ABSTRACT To well understand the characteristics of the oscillations of suspension bridges, we consider a class of viscoelastic plate equations with mixed boundary conditions consisting of simply supported and free boundary conditions to study the interactions between the viscoelastic dissipation, restoring force, frictional damping, and nonlinear source terms and their effects on the dynamical behavior of solution. Based on the so‐called potential well theory, we obtain the global existence and exponential decay of solution with positive initial energy that is less than the potential well depth. By weakening the viscoelastic dissipation so that the nonlinear source term is dominant, we obtain the finite‐time blowup of solution with negative initial energy and null initial energy , respectively. By further weakening the viscoelastic dissipation, we derive the finite‐time blowup of solution with positive initial energy controlled by the shrunk potential well depth . In addition, we provide estimates on the upper bound of the blow‐up time.
Liu et al. (Sun,) studied this question.