Mechanics of Deformable Solids
DOI: http://www.dx.doi.org/10.24866/2227-6858/2020-1-2
Sysoev O., Dobryshkin A.
OLEG SYSOEV, Doctor of Engineering Sciences, Professor, Dean of the Faculty of Cadastre and Construction,
ScopusID: 54080506700, e-mail: fks@knastu.ru
ARTEM DOBRYSHKIN, Candidate of Engineering Sciences, Associate Professor, Department Construction and Architecture,
ScopusID: 57199398851, e-mail: wwwartem21@mail.ru
Institution of Higher Education Komsomolsk-on-Amur State University
27 Lenin St., Komsomolsk-on-Amur, Russia, 681013
Natural vibrations of a shallow shell with mixed
jamming-hinge boundary conditions and a small attached mass
Abstract: Open cylindrical shells are widely used in today’s structures: for example, in construction, aviation, power generation, oil production and other industries. During operation, shell structures are affected by short-term cyclic effects which cause forced vibrations of structures and buildings resulting in activation of internal dynamic mechanisms. Such mechanisms modify own vibrations of structures, which significantly affects strength characteristics of the shell. Attached masses are often placed on such structures: such as aircraft engines, antenna installations, outboard fuel tanks, air conditioners, lights, and viewing platforms. The attached masses modify the stress–strain state and parameters of the shell’s natural vibrations. This leads to changes in frequency and amplitude of vibrations of the structures, and causes a resonance phenomenon, which can destroy the structure. The new mathematical model has been developed by the authors of this Article to improve accuracy of shell vibration calculations. Application of this model allows to avoid the probable undesirable consequences such as negative deformations of buildings and structures, shells, equipment, mechanisms, etc. The mathematical model is developed on the basis of the general equation of plate oscillations — the Germain–Lagrange equation with an additional term, the physical meaning of which is the initial irregularity of the form due to a small attached mass. The mathematical model is calculated under the mixed pinching–hinge boundary conditions. Kirchhoff–Love hypotheses are accepted as assumptions. The mechanism of natural vibrations of an open shell with mixed jamming–hinge boundary conditions and an attached mass is analyzed. Using the recursive perturbation theory convertible into a Padé approximation, the frequency characteristics and the values of the first eigenvalue of the problem are determined for wave-forming parameter, which equals to1. The behavior of an open shell with a small attached mass is considered using the method of integral equations. Dependences of influence of the length of the jamming sections on the first eigenvalue of frequencies of free vibrations are determined; dependences are calculated using the recursive perturbation theory, the Padé approximation, and the method of integral equations. All three curves provide almost identical results for all values of the parameter μ, which indicates high reliability of the developed mathematical model of oscillations of open thin-walled shells with a small attached mass. Results of studies described in the article can be useful for companies specialized in design of structures which consist of or have inclusions in the form of plates and sloping open shells.Keywords: open shell, vibrations, attached mass, frequency spectrum, hinged description, frequency.
See the reference in English at the end of the article