A Generalized Method of Solution

The method of solution of the considered problem is provided step-by-step. The application of the boundary perturbation technique, the Laplace transform w.r.t time, the variable separation technique, transform inversion, and stability loss criterion is presented. Expressions for different parameters (e.g., displacements, stresses, strains, constitutive relations, and boundary conditions) related to the zeroth and first approximation are derived. The sufficiency of the zeroth and first approximation values for the stability loss problem is also discussed. The equations of a previously developed technique to analyze buckling problems in viscoelastic media (using Bessel and Macdonald functions) are also presented herein. Using this method, the final form of equations for displacement are obtained which are used to find the critical buckling forces and critical buckling times.