In this paper we consider a nonlinear class viscoelastic plate equation with a lower order by perturbation of $\vec{p}(x,t)$-Laplace operator of the form $u_{tt}+{\Delta }^{2}u-{\Delta }_{\vec{p}(x,t)}u+{\int }_0^{t}g(t-s)\Delta u\left(s\right)ds-ϵ\Delta u_t+f\left(u\right)=0,(x,t)\in Q_T=\Omega \times (0,T),$ associated with initial and Dirichlet–Neumann boundary conditions.

Under suitable conditions on $g,$ $f$ and the variable exponent of the $\vec{p}(x,t)$-Laplace operator, we prove a blow up in finite time with negative initial energy in the presence of a strong damping $ϵ\Delta u_t$ $(ϵ>0)$ acting in the domain. This equation corresponds to a viscoelastic version arising in dynamics of elastoplastic flows and plate vibrations.

在本文中，我们通过扰动来考虑具有较低阶的非线性类粘弹性板方程 $\vec{p}（X，Ť）$-表格的拉普拉斯运算符 ${ü}_{ŤŤ}+{\Delta }^2ü-{\Delta }_{\vec{p}（X，Ť）}ü+{\int }_0^{Ť}G（Ť-s）\Delta ü（s）ds-ϵ\Delta {ü}_{Ť}+F（ü）=0，（X，Ť）\in {问}_{Ť}=\Omega \times （0，Ť），$ 与初始和Dirichlet-Neumann边界条件相关。

在合适的条件下 $G，$ $F$ 和变量的指数 $\vec{p}（X，Ť）$-拉普拉斯算子，我们证明了在强阻尼存在下具有负初始能量的有限时间内的爆炸 $ϵ\Delta {ü}_{Ť}$ $（ϵ>0）$在领域中行动。该方程对应于在弹塑性流动和板振动的动力学中产生的粘弹性形式。