Using semi-tensor product of matrices, the controllability and stabilizability of finite automata are investigated. By expressing the states, inputs, and outputs in vector forms, the transition and output functions ar...Using semi-tensor product of matrices, the controllability and stabilizability of finite automata are investigated. By expressing the states, inputs, and outputs in vector forms, the transition and output functions are represented in matrix forms.Based on this algebraic description, a necessary and sufficient condition is proposed for checking whether a state is controllable to another one. By this condition, an algorithm is established to find all the control sequences of an arbitrary length. Moreover, the stabilizability of finite automata is considered, and a necessary and sufficient condition is presented to examine whether some states can be stabilized. Finally, the study of illustrative examples verifies the correctness of the presented results/algorithms.展开更多
陶瓷基复合材料(ceramic matrix composites,CMC)作为一种优异的高温结构材料,在航空发动机领域得到了广泛应用。目前,依据GJB 10311—2021的双切口面内剪切实验方法存在明显局限性:切口位置处的应力集中效应导致标距区平均剪切应力计...陶瓷基复合材料(ceramic matrix composites,CMC)作为一种优异的高温结构材料,在航空发动机领域得到了广泛应用。目前,依据GJB 10311—2021的双切口面内剪切实验方法存在明显局限性:切口位置处的应力集中效应导致标距区平均剪切应力计算结果偏高,使得面内剪切模量测试结果与V形缺口剪切实验偏差可达30%。为此,本工作将数字图像相关方法(DIC)与双切口剪切实验相结合,开发一种面内剪切力学性能测试的新方法。为消除切口处应力集中的影响,提出采用有限元模型修正技术(finite element model updating,FEMU),利用DIC实测标距区内面内平均剪切应变与数值计算应变之间的方差构造目标函数,迭代获得材料的面内剪切模量。为便于工程应用,通过优化试样切口深度,实现单次实验即可获得材料的面内剪切模量和面内剪切强度,并采用SiC/SiC正交层合陶瓷基复合材料进一步验证了该实验方法的可行性和测试结果的可靠性。结果表明:该实验方法可同时准确测定陶瓷基复合材料的面内剪切模量和强度,测试结果与V形缺口实验结果偏差小于5%。相较V形缺口剪切实验,该方法实验工装和试样尺寸更小,更适用于高温面内剪切实验。SiC/SiC复合材料面内剪切应力-应变存在典型的屈服点,且屈服后剪切行为表现出典型的线性应变强化特征。展开更多
基金supported by the National Natural Science Foundation of China(61174094)the Tianjin Natural Science Foundation of China(13JCYBJC1740014JCYBJC18700)
文摘Using semi-tensor product of matrices, the controllability and stabilizability of finite automata are investigated. By expressing the states, inputs, and outputs in vector forms, the transition and output functions are represented in matrix forms.Based on this algebraic description, a necessary and sufficient condition is proposed for checking whether a state is controllable to another one. By this condition, an algorithm is established to find all the control sequences of an arbitrary length. Moreover, the stabilizability of finite automata is considered, and a necessary and sufficient condition is presented to examine whether some states can be stabilized. Finally, the study of illustrative examples verifies the correctness of the presented results/algorithms.
文摘陶瓷基复合材料(ceramic matrix composites,CMC)作为一种优异的高温结构材料,在航空发动机领域得到了广泛应用。目前,依据GJB 10311—2021的双切口面内剪切实验方法存在明显局限性:切口位置处的应力集中效应导致标距区平均剪切应力计算结果偏高,使得面内剪切模量测试结果与V形缺口剪切实验偏差可达30%。为此,本工作将数字图像相关方法(DIC)与双切口剪切实验相结合,开发一种面内剪切力学性能测试的新方法。为消除切口处应力集中的影响,提出采用有限元模型修正技术(finite element model updating,FEMU),利用DIC实测标距区内面内平均剪切应变与数值计算应变之间的方差构造目标函数,迭代获得材料的面内剪切模量。为便于工程应用,通过优化试样切口深度,实现单次实验即可获得材料的面内剪切模量和面内剪切强度,并采用SiC/SiC正交层合陶瓷基复合材料进一步验证了该实验方法的可行性和测试结果的可靠性。结果表明:该实验方法可同时准确测定陶瓷基复合材料的面内剪切模量和强度,测试结果与V形缺口实验结果偏差小于5%。相较V形缺口剪切实验,该方法实验工装和试样尺寸更小,更适用于高温面内剪切实验。SiC/SiC复合材料面内剪切应力-应变存在典型的屈服点,且屈服后剪切行为表现出典型的线性应变强化特征。
