On the Solution of Dynamic Stability Problem of Functionally Graded Viscoelastic Plates with Different Initial Conditions in Viscoelastic Media

The widespread use of structural elements consisting functionally graded (FG) materials in advanced technologies has led to extensive research. Due the difficulties encountered during modeling and problem solving, number studies on dynamic behavior made FG viscoelastic is quite limited compared examining elastic materials. This study one first attempts solve dynamical by mathematical plates (FG-VE-Ps) media together with different initial conditions. FG-VE-Ps foundations (VE-Fs) are assumed be under compressive edge load longitudinal direction. governing equations for VE-Fs derived using Boltzmann Volterra concepts. reduced solution integro-differential equation system Galerkin method. Then, performing Laplace transforms, new analytical expressions time-dependent deflection function critical time at conditions found. loss stability modeled cover three time-varying ranges: range which decreases; second transition interval; third increase function, leads stability. corresponding sharp defined as time, determined both theoretically numerically. results obtained various methods confirm their accuracy. Finally, effects VE-Fs, VE material properties, profiles studied