基于级数法的热弹各向异性层合板兰姆波频散特性分析  

ANALYSIS OF LAMB WAVE DISPERSION CHARACTERISTICS OF THERMOELASTIC ANISOTROPIC LAMINATES BASED ON THE POLYNOMIAL METHOD

作　　者：吕炎 林晓磊 高杰 何存富 Lyu Yan;Lin Xiaolei;Gao Jie;He Cunfu(Faculty of Information Technology,Beijing University of Technology,Beijing 100124,China;Faculty of Materials and Manufacturing,Beijing University of Technology,Beijing 100124,China)

机构地区：[1]北京工业大学信息学部,北京100124 [2]北京工业大学材料与制造学部,北京100124

出　　处：《力学学报》2023年第9期1939-1949,共11页Chinese Journal of Theoretical and Applied Mechanics

基　　金：国家自然科学基金(12072004);北京市教委科研计划(KZ202110005005);国家重点研发计划(2022YFC3005002);北京市科协青年人才托举工程(BYESS2023113)资助项目。

摘　　要：基于勒让德级数法,联立Green-Nagdhi热弹性理论,建立了含温度场各向异性层合板的超声导波频散特性理论模型,揭示温度场环境下多层复合材料中超声导波的传播过程.同时,构建了温度场环境下多层各向同性与各向异性层合板的声学频域仿真模型,以提取特定温度下层合板超声导波的频散曲线.通过对比仿真数据与理论计算的结果,验证了所提理论方法的有效性.随后,以不同铺层方向单向纤维材料组成的层合板为例,分析了相同温度条件下中间层纤维角度对各向异性层合板超声导波频散曲线的影响规律,并细节分析了特定频率处A0模态的位移及应力波结构的分布特征.此外,着重考虑温度场变化对碳纤维复合材料层合板中超声导波频散特性的影响机理,指出导波基础模态的偏移规律,并详细列举了不同频率与温度下的基础模态相速度值.最后,利用不同温度工况下的相速度差值,提取多层各向异性层合板相速度温度敏感度变化曲线,探究不同频率下对称和反对称模态的相速度温度敏感度,为多层复合材料力学性能的超声无损检测与评估提供了理论基础.A theoretical model of the dispersion characteristics of ultrasonic guided waves in anisotropic laminates with temperature field is developed based on Legendre's polynomial method and Green-Nagdhi thermoelasticity theory to reveal the propagation process of ultrasonic guided waves in multilayered composites under temperature field environment.At the same time,the acoustic frequency domain simulation model of multilayer isotropic and anisotropic laminates in a temperature field environment is constructed to extract the dispersion curves of ultrasonic guided waves of the laminates at specific temperatures.The validity of the proposed theoretical method is verified by comparing the simulation data with the theoretical calculations.After that,the dispersion curves of the ultrasonic guided waves of anisotropic laminates are analyzed by taking laminates composed of unidirectional fiber materials with different layup directions as an example,and the distribution characteristics of the displacement and stress wave structure of the A0 modes at a specific frequency are analyzed in detail concerning the fiber angle of the intermediate ply at the same temperature condition.In addition,the mechanism of the influence of temperature field changes on the dispersion characteristics of ultrasonic guided waves in carbon fiber composite laminates is focused on,the shift laws of the ultrasonic guided wave fundamental modes are pointed out,and the values of the fundamental mode phase velocities at different frequencies and temperatures are listed in detail.In the end,the phase velocity temperature sensitivity change curves of multilayer anisotropic laminates are extracted by utilizing the phase velocity difference values at different temperature conditions,and the phase velocity temperature sensitivity of symmetric and antisymmetric modes at different frequencies is explored,which provides a theoretical basis for ultrasonic nondestructive testing and evaluation of the mechanical properties of multilayer composites.

关 键 词：勒让德级数法 单向纤维层合板 温度场 超声导波 频散曲线 

分 类 号：O343[理学—固体力学]