WANG Yong-gang, GONG Jing, ZHANG Jing-hui. Linear Active Structures and Modes(Ⅱ)——Discrete Systems and Beams[J]. Applied Mathematics and Mechanics, 2004, 25(8): 779-786.
 Citation: WANG Yong-gang, GONG Jing, ZHANG Jing-hui. Linear Active Structures and Modes(Ⅱ)——Discrete Systems and Beams[J]. Applied Mathematics and Mechanics, 2004, 25(8): 779-786.

# Linear Active Structures and Modes(Ⅱ)——Discrete Systems and Beams

• Received Date: 2002-11-01
• Rev Recd Date: 2004-03-08
• Publish Date: 2004-08-15
• 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, specially, 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.
•  [1] Preumont A.Vibration Control of Active Structures[M].Dordrecht, The Netherland: Kluwer Academic Publishers, 1997. [2] 张景绘，龚静，王永刚.线性主动结构及模态(I)——基本概念及属性[J].应用数学和力学2004，25(8):771—778. [3] Ganesan R.Vibration analysis for stability of singular non-self-adjoint beam-columns using stochastic FEM[J].Computers and Structures,1998,68(5)：543—554. [4] 顾仲权,马扣根,陈卫东.振动主动控制[M].北京：国防工业出版社, 1979. [5] Mohammad K S,Al-Dmoour A S.Vibration control of unknown flexible beam structures[J].Journal of Vibration & Control,2002,8(1)：69—87.

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沈阳化工大学材料科学与工程学院 沈阳 110142

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