Nonlinear Flutter of Viscoelastic Rectangular Plates and Cylindrical Panels of a Composite with a Concentrated Masses
B. Kh. Eshmatov, Kh. Eshmatov, D. A. Khodzhaev
Keywords: Kirchhoff–Love hypothesis, composite materials, viscoelastic rectangular plate, viscoelastic cylindrical panel, concentrated mass, Bubnov–Galerkin method, nonlinear flutter
Abstract
The problem of flutter of viscoelastic rectangular plates and cylindrical panels with concentrated masses is studied in a geometrically nonlinear formulation. In the equation of motion of the plate and panel, the effect of concentrated masses is accounted for using the δ-Dirac function. The problem is reduced to a system of nonlinear ordinary integrodifferential equations by using the Bubnov–Galerkin method. The resulting system with a weakly singular Koltunov–Rzhanitsyn kernel is solved by employing a numerical method based on quadrature formulas. The behavior of viscoelastic rectangular plates and cylindrical panels is studied and the critical flow velocities are determined for real composite materials over wide ranges of physicomechanical and geometrical parameters.
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