Abstract
A new approach to numerically solving problems of the elastodynamics of arbitrarily shaped bodies with nonuniform material properties in rotation has been proposed in the present study. The present approach is based on first principles and is well suited to the study of problems of fluid-structure interaction and wave-based structural health monitoring. The governing hyperbolic partial differential equations of elastodynamics are cast in strong conservation form in the noninertial frame of reference and in generalized curvilinear coordinates. The results are obtained directly in the time domain. No special boundary treatment is required at material interfaces, and predictions can be made with and without material damage in a given structure for damage detection of the structure. The effect on the dynamics of a rotating annulus due to centrifugal force and, additionally, Coriolis force at high rates of rotation is studied. The partial differential equations are solved using a new dissipative time-centered leapfrog scheme presented here. A one-dimensional theoretical analysis of the numerical scheme shows that the new scheme has well-defined stability and dissipation characteristics. A comparison of the new scheme with a conventional dissipative time-centered leapfrog scheme shows that much larger time steps can be taken with the new scheme than allowed by the existing scheme. A dissipation-dependence study demonstrates that as the dissipation parameter is decreased, the steady-state solution uniformly approaches the exact solution. For larger values of this parameter, although the natural frequency of the system is not altered, the system vibrations damp too quickly, and the steady-state solution deviates from the exact steady-state solution. The larger the dissipation parameter, the larger this deviation from the exact steady state. The present scheme is very simple to incorporate in a finite difference simulation of elastodynamics in generalized curvilinear coordinates, and it has been used in the software FiDDLE, which solves the velocity-stress system of elastodynamic partial differential equations. It will be used in simulating fluid-elastodynamic interaction of the Mars Science Laboratory canopies and other decelerators such as inflatable aerodynamic devices as well as in wave-based structural health monitoring of these systems. Other applications include elastodynamics of turbomachinery blades, computer disk drive, and cutting-tool industry applications.
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