An Iterative Algorithm of Dynamic Design and Existence Condition of Solution for Vibration Systems
Gao Fu an(1), Cao Pingkuan(1), Gao Xiaoning(2)
(Chinese Aeronautical Computing Technique Research Institute, Xi'an 710068)
(2, Dept. of Computer Science and Engineering, Xi'an United University, Xi'an 710065)

Abstract: The dynamic design of vibration system is considered as an inverse problem for nonlinear generalized eigenvalue in this paper. If variable parameters PŁ˝(p₁,p₂,ˇ­,p_s) are contained in the vibration system, a nonlinear multivariate function can be constructed. Based on minimizing the function, an iterative algorithm for solving the inverse eigenvalue problem is presented here. The method is not limited in the prescribed order of vibration frequency and the given direction. The iterative algorithm is suitable to degenerated case with multiple eigenvalue, too. The material of the systems or the structures is arbitrary. Existence condition of solution is discussed. Explicit formulation for existence is obtained. The expression can be conveniently applied to engineering. Combining dynamic design for a type of helicopter rotor blade, numerical examples in engineering application are given. The results for a large number of numerical experiments and practice in engineering shows that the iterative method has a good convergence and a high accuracy.
Keywords: inverse eigenvalue problem, inversion, dynamic design, iterative algorithm, reliability design.