钢薄膜自制夹层复合梁,从静力拉伸、弯曲到静力轴压稳定性、动力参激稳定性,研究以实验为主,结合模态分析与数值模拟,探索了实验结合理论的研究方法,及复合梁大变形弯曲与参激稳定性特性。主要研究工作如下：首先,进行简单复合梁与夹层复合梁的力学拉伸试验,了解材料的基本力学性能,得到材料的基本常数。建立梁的非线性弯曲方程,并求出模态展开解。进行两种复合悬臂梁的弯曲实验,得到多组力与挠度数据,通过最小二乘法确定挠度在展开解中的参数,从而建立静弯曲模型。同时,也得到复合梁的理性认识。其次,建立梁静力稳定性的非线性弯曲方程,并求出其模态展开解。进行简单复合梁和夹层复合梁在固定-自由约束下轴向受压的稳定性实验,得到多组压力与挠度数据,通过模态展开解确定其中一些参数及临界压力,也可由压力-挠度曲线的渐近线直接确定临界压力。结果表明,夹层复合梁大大提高了简单复合梁的临界压力。最后,建立在基础运动激励下梁的非线性参激运动方程,并转化为模态运动的耦合参激非线性方程组。通过模态振动实验识别其中有关的动力参数。然后,编制MATLAB数值模拟程序,研究两种复合梁的参激稳定性。得到在不同激励频率下复合梁动力失稳时的激励幅值,并计算了动力失稳临界力的估计值,与静力临界压力进行比较。结果表明夹层复合梁大大提高了简单复合梁的临界力,但它也随激励频率而变化。更多还原

【Abstract】 Glass fiber reinforced epoxy composites have been widely applied in many fields. However, the researches on the nonlinear parametrically excited stability of the composite structures are seldom. Researches represented in this paper are the modal analysis and experimental modeling of the composite beam, and its static and dynamic stability. In the experiment glass fiber reinforced epoxy composite material and the stainless steel sheet are used to make the sandwich composite beam and then researches are done about the static tension and bending, static axial bearing stability and dynamic parametrically excited stability. Based on the experiment method together with modal analysis and numerical simulation, researches represent a method coupled experiment and theory and the feature about large deformation bending and parametrically excited stability of the composite beam.The main research work in this paper is as follows:Firstly, the tension test of the simple and sandwich composite beams are done to observe the mechanic feature of the composite material and obtain the basic material parameters. The nonlinear model of the composite beam is established and the modal expansion solution is obtained. The bending tests of simple and sandwich composite beam are done to get sufficient data of force and deflection. Based on the data available, the parameters in the modal expansion equations are identified via the least square approach. So the model of the static bending is established and the characteristic improvement of the composite beam is observed.Secondly, the static nonlinear model of the composite beam is established and the modal expansion solution is obtained. The stability experiment of simple and sandwich composite beam with fixed-free constraint under axial compression is done to obtain multi-group of data of compression and deflection. The critical compression and some parameters are determined by the modal expansion equations. Also the critical compression can be directly determined by the asymptote of the curve of compression and deflection. The results show that the sandwich composite improves the critical compression of the simple composite beam.Finally, the dynamic nonlinear parametrically excited model of the composite beam under the base motion is established and then transformed into the modal motion equations with coupled parametric excitations and nonlinearity. The dynamic parameters in the equations are determined by the modal vibration test. The MATLAB simulation program is coded to estimate the parametrically excited stability of the composite beams. The dynamic critical force is obtained and compared with the static critical force. The results show that the sandwich composite beam improves the dynamic critical compression of the simple composite beam and the dynamic critical force varies with the frequency of the excitation.更多还原