基于超声共振谱法的非规则固体材料弹性常数估计方法  

Elastic constant identification method for irregularly shaped solid materials based on resonant ultrasound spectroscopy

作　　者：王蕊 樊璠[1,2] 张强[1,2] 侯永威 沈飞[1,2] 牛海军[1,2] WANG Ru;FAN Fan;ZHANG Qiang;HOU YongWei;SHEN Fei;NIU HaiJun(School of Biological Science and Medical Engineering,Beihang University,Beijing 100083,China;Beijing Advanced Innovation Center for Biomedical Engineering,Beihang University,Beijing 100083,China)

机构地区：[1]北京航空航天大学生物与医学工程学院,北京100083 [2]北京航空航天大学生物医学工程高精尖创新中心,北京100083

出　　处：《中国科学：技术科学》2019年第12期1534-1540,共7页Scientia Sinica(Technologica)

基　　金：国家自然科学基金(批准号:31570945,11772037)资助项目

摘　　要：超声共振谱是一种测量固体材料弹性性质的成熟方法.其中,待测样本的固有频率通常使用瑞利-里兹法来计算,该方法要求将样本加工成特定的形状,这对于某些尺寸小或者具有特殊理化性质的材料来说是非常困难的.基于此,本文提出了一种结合有限元方法的超声共振谱技术来估计非规则固体材料的弹性常数.该方法首先测量待测材料样本在超声激励下进行自由振动时的实验共振频率;随后采用Micro-CT扫描获得样本的三维形状信息,建立有限元模型计算其理论共振频率;最后利用Levenberg-Marquardt算法优化有限元模型中的弹性常数直到模型输出的共振频率与实验共振频率的均方和误差达到最小值.方法的可行性利用非规则钛样本进行了验证.结果显示利用该方法估计出的非规则钛样本的弹性常数与利用传统超声共振谱方法估计出的长方体钛样本的弹性常数具有很好的一致性,相对差异在4%以内.本研究避免了传统测量方法中规则样本的加工过程,使非规则固体材料的弹性性质测量成为可能.Resonant ultrasound spectroscopy(RUS) is a well-established method for identifying the elastic coefficients of solid materials. The Rayleigh-Ritz method is usually used to calculate the natural frequencies of a sample, where the sample needs to be processed into certain regular bodies. This requirement is hard to meet for some materials with size limitations or special physical/chemical properties. To deal with these situations, a method that combines a finite element(FE) method and RUS is proposed in this paper to measure the elastic constants of an irregularly shaped solid. This method first measures the experimental resonant frequencies of a sample under ultrasonic excitation. Then, a micro-CT scan is used to obtain the three-dimensional shape information of the sample and a FE model is built to calculate the theoretical resonance frequencies. Finally, the Levenberg-Marquardt algorithm is chosen to optimize the elastic constants until the errors between the resonant frequencies calculated from the FE model and those determined experimentally reach a minimum. An irregularly shaped titanium sample was used to calibrate this method. The results show that the elastic constants of the irregular titanium sample estimated by this method were in good agreement with those of a rectangular titanium sample estimated by traditional RUS, with the relative differences below 4%. This study avoided the complicated processing of regular samples by traditional methods and makes it possible to measure the elastic properties of irregularly shaped solid materials.

关 键 词：超声共振谱 有限元方法 非规则固体材料 弹性性质 

分 类 号：TB302.5[一般工业技术—材料科学与工程]