中文摘要：

本文研究一个描述梁振动的非线性模型,其非线性由物理条件（Hooke律）导致,主要研究该模型在边界输入输出结构下局部光滑解的存在性.首先应用发展方程理论证明相关线性系统存在光滑解,然后由一系列能量估计结合不动点定理证明所考察的非线性系统局部光滑解的存在性.

英文摘要：

In this article a dynamical system modeling the bending vibrations of a quasilinear beam is considered,where the nonlinearity comes from Hooke＇s law.We are concerned with the existence of local smooth solutions to this quasi-linear beam with boundary input and output.Applying the evolution system theory,we first show that a related linear system admits a unique smooth solution.Then some energy estimates for the linear system are established. Finally the existence of local smooth solutions to the quasi-linear system is shown through fixed point arguments.