On the viscoelastic instability of Timoshenko viscoelastic beams and Mindlin viscoelastic plates under compressive loads

Abstract This paper proposes the time-dependent instability of Timoshenko viscoelastic beams and Mindlin viscoelastic plates with different geometrical and material properties subjected to constant axial and inplane compressive loads, respectively. The goal of this study is to introduce a novel crit...
Ausführliche Beschreibung

Abstract This paper proposes the time-dependent instability of Timoshenko viscoelastic beams and Mindlin viscoelastic plates with different geometrical and material properties subjected to constant axial and inplane compressive loads, respectively. The goal of this study is to introduce a novel critical condition in which the transversal displacements diverge to infinity with time, while the applied compressive load is much smaller than the critical compressive load at time zero. Assuming constant bulk modulus, the constitutive equations are written based on the Boltzmann integral law. Solving an eigenvalue problem in the Laplace–Carson domain, the time responses of Timoshenko viscoelastic beams and Mindlin viscoelastic plates are formulated explicitly. Numerical results show that the viscoelastic critical load depends only on the material properties and is independent of the geometrical properties. Several numerical results are presented to study the effect of geometrical and material parameters on the time behavior of moderately thick viscoelastic plates. Ausführliche Beschreibung