智能材料基于状态空间法的动力问题研究

发布时间：2018-11-25 20:03

【摘要】：在科学技术迅速发展的时期,材料的所具备属性也由传统只具有承载能力,逐步向多功能化、智能化的方向发展。压电智能材料在各个领域中都展现出了良好的应用前景,在土木工程中,压电智能材料在结构监测、控制、智能调节等方面都发挥了极大的作用。在众多的结构中,由压电智能材料组成的叠层构件是最常见的结构形式,对其力学性能尤其是动力问题的研究对设计者来说也非常重要。本文选取一般弹性材料单层梁、一般弹性材料叠层梁、弹性压电材料单层梁、弹性压电材料叠层梁进行动力问题的研究。对于压电智能材料,文中以压电材料的弹性力学基本方程和本构方程为基础,引入状态空间法,在忽略体力、体电荷和体电流的情况下,推导出了压电材料的状态变量方程。然后结合边界条件,得到了简支压电单层梁自由振动频率的精确解,并进一步推导出了压电简支叠层梁自由振动频率的精确解。这种方法对于单层梁与叠层梁均适用,不受厚度的限制,在叠层构件的求解中广泛应用。此解形式简单、精确,便于运用。文章最后利用Matlab软件对不同跨高比的一般弹性材料单层梁、一般弹性材料叠层梁、弹性压电材料单层梁和弹性压电材料叠层梁进行了数值计算,得到力学与电学相关物理量以及自由振动频率的解答,并与有限元软件ANSYS的模拟结果进行了对比。由结果对比可得到,无论是单层梁还是叠层梁,两种方法得到的对不同材料的计算结果均十分相近。在考虑了不同高跨比的情况下,本文方法计算结果与FEM模拟结果的误差也在允许范围之内。由此可知,本文提出基于状态空间理论研究智能结构的方法对于不同材料的单层梁与叠层梁的计算结果都十分准确,且此方法更适用于叠层结构与计算机编程。
[Abstract]:In the period of rapid development of science and technology, the properties of materials have been developed from traditional only carrying capacity to multifunctional and intelligent. Piezoelectric smart materials have shown good application prospects in various fields. In civil engineering, piezoelectric intelligent materials play a great role in structure monitoring, control, intelligent regulation and so on. Among many structures, laminated members composed of piezoelectric smart materials are the most common structural forms, and the study of their mechanical properties, especially dynamic problems, is also very important for designers. In this paper, the dynamic problems of single layer beam with elastic material, single layer beam with elastic piezoelectric material and laminated beam with elastic piezoelectric material are studied. For piezoelectric intelligent materials, based on the basic equations and constitutive equations of the elastic mechanics of piezoelectric materials, the state space method is introduced, and the equation of state variables of piezoelectric materials is derived without regard to the physical force, bulk charge and body current. Then the exact solution of the free vibration frequency of the simple supported piezoelectric single layer beam is obtained by combining the boundary conditions, and the exact solution of the free vibration frequency of the simple supported piezoelectric laminated beam is derived. This method is suitable for both single-layer beam and laminated beam, and is not limited by thickness, so it is widely used in the solution of laminated members. This solution is simple, accurate and easy to use. At last, Matlab software is used to numerically calculate the single layer beam of general elastic material, the laminated beam of general elastic material, the single layer beam of elastic piezoelectric material and the laminated beam of elastic piezoelectric material with different ratio of span to height. The solutions of mechanical and electrical physical quantities and free vibration frequency are obtained and compared with the simulation results of finite element software ANSYS. From the comparison of the results, it can be found that the results obtained by the two methods are very similar to those of different materials, whether they are single-layer beams or laminated beams. In the case of different aspect ratio, the error between the method and the FEM simulation results is also within the allowable range. It can be seen that the method of studying intelligent structure based on state space theory is very accurate for single-layer beam and laminated beam with different materials, and this method is more suitable for laminated structure and computer programming.
【学位授予单位】：合肥工业大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：TB381

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