Akademik Veri Yönetim Sistemi
18th International Conference Acoustics and Vibration of Mechanical Structures, AVMS 2025, Timisoara, Romanya, 30 - 31 Mayıs 2025, cilt.345 SPPHY, ss.23-33, (Tam Metin Bildiri)
Some of the recent developments in perturbation methods are discussed. A severe restriction of the classical perturbation methods is the validity of solutions for small perturbation parameters. There are attempts to validate the solutions for large perturbation parameters. One such attempt is the combination of Multiple Scales and Lindstedt Poincare method called the Multiple Scales Lindstedt Poincare method. With a special expansion of the frequency, it was shown that admissible solutions can be constructed for a variety of nonlinear dynamics problems for arbitrarily large perturbation parameters. Another attempt to validate solutions for larger perturbation parameters is to incorporate iteration techniques with the perturbation expansions. A systematic theory was constructed in which the general method was called Perturbation Iteration Method. The method is a unification of several perturbation iteration algorithms. Finally, a new interpretation of the advanced perturbation techniques which eliminates the deficiencies of the regular perturbation expansions is given. In this new interpretation, the functional shift theory is employed to explain the differences between the regular expansions and the more advanced techniques. While the regular expansions allow for functional shifts only in the vertical direction, the advanced techniques incorporate also the horizontal shifts so that the secular non-physical blow-up terms can be eliminated. Based on the functional shift theory, a new perturbation method namely the shift perturbation method is also discussed. A variant of this new method enables admissible solutions for large perturbation parameters in treating some of the strongly nonlinear systems also.