应变梯度弹性杆中波传播的反问题  

Inverse Problems of Waves Propagation in the Strain Gradient Elastic Rods

作　　者：邓丽莉[1] 那仁满都拉[1] 

机构地区：[1]内蒙古民族大学物理与电子信息学院,内蒙古通辽028043

出　　处：《内蒙古民族大学学报（自然科学版）》2015年第3期192-196,共5页Journal of Inner Mongolia Minzu University：Natural Sciences

基　　金：国家自然科学基金资助项目(11462019;10862003);内蒙古民族大学科研创新团队资助项目

摘　　要：研究了应变梯度弹性细杆中谐波和波包传播的反问题.首先基于Mindlin理论,介绍了描述应变梯度弹性杆中纵波传播的波方程.其次由频散关系、相速度和群速度给出的相关信息,研究了谐波和波包传播的反问题.结果表明,在频散谐波传播时,由三种不同波数相应的频散关系,可以唯一地确定波方程的未知系数;在频散波包传播时,利用相速度、群速度以及可测参数d可以唯一地确定波方程的未知系数,即杆材料的未知参数.本文结果可用于应变梯度弹性杆的无损检测问题.In this paper, we studied the inverse problems of harmonic waves and wave packets propagation in the strain gradient elastic thin rods. Firstly, a wave equation which describes longitudinal wave propagation in strain gra-dient elastic rod was introduced based on the Mindlin theory. Secondly, the inverse problem for harmonic waves and wave packets was investigated based on relevant informations given from the dispersion relation, phase and group ve-locities. The results showed that the unknown coefficients of wave equation could be uniquely determined by the cor-responding dispersion relations of three kind wave number, when the dispersive harmonic wave propagation;the un-known parameters of the wave equation, namely the unknown parameters of rod material would be uniquely deter-mined in the case of dispersive wave packet propagation, by using the phase velocity, group velocity and measurable parameter d . Our results could be used in the nondestructive testing(NDT)of strain gradient elastic rods.

关 键 词：应变梯度弹性杆 相速度 群速度 反问题 

分 类 号：TB34[一般工业技术—材料科学与工程] O347.4[理学—固体力学]