Journal ArticleDOI
Numerical methods for the treatment of periodic systems with applications to structural dynamics and helicopter rotor dynamics
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TLDR
The numerical techniques available for analyzing the stability, linear response and nonlinear response of periodic systems, which are governed by ordinary differential equations with periodic coefficients, are discussed in this article.About:
This article is published in Computers & Structures.The article was published on 1990-01-01. It has received 42 citations till now. The article focuses on the topics: Numerical stability & Nonlinear system.read more
Citations
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Variational time integrators
TL;DR: In this paper, the authors review and further develop the subject of variational integration algorithms as it applies to mechanical systems of engineering interest, and present selected numerical examples which demonstrate the excellent accuracy, conservation and convergence characteristics of AVIs.
Galerkin's Procedure for Nonlinear Periodic Systems (関数方程式の近似解法研究会報告集)
TL;DR: In this paper, it was shown that Galerkin's procedure is always available for twice continuously differentiable periodic differential systems if a periodic solution is restricted to an isolated periodic solution.
Journal ArticleDOI
A multiharmonic method for non‐linear vibration analysis
TL;DR: In this article, a multiharmonic method for analysis of non-linear dynamic systems submitted to periodic loading conditions is presented, based on a systematic use of the fast Fourier transform.
Journal ArticleDOI
Dynamic Analysis of Planetary Gears With Bearing Clearance
Yi Guo,Robert G. Parker +1 more
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Nonlinear dynamics and stability of wind turbine planetary gear sets under gravity effects
TL;DR: In this article, a modified harmonic balance method that includes simultaneous excitations is applied to a lumped-parameter planetary gear model including gravity, fluctuating mesh stiffness, bearing clearance, and nonlinear tooth contact to obtain the dynamic response of the system.
References
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Journal ArticleDOI
Numerical Recipes, The Art of Scientific Computing
Book
Ordinary differential equations
TL;DR: In this article, the Poincare-Bendixson theory is used to explain the existence of linear differential equations and the use of Implicity Function and fixed point Theorems.
Journal ArticleDOI
Nineteen Dubious Ways to Compute the Exponential of a Matrix
Cleve B. Moler,Charles Van Loan +1 more
TL;DR: In this article, the exponential of a matrix could be computed in many ways, including approximation theory, differential equations, the matrix eigenvalues, and the matrix characteristic polynomial.
Book
Applied Linear Algebra
TL;DR: In this article, the authors introduce geometric vectors and vector spaces, as well as linear transformations and matrix algebras, for solving equations and finding inverses in matrix algebra.
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