On certain methods of solving systems of integrodifferential equations encountered in viscoelasticity problems

Flutter of a viscoelastic plate in a supersonic gas flow

“…As the parameter increases from 2.2 to 3.2, the difference between the critical speeds defined by (1), (2), and (3) increases. For example, when l = 2.2, the flutter speed is 1575 m/sec by formula (1), 1302 m/sec by formula (2), and 1288 m/sec by formula (3). The difference is significant.…”

“…In the elastic case, the flutter speeds of a square plate found by formulas (1), (2), and (3) are the following, respectively: 1025, 1009, 1003 m/sec. The difference is insignificant.…”

“…Eliminating F nm (t) from this system, we get the following nonlinear IDE for w nm (t): To solve the nonlinear flutter problem for viscoelastic plates described by (5), (7), and (9), we use a numerical method that eliminates the weak singularities of the integral and integro-differential equations [1,2]. We will apply this method to systems (9).…”

Dynamic Instability of Viscoelastic Plate in Supersonic Flow

“…Destabilization effect of the internal friction in a material was mentioned first in [5] and later in other works [6][7]. The buckling analysis of viscoelastic plates subjected to dynamic loading in a nonlinear formulation with weak singular relaxation kernel is presented in [8][9][10]. The dynamic stability of fiber-reinforced laminated rectangular plates used first-order shear deformation theory was carried out in [11].…”

“…Viscoelastic body model is utilized to describe material damping was discussed in [12]. This relates the stability problem for elastic systems with that for viscoelastic systems [10,12]. The BubnovGalerkin method is usually applied for solving the problems.…”