Formulation of the flutter problem of a plate of variable thickness of arbitrary shape in the plan


DOI: 10.34759/trd-2022-125-04

Аuthors

Algazin S. D.1*, Solovyov G. H.2**

1. Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences, 101-1, prospekt Vernadskogo, Moscow, 119526, Russia
2. Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia

*e-mail: algazinsd@mail.ru
**e-mail: 19tatarin45@rambler.ru

Abstract

By the method of mathematical modeling the flutter of orthotropic plate of rectangular shape in plan at different angles of attacking stream is investigated. For numerical modeling of unstable oscillations of a plate the effective numerical algorithm without saturation which allows on a rare grid to receive admissible accuracy in the approached decision is offered. The type of eigenform depending on the angle of direction of the attacking flow velocity vector is studied numerically. The resulting quadratic eigenvalue problem can be reduced to a double sized standard linear eigenvalue problem. The term «panel flutter» refers to the flutter of a thin plate, shell, or membrane when typically, one of the surfaces is exposed to airflow and the other to still air. The panel then experiences elastic, inertial and aerodynamic forces, which can lead to dynamic instability of the structure. The paper shows that the resulting quadratic problem for eigenvalues can be reduced to a standard linear problem for eigenvalues of twice the size. Questions related to the existence, uniqueness and regularity of the solution are not considered in the work. We refer the interested reader to the work. The first recorded occurrence of flutter for circular cylindrical projectiles appears to have been on a German V-2 rocket. The study of the stability of the oscillations of a thin plate of arbitrary thickness in the plan, which in the plane , occupies the region with the boundary and is blown by the gas flow, leads to a non-self-adjoint spectral problem for the amplitude value of the deflections , , which is obtained by generalizing the results of Kiyko I. A. and Ilyushin A. A.

Keywords:

numerical methods without saturation, plate flutter № АААА-А20-120011690132-4

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