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文章编号： 1672-6987（2024）03-0147-05； DOI： 10.16351/j.1672-6987.2024.03.020
霍鑫泰， 王苹*（青岛科技大学 数理学院; 数学与跨学科科学研究所，山东 青岛 266061）
摘要： 通过将超大型浮式结构物（a very large floating structure,简称VLFS）模拟为黏弹性薄板，本工作对VLFS的非线性水弹性响应进行了解析研究。运用同伦分析方法（the homotopy analysis method,简称HAM），计算出速度势和板挠度的近似迭代解，并根据计算结果着重探究了几个重要的物理参数对黏弹性板形变的影响。结果发现：黏弹性板的挠度随着黏弹性时间、杨氏模量和板厚度增加而减少，而板挠度随着入射波波幅的增加而增加。最后，还对非线性色散关系和波幅之间的联系进行了探讨。
关键词： 黏弹性板； 同伦分析方法； 非线性水弹性
中图分类号： O 352; O 343文献标志码： A
引用格式： 霍鑫泰， 王苹. 黏弹性板水弹性响应的非线性分析［J］. 青岛科技大学学报(自然科学版), 2024, 45(3): 147-151.
HUO Xintai, WANG Ping. Nonlinear analysis of a viscoelastic floating structure［J］. Journal of Qingdao University of Science and Technology（Natural Science Edition), 2024， 45（3）： 147-151.
Nonlinear Analysis of A Viscoelastic Floating Structure
HUO Xintai, WANG Ping(College of Mathematics and Physics； Institute of Mathematics and Interdisciplinary Science,
Qingdao University of Science and Technology, Qingdao 266061, China)
Abstract: The nonlinear hydroelastic respond of a very large floating structure (VLFS), which is modeled as a thin viscoelastic plate, is studied analytically. With the aid of the homotopy analysis method(HAM), we derive the iterative solutions of the velocity potential and the plate deflection, and consider the influences of several important physical parameters on the viscoelastic plate. It is found that the deflection of the viscoelastic plate decreases when the retardation time of the plate, Young′s modulus, and the thickness of the plate increase. While the deflection increases with an increasing wave amplitude of the incident wave. Further, the connection between the nonlinear dispersion relation and the wave amplitude is also discussed.
Key words: viscoelastic plate; homotopy analysis method (HAM); nonlinear hydroelasticity
收稿日期： 2023-06-09
基金项目： 青岛市博士后人员应用研究项目(020022034).
作者简介： 霍鑫泰(1999—),男,硕士研究生.*通信联系人.
