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Floquet Theory and Newton’s Method
- Source :
- Journal of Applied Mechanics. 40:1091-1096
- Publication Year :
- 1973
- Publisher :
- ASME International, 1973.
-
Abstract
- Application of Newton’s method to nonlinear vibration problems can lead to a sequence of nonhomogeneous ordinary differential equations with periodic coefficients. The form of the complementary solutions are known from Floquet theory. This paper suggests a method for avoiding “secular terms” that grow with time in the particular solution. The method consists of finding a single periodic solution of the complementary solutions and its adjoint. If the periodic solution exists, a frequency correction can be computed that eliminates secular terms. After the frequency correction, the rest of the particular solution is periodic and can be computed by the infinite determinant method or other numerical methods. In oversimplified terms, the procedure is to find the improved approximation to the period by variation of parameters and the next approximation to the amplitudes by undetermined coefficients which is a simpler computation than variation of parameters.
- Subjects :
- Floquet theory
Mechanical Engineering
Numerical analysis
Mathematical analysis
Condensed Matter Physics
Variation of parameters
Poincaré–Lindstedt method
Method of undetermined coefficients
symbols.namesake
Mechanics of Materials
Ordinary differential equation
symbols
Newton's method
Annihilator method
Mathematics
Subjects
Details
- ISSN :
- 15289036 and 00218936
- Volume :
- 40
- Database :
- OpenAIRE
- Journal :
- Journal of Applied Mechanics
- Accession number :
- edsair.doi...........d61695639ada80b3e7fe07afec7c8b76