Structure of integrals of equations of oscillations of a conical shell closed at a vertex
DOI:
https://doi.org/10.37863/umzh.v73i10.6702Keywords:
варіаційні метроди, сингулярно збурені крайові задачі, тонкостінні оболонки обертанняAbstract
We consider a system of differential equations, which describes the free oscillations of a thin-walled conical shell of rotation with a vertex. Based on the analytical theory of systems of differential equations with a small parameter at the highest derivative and equations with a regular singular point, we establish the formal structure of regular integrals of the original equations.
References
A. G. Aslanyan, V. B. Lidskij, Raspredelenie sobstvennyh chastot tonkih uprugih obolochek, Nauka, Moskva (1974).
B. Vazov, Asimptoticheskie razlozheniya reshenij obyknovennyh differencial'nyh uravnenij, Mir, Moskva(1968).
M. I. Vishik, L. A. Lyusternik, Regulyarnoe vyrozhdenie i pogranichnyj sloj dlya linejnyh differencial'nyh uravnenij s malym parametrom, Uspekhi mat. nauk, 1957, 12, vyp. 5(77), 3 – 122 (1957).
G. I. Pshenichnov, Malye svobodnye kolebaniya uprugih obolochek vrashcheniya, Inzh. zhurn., 5, vyp. 4, 685 – 690 (1965).
A. L. Gol'denvejzer, V. B. Lidskij, P. E. Tovstik, Svobodnye kolebaniya tonkih uprugih obolochek, Nauka, Moskva (1979).
A. B. Vasil'eva, V. F. Butuzov, Asimptoticheskie razlozheniya reshenij singulyarno vozmushchennyh uravnenij, Nauka, Moskva (1973)