TY - JOUR

T1 - Free Vibrations of a Cylindrical Shell with a Cap. II. Analysis of the Spectrum

AU - Nesterchuk, Grigory A.

AU - Смирнов, Андрей Леонидович

AU - Филиппов, Сергей Борисович

PY - 2023/6/1

Y1 - 2023/6/1

N2 - Abstract: In this paper, the lowest eigenfrequencies and vibration modes of a structure consisting of a closed circular cylindrical shell with an end cap attached to it in the shape of a shallow spherical segment are analyzed using numerical and analytical methods. Three types of free vibrations of the structure are described. Eigenfrequencies and modes of the first-type vibrations have been studied in previous papers, being close to the frequencies and vibration modes of a shallow spherical shell. In this study, modes and frequencies of second-type- (a cylindrical shell) and third-type vibrations (a cantilever beam with a load) are analyzed. An optimization problem is solved in order to determine the values of the structure parameters and the relative thickness of elements as well as the curvature of the end cap at which the minimum value of the eigenfrequency is maximal. A comparison between the asymptotic results and the numerical ones demonstrates their good agreement.

AB - Abstract: In this paper, the lowest eigenfrequencies and vibration modes of a structure consisting of a closed circular cylindrical shell with an end cap attached to it in the shape of a shallow spherical segment are analyzed using numerical and analytical methods. Three types of free vibrations of the structure are described. Eigenfrequencies and modes of the first-type vibrations have been studied in previous papers, being close to the frequencies and vibration modes of a shallow spherical shell. In this study, modes and frequencies of second-type- (a cylindrical shell) and third-type vibrations (a cantilever beam with a load) are analyzed. An optimization problem is solved in order to determine the values of the structure parameters and the relative thickness of elements as well as the curvature of the end cap at which the minimum value of the eigenfrequency is maximal. A comparison between the asymptotic results and the numerical ones demonstrates their good agreement.

KW - asymptotic methods

KW - free vibrations

KW - joined shells

KW - optimization

UR - https://www.mendeley.com/catalogue/4c2b3b6f-55dc-38e1-acf3-01ee1de3e6a3/

U2 - 10.1134/s1063454123020139

DO - 10.1134/s1063454123020139

M3 - статья

VL - 56

SP - 245

EP - 251

JO - Vestnik St. Petersburg University: Mathematics

JF - Vestnik St. Petersburg University: Mathematics

SN - 1063-4541

IS - 2

ER -