Qiu Zhi-ping, Chen Su-huan, Liu Zhong-sheng. Matrix Perturbation Methol for the Vibration Problem of Structures with Interval Parameters[J]. Applied Mathematics and Mechanics, 1994, 15(6): 519-527.
 Citation: Qiu Zhi-ping, Chen Su-huan, Liu Zhong-sheng. Matrix Perturbation Methol for the Vibration Problem of Structures with Interval Parameters[J]. Applied Mathematics and Mechanics, 1994, 15(6): 519-527.

Matrix Perturbation Methol for the Vibration Problem of Structures with Interval Parameters

• Received Date: 1993-12-03
• Publish Date: 1994-06-15
• When the parameters of the structures are uncertain, the structural natural frequencies become uncertain.In this paper, we deal with the vibration problem of the structure with interval parameters,the eigenvalue problem of the structures with interval parameters is transferred into two different eigenvalue problems to be solved. The perturbation method is applied to the vibration problem of the structures with interval parameters, the numerical results show that the proposed method is sufficiently accurate and needs little computational efforts.
•  [1] Moore,R.,Method and Applications of Int0rval Analysis,SIAM.Publ.,Philadelphia(1979). [2] Alefeld,G.and J.Herzberger,Introduction to Interval Computations,Academic press,New York(1983). [3] Deif,A.,Advanced Matrix Theory for Scientists and Engineers (2nd Edition),Abacuss Press(1991).262-281. [4] Chen Su-huan,Matrix Perturbation Theory in Structural Dynamics,International Academic Publishers (1993). [5] Ben-Haim,Y.and I.Elishakoff,Convex Models of Uncertainty in Applied Mechanics,Elscvier,New York(1990). [6] Wang Guang-yuan and Qu Jin-ping,Fuzzy random vibration of mutt-degree-fredom hysterestic systems subjected to earthquakes,Earthquake Engineering and Structural Dynamics,15(5)(1987). [7] Huang Wen-liu,Vibration of some structures with random parameters,AIAA J.,20(1982),1001-1008. [8] Shi,Z.C.and W,B.G ao,A necessary and sufficient condition for the positive-definiteness of interval sy m metric matrices,Int,J.Control,43(1)(1986),325-328. [9] Franklin,J,N.,Matrix Theory,Prentice-Hall,Inc,Englewood Cliffs,New Jersey(1968),141-193. [10] Bellman,R.,Introduction to Matrix.Analysis,McGraw-Hill,New York(1970),80-64.

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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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