• Transactions of the Korean Society of Mechanical Engineers A
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• v.24 no.6 s.177
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• pp.1419-1426
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• 2000

A dynamic analysis of rectangular Reissner-Mindlin plate was carried out using pseudospectral method. The pseudospectral method is superior to the finite element method because of more rapid conver gence speed of approximate solutions. Especially, the improvement in accuracy of the pseudospectral method is remarkable. Numerical examples demonstrate the excellent performance and robustness of the pseudospectral method with respect to thickness ratio of rectangular Reissner-Mindlin plate. The natural frequencies of rectangular Reissner-Mindlin plate calculated with the pseudospectral method are more reliable than those calculated with other numerical methods.

• International Journal of Aeronautical and Space Sciences
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• v.16 no.1
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• pp.64-76
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• 2015

This paper suggests applying pseudospectral model predictive method for exo-atmospheric guidance. The method is a fusion of pseudospectral law and model predictive control, in which a two point boundary value problem is formulated using model predictive approach and solved by applying pseudospectral law. In this work, the method is applied to exo-atmospheric guidance with specific target requirement. The existing exo-atmospheric guidance methods suffice general requirements for guidance, but cannot ensure specific target constraints; whereas, the presented method is able to do so. The proposed guidance law is assessed through simulation of perturbed cases, and the tests suggest that the method is able to operate semi-autonomously under control and thrust vector perturbations.

• Communications of the Korean Mathematical Society
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• v.13 no.4
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• pp.889-901
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• 1998

Numerical approximations by pseudospectral method are obtained for the damped Boussinesq equation which is a modification of the good Boussinesq equation. The consistency and stability of the method are obtained using the extended Lax-Richtmyer equivalence theorem, which imply the convergence of the method. We obtain error estimates of O(h$^{s}$ ＋ k$^2$) for a fully discrete pseudospectral method.

• Journal of Mechanical Science and Technology
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• v.17 no.3
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• pp.370-379
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• 2003

A study of free vibration of rectangular Mindlin plates is presented. The analysis is based on the Chebyshev pseudospectral method, which uses test functions that satisfy the boundary conditions as basis functions. The result shows that rapid convergence and accuracy as well as the conceptual simplicity are achieved when the pseudospectral method is applied to the solution of eigenvalue problems. Numerical examples of rectangular Mindlin plates with clamped and simply supported boundary conditions are provided for various aspect ratios and thickness-to length ratios.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.2 no.2
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• pp.1-19
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• 1998

A Chebyshev pseudospectral-finite element method is proposed for two-dimensional unsteady Navier-Stokes equation. The generalized stability and the convergence are proved strictly. The numerical results show the advantages of this method.

• Journal of Information Processing Systems
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• v.19 no.5
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• pp.563-575
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• 2023

Trajectory planning is a key technology for unmanned aerial vehicles (UAVs) to achieve complex flight missions. In this paper, a terminal constraints conversion-based Gauss pseudospectral trajectory planning optimization method is proposed. Firstly, the UAV trajectory planning mathematical model is established with considering the boundary conditions and dynamic constraints of UAV. Then, a terminal constraint handling strategy is presented to tackle terminal constraints by introducing new penalty parameters so as to improve the performance index. Combined with Gauss-Legendre collocation discretization, the improved Gauss pseudospectral method is given in detail. Finally, simulation tests are carried out on a four-quadrotor UAV model with different terminal constraints to verify the performance of the proposed method. Test studies indicate that the proposed method performances well in handling complex terminal constraints and the improvements are efficient to obtain better performance indexes when compared with the traditional Gauss pseudospectral method.

• International Journal of Precision Engineering and Manufacturing
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• v.3 no.3
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• pp.44-49
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• 2002

A study of free vibration of axisymmetric circular plates based on Mindlin theory using a pseudospectral method is presented. The analysis is based on Chebyshev polynomials that are widely used in the fluid mechanics research community. Clamped, simply supported and flee boundary conditions are considered, and numerical results are presented for various thickness-to-radius ratios.

• Journal of Mechanical Science and Technology
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• v.17 no.8
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• pp.1156-1163
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• 2003

The pseudospectral method is applied to the analysis of in-plane free vibration of circularly curved Timoshenko beams. The analysis is based on the Chebyshev polynomials and the basis functions are chosen to satisfy the boundary conditions. Natural frequencies are calculated for curved beams of rectangular and circular cross sections under hinged-hinged, clamped-clamped and hinged-clamped end conditions and the results are compared with those by transfer matrix method. The present method gives good accuracy with only a limited number of collocation points.

• Journal of Astronomy and Space Sciences
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• v.32 no.4
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• pp.379-386
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• 2015

This work presents fuel-optimal altitude maintenance of Low-Earth-Orbit (LEO) spacecrafts experiencing non-negligible air drag and J2 perturbation. A pseudospectral (direct) method is first applied to roughly estimate an optimal fuel consumption strategy, which is employed as an initial guess to precisely determine itself. Based on the physical specifications of KOrea Multi-Purpose SATellite-2 (KOMPSAT-2), a Korean artificial satellite, numerical simulations show that a satellite ascends with full thrust at the early stage of the maneuver period and then descends with null thrust. While the thrust profile is presumably bang-off, it is difficult to precisely determine the switching time by using a pseudospectral method only. This is expected, since the optimal switching epoch does not coincide with one of the collocation points prescribed by the pseudospectral method, in general. As an attempt to precisely determine the switching time and the associated optimal thrust history, a shooting (indirect) method is then employed with the initial guess being obtained through the pseudospectral method. This hybrid process allows the determination of the optimal fuel consumption for LEO spacecrafts and their thrust profiles efficiently and precisely.

• International Journal of Precision Engineering and Manufacturing
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• v.5 no.2
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• pp.53-59
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• 2004

The pseudospectral method is applied to the analysis of out-of$.$plane free vibration of circularly curved Timoshenko beams. The analysis is based on the Chebyshev polynomials and the basis functions are chosen to satisfy the boundary conditions. Natural frequencies are calculated for curved beams of circular cross sections under hinged-hinged, clamped-clamped and hinged-clamped end conditions. The present method gives good accuracy with only a limited number of collocation points.