Inverse eigenvalue problem in structural design

A method is presented for the design of a structure with specified low-order natural frequencies. The method can also be used for design problems in which certain bands, devoid of any frequency constraints, are specified. This can further be used to generate initial feasible designs for optimum design problems with frequency constraints.

[1]  Alston S. Householder,et al.  Some Inverse Characteristic Value Problems , 1956, JACM.

[2]  Harry Hochstadt,et al.  On some inverse problems in matrix theory , 1967 .

[3]  R. B. Corr,et al.  A simultaneous iteration algorithm for symmetric eigenvalue problems , 1976 .

[4]  Ole H. Hald,et al.  Inverse eigenvalue problems for Jacobi matrices , 1976 .

[5]  Victor Barcilon,et al.  On the Multiplicity of Solutions of the Inverse Problem for a Vibrating Beam , 1979 .

[6]  F. Biegler-König,et al.  Construction of band matrices from spectral data , 1981 .

[7]  Harry Hochstadt,et al.  On the construction of band matrices from spectral data , 1981 .

[8]  F. Biegler-König,et al.  A Newton iteration process for inverse eigenvalue problems , 1981 .

[9]  A. J. Morris,et al.  Foundations of Structural Optimization: A Unified Approach , 1982 .

[10]  John E. Dennis,et al.  Numerical methods for unconstrained optimization and nonlinear equations , 1983, Prentice Hall series in computational mathematics.

[11]  Richard Evelyn Donohue Bishop,et al.  Qualitative Properties of vibrating systems , 1985, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[12]  G. M. L. Gladwell,et al.  Inverse Problems in Vibration , 1986 .

[13]  Carlos A. Mota Soares,et al.  Computer Aided Optimal Design: Structural and Mechanical Systems , 1987, NATO ASI Series.

[14]  I. U. Ojalvo,et al.  Efficient Computation of Mode-Shape Derivatives for Large Dynamic Systems , 1986 .

[15]  Ramana V. Grandhi,et al.  Structural optimization with frequency constraints , 1988 .

[16]  Y. G. Tsuei,et al.  A Method for Modifying Dynamic Properties of Undamped Mechanical Systems , 1989 .

[17]  Y. G. Tsuei,et al.  Method for Shifting Natural Frequencies of Damped Mechanical Systems , 1991 .