A simplified procedure is presented for the determination of the derivatives of eigenvectors of nth order algebraic eigensystems. The method is applicable to symmetric or nonsymmetric systems, and requires knowledge of only one eigenvalue and its associated right and left eigenvectors. In the procedure, the matrix of the original eigensystem of rank (/?-!) is modified to convert it to a matrix of rank /?, which then is solved directly for a vector which, together with the eigenvector, gives the eigenvector derivative to within an arbitrary constant. The norm of the eigenvector is used to determine this constant and complete the calculation. The method is simple, since the modified n rank matrix is formed without matrix multiplication or extensive manipulation. Since the matrix has the same bandedness as the original eigensystems, it can be treated efficiently using the same banded equation solution algorithms that are used to find the eigenvectors.

Simplified calculation of eigenvector derivatives

Methods for calculating sensitivity derivatives for discrete structural systems are surveyed, primarily covering literature published during the past two decades. Methods are described for calculating derivatives of static displacements and stresses, eigenvalues and eigenvectors, transient structural response, and derivatives of optimum structural designs with respect to problem parameters. The survey is focused on publications developed in nonstructural fields such as electronics, controls, and physical chemistry which are directly applicable to structural problems. Most notable among the nonstructural-based methods are the adjoint variable technique from control theory, and the Green's function and FAST methods from physical chemistry.

Sensitivity Analysis of Discrete Structural Systems

Panel flutter theory applied to aeroelastic stability of flat unloaded plates and cylindrical shells

Panel flutter - A review of the aeroelastic stability of plates and shells

Uncertainties and dynamic problems of bolted joints and other fasteners

Dynamic stability of columns subjected to follower loads : A survey

Derivatives of eigenvalues and eigenvectors in non-self-adjoint systems.

Conclusions Wind-tunnel Magnus data obtained to date on canted fin configurations may be invalid in that a severe normal force interaction may be present. Although it may be possible in some cases to correct for this interaction, it is in general best to remove the interaction by subtracting the zero spin data at each angle of attack. This requires a system in which the model can be kept at zero spin during an angle of attack sweep of the configuration.

Determining the Nature of Instability in Nonconservative Problems

The nonlinear problem of dynamic instability of snap-through of clamped shallow arches subjected to timewise step loads is investigated. Established are separate sufficient conditions for stability and for instability. For arches with parameters in certain special ranges, these two sufficient conditions coincide and, thus, yield the necessary and sufficient condition for stability. Specific problems investigated are "simple" clamped arches under "simple" loads, clamped sinusoidal arches under uniformly distributed loads, clamped parabolic arches under uniformly distributed loads and clamped sinusoidal arches under concentrated loads which may be located eccentrically. The criteria given in this paper are reliable to the extent that no approximation is made or is required in the mathematical analysis.

Dynamic stability criteria for clamped shallow arches under timewisestep loads

Linear elastic columns dynamic stability under time dependent axial load, investigating almost- sure asymptotic stability

/pdf/stability-of-a-column-subjected-to-a-time-dependent-axial-2r6jr1zrr8.pdf

Raymond H. Plaut

Papers

Derivatives of eigenvalues and eigenvectors in non-self-adjoint systems.

Determining the Nature of Instability in Nonconservative Problems

Dynamic stability criteria for clamped shallow arches under timewisestep loads

Stability of a column subjected to a time- dependent axial load.

Structural optimization of a panel flutter problem