【作者】 夏贤坤；

【导师】 沈惠申；

【作者基本信息】 上海交通大学 ， 工程力学， 2008， 博士

【摘要】 功能梯度材料(Functionally Graded Materials,简称FGMs)通常是由陶瓷和金属复合而成的一种新型先进非均匀复合材料,在航空航天、核工业、动力机械等领域内有着极为广阔的应用前景。关于该类材料结构在复杂的机械荷载、热荷载及电荷载作用下屈曲前和屈曲后的振动特性研究具有重要的理论与应用价值。本文的研究工作主要包括:(1)基于Reddy高阶剪切变形板理论和广义Kármán型方程,给出了几类现有研究成果较少或没有彻底解决的FGM混合板结构的屈曲前和屈曲后振动特性研究的控制方程,成功将摄动-Galerkin混合法应用于求解过程,并给出了各控制方程相对直观且易于计算的解析解形式;(2)单向压电纤维增强复合材料(Piezoelectric Fiber Reinforced Composite,简称PFRC)是一种新型压电材料,本文将其应用到了结构振动控制研究当中,发现通过压电纤维体积含量的选择可以实现混合板结构的优化振动控制;(3)围绕几种有代表性的FGM混合板结构,讨论其屈曲后的振动特性,在分析中同时考虑热传导,材料物性参数的温度相关性,以及机/热/电荷载耦合效应对非线性振动特性的影响,最后给出了大量数值计算结果。着重讨论了FGM材料组分指数、温度变化、长宽比、边厚比、屈曲与振动模态、PFRC压电纤维体积含量、控制电压、芯层与面板厚度比等因素对各类FGM混合板结构屈曲前及屈曲后振动特性的影响。针对功能梯度材料主要应用于高温环境中的特点,本文考虑了所有参与分析材料的物性参数的温度相关性。又由于金属和陶瓷的储热能力不同,热传导难以避免,故在每章开头都先给出了各类功能梯度材料混合板结构在热场中的温度分布函数。随后,基于Reddy高阶剪切变形板理论和广义Kármán型方程,给出了各类功能梯度材料混合板结构的振动以及屈曲后的振动的控制方程,并采用改进的摄动-Galerkin混合法进行求解。接着,重点分析了表面覆盖纤维增强压电材料作动器的功能梯度材料混合板结构的非线性自由振动和受迫振动,具体讨论了材料组分指数、温度变化、压电纤维体积含量及控制电压等因素对表面覆盖纤维增强压电材料作动器的功能梯度材料混合板结构的非线性振动和动力响应的影响。在这之后,详细分析了对称功能梯度材料板结构屈曲后的振动特性,将控制方程拆分为屈曲和振动两个部分并分别用摄动-Galerkin混合法进行求解,具体讨论了材料组分指数、温度变化、边厚比、长宽比、屈曲与振动模态等因素对对称功能梯度材料板结构屈曲后的振动特性的影响,并对由两组不同材料构成的对称功能梯度材料板结构的屈曲后的振动特性进行了比较。还研究了热环境下表面覆盖或埋置纤维增强压电材料作动器的功能梯度材料混合板结构的屈曲后的振动特性,通过参数分析讨论了材料组分指数、温度变化、压电纤维体积含量及控制电压等因素对表面覆盖或埋置纤维增强压电材料作动器的功能梯度材料混合板屈曲后的振动特性的影响。最后,研究了以FGM为面板的夹芯板在热环境下屈曲后的线性自由振动以及非线性振动。详细讨论了材料组分指数、温度变化、芯层与面板厚度比等因素对FGM夹芯板屈曲后的振动特性的影响。在本文在理论分析结果的基础上,采用FORTRAN语言编制扩充了多个数值分析程序包,分别用于各类功能梯度材料复合板结构的振动以及屈曲后的振动特性计算。本文所取得的研究成果有助于加深对功能梯度复合材料板结构的振动特性的认识,且对于此类新型复合材料结构的工程实际应用具有一定的积极意义。更多还原

【Abstract】 Functionally graded materials (FGMs), usually made from a mixture of metals and ceramics, have been regarded as one of the advanced inhomogeneous composite materials with great application potential in many engineering sectors such as aerospace vehicles, nuclear reactors, power generators and so on. Investigations on the vibration characteristics of pre- and post-buckled FGM hybrid plate structures under various combinations of mechanical, thermal and electrical loading conditions have been, therefore, receiving considerably more attention in recent years due to their prime importance in both theoretical and practical aspects.This paper mainly consists of three parts: (1) Based on the Reddy’s higher-order shear deformation plate theory and general von Kármán-type equations, put forward the governing equations of pre- and post-buckled vibration of several hybrid FGM plate forms which have not been studied adequately, triumphantly applying the perturbation technique combined with Galerkin method into equations solving, and get the comparatively simple result forms with complicated deduction at last; (2) As a new type of materials, piezoelectric fiber reinforced composite (PFRC) actuators were applied to optimal vibration control, interrelated informatons be depicted in this paper; (3) During the investigative cource, some factors not been considered adequently in other researches were discussed fully in the postbuckled vibration analysis, such as the temperature-dependent material coefficients, heat conduction and nonlinear vibration characteristic etc. Bring forward a great deal of numerical results, and discuss the effect of volume fraction index, temperature change, aspect ratio, side-to-thickness ratio, mode, piezoelectric fiber volume fraction, control voltage and substrate-to-face sheet thickness ratio on the pre- and postbuckled vibration characteristics of FGM hybrid plates.Since FGM are used in high-temperature environments, all the constituents of FGM sheets considered herein possess temperature-dependent properties. On the other hand, ceramics and metal used in FGM do store different amounts of heat, and therefore heat conduction usually occurs, therewith temperature distribution was deduced at the beginning of every chapter.Subsequently, based on the Reddy’s higher-order shear deformation plate theory and general von Kármán-type equations, the governing equations of nonlinear vibration and postbuckling vibration are advanced for FGM hybrid plates and solved by using an improved perturbation technique combined with Galerkin method.In succession, the free and forced vibration of FGM hybrid plates bonded with PFRC actuators in thermal environments are analyzed, the effect of volume fraction index, temperature change, piezoelectric fiber volume fraction, and control voltage on the nonlinear vibration and dynamic response of FGM hybrid plates are discussed. After that, the pre- and postbuckled vibration characteristics of symmetrical FGM plates are studied, through dividing the governing equations into two sets for postbuckling and vibration separately, and solving them with an improved perturbation technique combined with Galerkin method, the effect of volume fraction index, temperature change, side-to-thickness ratio, aspect ratio and mode on the postbuckling vibration characteristics of symmetrical FGM plates are discussed amply. Afterwards, comparisons of the pre- and postbuckled vibration characteristics of two type of symmetrical FGM plates with different constituents are given. whereafter, the pre- and postbuckled vibration characteristics of FGM plates bonded or imbedded with PFRC actuators in thermal environments are canvassed, including probe into the effect of volume fraction index, temperature change, piezoelectric fiber volume fraction, and control voltage on the postbuckling vibration characteristics of FGM hybrid plates. At last, the vibration of pre- and post-buckled sandwich plates with FGM face sheets in thermal environment is discussed. The effect of volume fraction index, temperature change, and substrate-to-face sheet thickness ratio on the vibration characteristics are studied.As the result of extensive theoretical and numerical analysis by using the computer program packages developed with FORTRAN language, this paper provides comprehensive first-ever-known results which are helpful for better understanding the vibration behavior of the FGM plate structures.更多还原