We present an efficient isogeometric analysis (IGA) formulation for nonlinear vibration problems of viscoelastic plates. The formulation is based on higher-order shear deformation theory (HSDT), which is guaranteed by $p$-order nonuniform rational B-splines (NURBS) resulting in $C^{p-1}$ continuity in the domain. The governing equations of motion are derived from Hamilton’s principle. The generalized multi-axial Maxwell model is used to express the viscoelastic constitutive equations in global coordinates. The performance of developed approach is demonstrated through several numerical examples. We show that our approach yields more realistic solutions than conventional FEA, especially for coarse discretizations. We find that $C^3$-NURBS provide higher accuracy concerning the nonlinear vibration amplitude than $C^2$-NURBS. Viscoelastic plates have several active vibration modes adjacent to the fundamental oscillation mode due to the combination of long-time creep and short-time shear moduli. Furthermore, the resultant creep strain leads to large deformations of viscoelastic plates and intensifies the dynamic stress concentration factors. The creep deflection of the plates rapidly increases with damping under sustained loads when the support restrains are released. We observe that the long-time stress-to-thickness ratio is constant for various slenderness ratios, which is relevant during creep.

我们为粘弹性板的非线性振动问题提供了一种有效的等几何分析（IGA）公式。该公式基于高阶剪切变形理论（HSDT），可以通过$p$阶非均匀有理B样条（NURBS）导致 $C^{p-\mathrm{1个}}$域的连续性。运动的控制方程式是从汉密尔顿原理导出的。用广义的多轴麦克斯韦模型在整体坐标系下表示粘弹性本构方程。通过几个数值示例证明了所开发方法的性能。我们证明，与传统的有限元分析相比，我们的方法可提供更现实的解决方案，尤其是对于粗离散化而言。我们发现$C^3$-NURBS提供比非线性振动幅度更高的精度 $C^2$-NURBS。由于长期蠕变和短期剪切模量的结合，粘弹性板具有与基本振荡模式相邻的几种主动振动模式。此外，所产生的蠕变应变导致粘弹性板的大变形并加剧了动态应力集中系数。当释放支撑约束时，在持续载荷下，板的蠕变挠度随着阻尼而迅速增加。我们观察到，长时间的应力-厚度比对于各种细长比是恒定的，这在蠕变期间是相关的。