Interval analysis method for vibration of composite laminate with uncertain parameters
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摘要: 提出了求解具有不确定参数的复合材料板的振动固有频率区间分析法.区间分析法利用区间数学和泰勒定理,把不确定变量简化为区间向量.这样可以在较少的结构信息的情况下确定结构响应的变化区间.在样本比较小,概率统计特性缺乏,从而通常的概率统计方法不能有效应用时,区间分析仍然有效. 对复合材料板的振动固有频率的区间法公式进行了推导,并用2个数值例子与凸模型方法的解进行比较.结果表明区间分析法比凸模型方法的解区间小.Abstract: A new method named interval analysis method, which solves the natural frequencies of composite laminate with uncertain parameters, was presented. Based on interval mathematics and Taylor series expansion, interval analysis method simplifies the uncertain parameters to interval vectors so that it can get the intervals within which the response of structure varies when less information of structure is known. The interval analysis method is efficient under the condition that probability approach cannot work because of small samples and spare statistics characteristics. The formulation of natural frequencies of composite laminate using interval analysis method was formulated. Two numerical examples of comparisons between interval analysis method and convex model were given. The results show that the solutions of interval analysis method are sharper than those of convex model.
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Key words:
- composite materials /
- vibration /
- interval mathematics /
- uncertain parameters
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[1] Goggin P R. The elastic constants carbon-fiber composite[J]. Journal Material Science, 1973, 8:233~244 [2]Qiu Zhiping, Chen Suhuan, Na Jingxin. The Rayleigh quotient method for computing eigenvalue bounds of vibrational systems with interval parameters . Acta Solid Mechanics Sinica, 1993, 6:309~318 [3]Qiu Z P, Chen Suhuan, Elishakoff I. Natural frequencies of structures with uncertain but nonrandom parameters[J]. Journal of Optimization Theory and Applications, 1995, 86:669~683 [4]Qiu Z P, Mueller P C,Frommer A. Stability robustness bounds for linear state-space models with structured uncertainty based on ellipsoidal set-theoretic approach[J]. Mathematics and Computers in Simulation, 2001, 56:35~53 [5]Qiu Z P,Elishakoff I. Antioptimization of structures with large uncertain-but-non-random parameters via interval analysis[J]. Computer Methods in Applied Mechanics and Engineering, 1998, 152(3-4):361~372 [6]Moore R E. Methods and applications of interval analysis[M]. Philadelphia, SIAM, 1979 [7]Ben-Haim Y. A non-probabilistic measure of reliability of linear systems based on expansion of convex models[J]. Structural Safety, 1995, 17:91~109 [8]Elishakoff I, Li Y W, Starnes J J H. A deterministic method to predict the effect of unknown-but-bounded elastic moduli on the buckling of composite structures[J]. Computer Methods in Applied Mechanics and Engineering, 1994, 111:155~167 -
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