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Journal of Applied Mechanics and Technical Physics

2013 year, number 4

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: KirchhoffLove hypothesis, composite materials, viscoelastic rectangular plate, viscoelastic cylindrical panel, concentrated mass, BubnovGalerkin 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 KoltunovRzhanitsyn 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.