Nonconservative stability of viscoelastic plates subject to triangularly distributed follower loads

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.