We investigate the longitudinal and transversal vibrations of the viscoelastic beam with nonlinear tension and nonlinear delay term under the general decay rate for relaxation function. The existence theorem is proved by the Faedo–Galerkin method and using suitable Lyapunov functional to establish the general decay result.

中文翻译：

---

非线性时滞非线性粘弹性二维梁解的存在性和一般衰减

我们研究了在松弛函数的一般衰减率下具有非线性张力和非线性延迟项的粘弹性梁的纵向和横向振动。存在定理由 Faedo-Galerkin 方法证明，并使用合适的 Lyapunov 泛函建立一般衰减结果。