Engineering topics
Publications and source records attributed to Rudisill, C. S..
A numerical procedure was developed for minimizing the structural mass of an aircraft structure which must have a specified minimum flutter velocity or divergence velocity. During the optimization process the arrangement of the structural members remains fixed, while the stiffness parameters of the structure are varied.
A method for optimizing an active control system which will suppress flutter and minimize the response of a lifting surface to atmospheric turbulence is presented. A mathematical search method is developed which will find a control law which will cause an active control system to flutter at a specified freestream velocity, air density, and Mach number. With the flutter velocity of the system held constant, the control law is then modified in such a way that the peak output power spectral density function of the angular response of a lifting surface (as a result of atmospheric turbulence) is minimized for a specified flight velocity which is less than the flutter velocity. The von Karman generalized power spectrum for the transverse components of turbulence is used in an example problem to increase the flutter velocity and minimize the turbulence response of a simplified delta-wing model which has leading and trailing edge control surfaces.
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Two numerical methods are presented for computing the derivatives of eigenvalues and eigenvectors which do not require complete solution of the eigenvalue problem if only a few derivatives are sought. The 'iterative' method may be used to find the first derivative of one or all of the eigenvectors together with the second derivative of their eigenvalues in a self-adjoint system. If the left- and right-hand eigenvectors are known, the first derivative of the eigenvector corresponding to the largest eigenvalue and the second derivative of the largest eigenvalue may be obtained for a nonself-adjoint system. The 'algebraic' method may be used to find all orders of the derivatives, provided they exist, without requiring the left-hand eigenvectors.
A method for the optimization of structures to satisfy flutter velocity constraints is presented along with a method for determining the flutter velocity. A method for the optimization of structures to satisfy divergence velocity constraints is included.
Expressions are obtained for the derivatives of the eigenvalues and eigenvectors which are expressions of only one left-hand and one right-hand eigenvector. The approach described makes use of a Choleski decomposition or some other decomposition method. The method may be extended to find any order of derivative of the eigenvalue and eigenvector. The expressions obtained for finding the derivatives of eigenvalues and eigenvectors for nonself-adjoint systems may be applied to self-adjoint systems.
Equations for the second partial derivatives of the eigenvalues of the flutter equation along with the equations for finding the second partial derivatives of the flutter velocity of an aircraft structure with respect to the structural parameters are derived. These partial derivatives are used to develop expressions for the step size in a projected gradient search along a constant mass hyperlane. A projected gradient search along with a gradient mass and a gradient velocity search is used to minimize the mass of a box beam which supports a lifting surface.
Aircraft structural parameters optimization satisfying flutter velocity constraint and minimum mass, applying to box beam design
Numerical analysis of derivatives of flutter velocity of aircraft structures to determine optimization of complex structures