Nonconservative stability of viscoelastic rectangular plates with free edges under uniformly distributed follower force

• Dynamic stability of viscoelastic plates under nonconservative loading is studied.
• CFFF plates exhibit flutter instability while SFSF plates divergence instability.
• Viscoelastic material has more effect on the stability behavior of CFFF plates.
• Critical load for loss of stability is smaller for SFSF as compared to CFFF plates.
• Aspect ratio is found to be of minor influence on the critical load.

Dynamic stability of viscoelastic rectangular plates under a uniformly distributed tangential follower load is studied. Two sets of boundary conditions are considered, namely, clamped in one boundary and free in other boundaries (CFFF) and two opposite edges simply supported and other two edges free (SFSF). By considering the Kelvin–Voigt model of viscoelasticity, the equation of motion of the plate is derived. The differential quadrature method is employed to obtain the numerical solution and it is verified against known results in the literature. Numerical results are given for the real and imaginary parts of the eigenfrequencies to investigate the divergence and flutter instabilities. It is observed that the type of stability differs for CFFF and SFSF plates indicating the strong influence of the boundary conditions on the dynamic stability of viscoelastic plates. In particular it is found that CFFF plates undergo flutter instability and SFSF plates divergence instability. One consequence is that SFSF plates become unstable at a load less than the load for CFFF plates as the effects of viscoelasticity as well as the aspect ratio are found to be minor for SFSF plates.