LETTERS TO THE EDITOR SOME OBSERVATIONS ON THE SINHA APPROACH TO DYNAMIC RESPONSE CALCULA nONS
نویسنده
چکیده
Reference [1] introduces a method for the computation of the Floquet matrix, which is a time-history solution of a periodic-coefficient system over one period. Reference [2] generalizes both first order and second order forms to the case for which all coefficients are periodic. Numerical results for rotor flap-lag response show the Sinha method to be much more efficient than conventional time-marching algorithms. Thus, the method has been shown to be a viable alternative for stability analysis of periodic coefficient systems. In this present note, we wish to show that the method is actually a type of PetroffGalerkin scheme, often referred to as a p-version finite element method in the time domain. In particular, the procedure for first order systems is a weak mixed method, and the procedure for second order systems is a weak displacement method. Having identified the approach as a p-version finite element method, one can then use the theorems and results of finite-element theory to show how the method might be improved even further. This will be done with supporting documentation from numerical results. An inherent feature of the Sinha method (in addition to the finite-element character) is the use of special operational matrices to compute the numerical integrals required by the theory. These operational matrices are predicated on the use ofChebyshev polynomials for the trial functions. As it turns out, these matrix operators could also be used to do the quadratures in conventional p-version finite elements. Thus, an interesting line of investigation would be to compare numerical quadrature by the Chebyshev matrices with conventional methods (such as Gauss quadrature). Such an investigation was not done in reference [1] or [2] but will be pursued here.
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تاریخ انتشار 2007