Topic
Frobenius method
About: Frobenius method is a research topic. Over the lifetime, 221 publications have been published within this topic receiving 3652 citations. The topic is also known as: method of Frobenius.
Papers published on a yearly basis
Papers
1 Jan 2000
TL;DR: In the 1890s, Henri Poincare took upon himself the task of gleaning as much information from the DEs describing the whole solar system as was possible and the result was the invention of one of the most powerful branches of mathematics (topology) and the realization that the qualitative analysis of (nonlinear) DEs could be very useful.
Abstract: A variety of techniques including the Frobenius method of infinite power series could solve almost all linear DEs of physical interest. However, some very fundamental questions such as the stability of the solar system led to DEs that were not linear, and for such DEs no analytic (including series representation) solution existed. In the 1890s, Henri Poincare, the great French mathematician, took upon himself the task of gleaning as much information from the DEs describing the whole solar system as was possible. The result was the invention of one of the most powerful branches of mathematics (topology) and the realization that the qualitative analysis of (nonlinear) DEs could be very useful.
809 citations
TL;DR: In this article, the free bending vibration of rotating tapered beams is investigated by using the dynamic stiffness method, and the expressions for bending rotation, shear force and bending moment at any cross-section of the beam are also obtained in explicit analytical form.
215 citations
TL;DR: In this article, an exact solution procedure is formulated for the buckling analysis of rectangular plates having two opposite edges (x = 0 and a) simply supported when these edges are subjected to linearly varying normal stresses σx−−N0[1−α(y/b)]/h, where h is the plate thickness.
147 citations
TL;DR: In this paper, exact solutions for free vibration and buckling of rectangular plates having two opposite edges (x = 0 and a) simply supported and the other two (y=0 and b) clamped, with the simply supported edges subjected to a linearly varying normal stress σx=−N0[1−α(y/b)]/h, where h is the plate thickness.
142 citations
TL;DR: In this paper, the in-plane free vibration analysis of rotating beams using an exact dynamic stiffness method is addressed. But the analysis includes the Coriolis effects in the free vibratory motion as well as the effects of an arbitrary hub radius and an outboard force.
89 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 14 |
| 2020 | 21 |
| 2019 | 18 |
| 2018 | 10 |
| 2017 | 6 |
| 2016 | 7 |