LINEAR ACTIVE STRUCTURES AND MODES (Ⅰ)--BASIC CONCEPTS AND PROPERTIES

Some basic concepts about the active structures were firstly explained, and the main subjects to study in the field of active structure dynamics were synthesized. For the linear active structures, the annotations on the modes were done in detail. The physical meanings of the right and left eigenvectors were explained. The right eigenvectors are the modal shapes and the modal responses of an active structure depend on the left ones. The adjoint structure of an active structure was defined and the reciprocity theorem was interpreted. For two active structures, which are adjoint to each other and with the reciprocal gain-matrices, the right and left eigenvector are reciprocal. The relationship between an active structure and the corresponding passive structure is expressed with the transfer functions, which is employed to resolve the estimation problems.     

LINEAR ACTIVE STRUCTURES AND MODES (Ⅱ) —DISCRETE SYSTEMS AND BEAMS

IntroductionThestudiedobjectintheclassicstructuredynamicsisthepassivestructureswhicharechangedintoactivestructurewhencontroldevicesorsmartmaterialsareintroducedintoandthecontrolfunctionisapplied .Anactivestructureisgenerallycalledactivesystem .Asforthedefinitionofactivestructure ,itistheconceptofworthydiscussion[1].Thedefinitionshouldbebecomingrigorouswiththestudyontheactivestructuraldynamics.Withincertaincategoryofactivestructuresinpaper (Ⅰ ) [2 ],someattributesaboutthemodesoflinearactivest…     

LINEAR ACTIVE STRUCTURES AND MODES (Ⅱ)--DISCRETE SYSTEMS AND BEAMS

The basic concepts about the active structures and some attributes of the modes were presented in paper "Liner Active Structures and Modes ( Ⅰ ) ". The characteristics of the active discrete systems and active beams were discussed, especially, the stability of the active structures and the orthogonality of the eigenvectors. The notes about modes were portrayed by a model of a seven-storeyed building with sensors and actuators. The concept of the adjoint active structure was extended from the discrete systems to the beams that were the representations of the continuous structures. Two types of beams with different placements of the measuring and actuating systems were discussed in detail. One is the beam with the discrete sensors and actuators, and the other is the beam with distributed sensor and actuator function. The orthogonality conditions were derived with the modal shapes of the active beam and its adjoint active beam. An example shows that the variation of eigenvalues with feedback amplitude for the homo-configuration and non-homo-configuration active structures.     

线性主动结构及模态（I）——基本概念及属性

阐明了主动结构的若干基本概念，归纳了主动结构动力学的主要问题．对线性主动结构的模态做了注释，注释包括：右和左特征向量的物理意义，右特征向量为振型，左特征向量表征响应的模态分量；伴随结构及互易定理，两个互为伴随主动结构，且有对偶反馈增益矩阵，左和右特征向量互易；主动结构与被动结构的关联用传递函数表示，可用于主动结构的估计问题．     

LINEAR ACTIVE STRUCTURES AND MODES （ Ⅰ ） — BASIC CONCEPTS AND PROPERTIES

Some basic concepts about the active structures were firstly explained, and the main subjects to study in the field of active structure dynamics were synthesized. For the linear active structures, the annotations on the modes were done in detail. The physical meanings of the right and left eigenvectors were explained. The right eigenvectors are the modal shapes and the modal responses of an active structure depend on the left ones. The adjoint structure of an active structure was defined and the reciprocity theorem was interpreted. For two active structures, which are adjoint to each other and with the reciprocal gain-matrices, the right and left eigenvector are reciprocal The relationship between an active structure and the corresponding passive structure is expressed with the transfer functions, which is employed to resolve the estimation problems.     

线性主动结构及模态(Ⅱ)——离散系统及梁

在“线性主动结构及模态(Ⅰ)”中给出了主动结构的基本概念及模态的若干属性的基础上,对主动离散系统及主动梁的属性做了进一步的讨论,包括稳定性和正交性,并用具体实例对模态做了解释．将伴随结构概念在梁结构中推广,具体讨论了两种配置的主动梁,它们分别代表离散传感和作动及分布传感和作动的配置,并给出了用主动梁振型和伴随主动梁振型表示的正交性条件．用实例给出了同位和非同位主动刚度梁的特征值随反馈大小的变化．     

LINEAR ACTIVE STRUCTURES AND MODES (Ⅰ) —BASIC CONCEPTS AND PROPERTIES

IntroductionThestudyobjectoftheclassicstructuredynamicsispassivestructure .Whencontroldevicesorsmartmaterialareintroducedintoitwiththeapplicationofcontrolfunction ,thepassivestructuresarechangedintotheactivestructures.Theactivestructureisgenerallycalledactivesystem .Withtherapiddevelopmentofadaptivestructures,controlledstructuresandsmartstructures,therewillbemoreandmorekindsoftheactivestructures.Alotofspecialstudyontheactivestructureswillbedevelopedintooneofanewknowledgebranchinthefieldofthes…     

线性主动结构及模态(Ⅰ)——基本概念及属性

阐明了主动结构的若干基本概念,归纳了主动结构动力学的主要问题．对线性主动结构的模态做了注释,注释包括:右和左特征向量的物理意义,右特征向量为振型,左特征向量表征响应的模态分量;伴随结构及互易定理,两个互为伴随主动结构,且有对偶反馈增益矩阵,左和右特征向量互易;主动结构与被动结构的关联用传递函数表示,可用于主动结构的估计问题．     

LINEAR ACTIVE STRUCTURES AND MODES （ Ⅱ ） — DISCRETE SYSTEMS AND BEAMS

The basic concepts about the active structures and some attributes of the modes were presented in paper “Liner Active Structures and Modes ( Ⅰ ) “. The characteristics of the active discrete systems and active beams were discussed, especially, the stability of the active structures and the orthogonality of the eigenvectors. The notes about modes were portrayed by a model of a seven-storeyed building with sensors and actuators. The concept of the adjoint active structure was extended from the discrete systems to the beams that were the representations of the continuous structures. Two types of beams with different placements of the measuring and actuating systems were discussed in detail. One is the beam with the discrete sensors and actuators, and the other is the beam with distributed sensor and actuator function. The orthogonality conditions were derived with the modal shapes of the active beam and its adjoint active beam. An example shows that the variation of eigenvalues with feedback amplitude for the homo-configuration and non-homo-configuration active structures.