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This paper provides details of developments pertaining to vibration analysis of gyroscopic systems, that involves a finite element structural discretization followed by the solution of the resulting matrix eigenvalue problem by a... more
This paper provides details of developments pertaining to vibration analysis of gyroscopic systems, that involves a finite element structural discretization followed by the solution of the resulting matrix eigenvalue problem by a progressive, accelerated simultaneous iteration technique. Thus Coriolis, centrifugal and geometrical stiffness matrices are derived for shell and line elements, followed by the eigensolution details as well as solution of representative problems that demonstrates the efficacy of the currently developed numerical procedures and tools.
Along with the sensitivity equations, the co-state equations and their boundary conditions are derived. Thereafter, based on the modal analysis of Von Neumann theory, the stability limits of the co-state equations are investigated. The... more
Along with the sensitivity equations, the co-state equations and their boundary conditions are derived. Thereafter, based on the modal analysis of Von Neumann theory, the stability limits of the co-state equations are investigated. The stability characteristics of the co-state ...
The non-dimensional Continuity, Momentum, Energy, Mass-Fraction equations and Equation of State governing the two-dimensional, unsteady motion of a compressible, reacting gas in the boundary layer to the leading order in a Reynolds number... more
The non-dimensional Continuity, Momentum, Energy, Mass-Fraction equations and Equation of State governing the two-dimensional, unsteady motion of a compressible, reacting gas in the boundary layer to the leading order in a Reynolds number are derived. The resulting coupled momentum and energy equations are numerically solved for both adiabatic and isothermal boundary conditions with different values of the independent parameters like Mach number, surface temperature and Prandtl number. The effect of these parameters on temperature and velocity profile are presented. For comparison purposes, the inert-state problem for the linear temperature viscosity law is also solved for different values of independent parameters.
Variational method (VM) is employed to derive the co-state equations, boundary (transversality) conditions, and functional sensitivity derivatives. The converged solutions of the state equations together with the steady state solution of... more
Variational method (VM) is employed to derive the co-state equations, boundary (transversality) conditions, and functional sensitivity derivatives. The converged solutions of the state equations together with the steady state solution of the co-state equations are ...
Variational method is applied to the state equations in order to derive the costate equations and their boundary conditions. Thereafter, the analyses of the eigenvalues of the state and costate equations are performed. It is shown that... more
Variational method is applied to the state equations in order to derive the costate equations and their boundary conditions. Thereafter, the analyses of the eigenvalues of the state and costate equations are performed. It is shown that the eigenvalues of the Jacobean matrices of the state and the transposed Jacobean matrices of the costate equations are analytically and numerically the