A note on blow-up of solutions for a class of fourth-order wave equation with viscous damping term

In this note, we study a class of fourth-order wave equation with viscous damping term and illuminate that the condition on the relationship between and p in Theorem 4.2 of Xu et al. (Appl Anal. 2013;92(7):1403–1416) can be removed. This is achieved by adopting and modifying the so-called concavity method. Furthermore, we establish a blow-up result for positive initial energy without the relationship between and p as well.