Nonconservative stability of viscoelastic plates subject to triangularly distributed follower loads

Abstract

Divergence and flutter instabilities of viscoelastic rectangular plates under triangularly distributed tangential follower loads are studied. Two sets of boundary conditions are considered, namely, simply supported plates and plates with a combination of clamped and simply supported edges. The constitutive relations for the viscoelastic plates are of Kelvin-Voigt type with the effect of viscoelasticity on stability studied numerically. The method of solution is differential quadrature which is employed to discretize the equation of motion and the boundary conditions leading to a generalized eigenvalue problem. After verifying the method of solution, numerical results are given for the real and imaginary parts of the eigenfrequencies to investigate flutter and divergence characteristics and dynamic stability of the plates with respect to various problem parameters.

Systematic use of mathematical concepts in professional training of students

“…Therefore, the methods and problems of the theory of hereditary elasticity attract much attention from researchers. There are a significant number of publications devoted to solving problems of calculating the characteristics of viscoelastic thin-walled structures [2][3][4][5][6][7]. Despite the numerous studies devoted to viscoelastic thin-walled structures, the bending-torsional flutter of the viscoelastic wing of aircraft has not been studied so far.…”

Computer simulation of oscillatory processes of viscoelastic elements of thin-walled structures in a gas flow

“…The development of problems on the flutter-plate strip, plates and panels with account of viscoelastic properties of structure material is reflected in publications by Mojtaba Asgari, Mohammad Reza Permoon, Hassan Haddadpou [5], Tytti Saksa et al [6], Wei Tao Zhao, Tian JunYu, Xiao Dong Yang [7], Mouafo T.A. Robinson, Sarp Adali [8], Mouafo T.A. Robinson, Sarp Adali [9], Xiaochen Wang, Zhichun Yang, Wei Wang, WeiTian [10], B.Kh.Eshmatov et al [11], M.Mirsaidov et al [34,35] and others.…”

“…Robinson, Sarp Adali [9], Xiaochen Wang, Zhichun Yang, Wei Wang, WeiTian [10], B.Kh.Eshmatov et al [11], M.Mirsaidov et al [34,35] and others. In [5][6][7][8][9], the Kelvin-Voigt model is used to describe the strain processes occurringin viscoelastic materials.…”