矩形薄膜受迫横振动问题的求解及可视化  

Solution and visualization of forced transverse vibration of rectangular thin films

作　　者：周纪晨 郭琴[1] ZHOU Ji-chen;GUO Qin(College of Physics and Communication Electronics,Jiangxi Normal University,Nanchang,Jiangxi 330022,China)

机构地区：[1]江西师范大学物理与通信电子学院,江西南昌330022

出　　处：《大学物理》2022年第3期56-60,共5页College Physics

基　　金：江西省高等学校教学改革研究重点项目(JXJC-20-2-11)资助。

摘　　要：膜的横振动分析在乐器膜、耳膜以及植物细胞膜中有着广泛的应用价值.相比自由振动,受迫膜振动问题的研究更符合应用实际.本文采用数学物理定解问题的傅里叶级数法与冲量定理法,对四周固定的均匀矩形薄膜振动问题进行了研究,得到了此类问题在受迫振动下的解析解,并对其振动状态进行了可视化分析.研究发现:一维弦振动解法同样可为二维有界膜振动问题提供简便的求解途径,且膜振动将呈现更加丰富的特点.本文的二维非齐次振动问题的冲量定理解法还可推广到二维有源(汇)输运问题中去.Transverse vibration analysis of membranes is widely used in musical instrument membranes,ear membranes and plant cell membranes.Comparing with free vibration,the study of forced membrane vibration is more practical.In this paper,the vibration problem of a uniform rectangular thin film fixed on all sides is studied by using the Fourier series method and the impulse theorem,the analytical solution of the problem under forced vibration is obtained,and its vibration state is analyzed visually.It is found that the solution of one-dimensional string vibration can also provide a simple and convenient way to solve the problem of two-dimensional bounded membrane vibration,and the membrane vibration will present more abundant characteristics.The impulse theorem solution of the two-dimensional non-homogeneous vibration problem can also be extended to the two-dimensional active(sink)transport problem.

关 键 词：矩形薄膜 受迫振动 冲量定理法 傅里叶级数法 

分 类 号：O411.1[理学—理论物理]