Flutter instability of damped plates under combined conservative and nonconservative loads

Abstract

The combined flutter and divergence instability of plates of arbitrary geometry subjected to any type of boundary conditions under interior and edge conservative and nonconservative loads are solved in presence of external and internal damping. In contrast to previous investigations, the membrane stress resultants are not in general uniform, since they result from plane stress problem under the given body forces (conservative and nonconservative) and the prescribed inplane boundary conditions. The differential equations of the problem are derived using Hamilton's principle. The resulted initial boundary value problem is solved using the analog equation method (AEM), which is a BEM-based domain meshless method. The combined action of conservative and nonconservative forces is also investigated. Several plates have been studied and useful conclusions on the effect of boundary conditions and damping on flutter load have been drawn. The obtained numerical results demonstrate the accuracy of the developed method and its capability to solve realistic engineering problems.

BEM for Other Plate Problems

“…This technique has been successfully employed to solve plate problems [9][10][11]. (3.20b), which involves the kernel v 1 x, y ð Þ.…”

BEM for Dynamic Analysis of Plates

“…Another method that has been widely used is the Laplace transform method. The AEM has been employed to solve many dynamic plate problems such as plates with variable thickness [11,12], plates reinforced with beams [13][14][15], stability and post-buckling plate problems and plates under nonconservative loads (linear and nonlinear flutter instability) [16,17], nonlinear vibrations of viscoelastic plates described with integer or fractional derivative models [18], as well as plate thickness optimization problems under constant material volume to maximize the aerodynamic pressure [19]. The inverse Laplace transform gives the solution in the time domain [5].…”

“…With increasing the nonconservative load, it reaches a critical value, for which the plate becomes unstable as it performs large amplitude vibrations. The BEM has been employed recently and has successfully solved linear [16] and nonlinear [17] flutter problems for plates of arbitrary geometry and boundary conditions. The consequence of this response is the failure of the structure.…”

Nonlinear flutter instability of thin damped plates: A solution by the analog equation method

“…Due to the complexity of the governing equations, only approximate and numerical techniques such as the Rayleigh-Ritz method and the FEM have been used, which however treat plates with relatively simple geometry (rectangular, triangular) under simple load distributions and boundary (support) conditions. Finally, the linear flutter and divergence instability of a plate of arbitrary geometry with any type of boundary conditions has been investigated recently by Babouskos and Katsikadelis [2009].…”