TY - JOUR

T1 - Free Vibration Frequencies of a Circular Thin Plate with Variable Parameters

AU - Smirnov, A. L.

PY - 2020/7/1

Y1 - 2020/7/1

N2 - Abstract: We study transverse vibrations of an inhomogeneous circular thin plate in this work. Using the perturbation method, asymptotic formulas are obtained for free-vibration frequencies of a plate whose thickness and Young’s modulus linearly depend on radius. The effect of the boundary conditions on frequencies and the behavior of frequencies for a plate with the fixed mass are analyzed. For lower frequencies of the plate, the asymptotic results are compared with the results of analysis by finite elements.

AB - Abstract: We study transverse vibrations of an inhomogeneous circular thin plate in this work. Using the perturbation method, asymptotic formulas are obtained for free-vibration frequencies of a plate whose thickness and Young’s modulus linearly depend on radius. The effect of the boundary conditions on frequencies and the behavior of frequencies for a plate with the fixed mass are analyzed. For lower frequencies of the plate, the asymptotic results are compared with the results of analysis by finite elements.

KW - free vibrations of plates

KW - inhomogeneous circular plate

KW - perturbation method

KW - TRANSVERSE VIBRATION

KW - THICKNESS

UR - http://www.scopus.com/inward/record.url?scp=85090030763&partnerID=8YFLogxK

U2 - 10.1134/S1063454120030140

DO - 10.1134/S1063454120030140

M3 - Article

AN - SCOPUS:85090030763

VL - 53

SP - 351

EP - 357

JO - Vestnik St. Petersburg University: Mathematics

JF - Vestnik St. Petersburg University: Mathematics

SN - 1063-4541

IS - 3

ER -