波导结构的特征频率法及其超声导波声弹性效应研究
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摘要
超声导波技术作为一种高效的无损检测方法，可同时实现缺陷与应力的检测，对主要的钢结构构件（如矩形管、H型钢、钢杆等）此类波导结构的无损检测具有潜在的优势。然而，钢结构中的板条类波导结构由于截面形状不规整，超声导波在其中的传播特性无法利用传统的波动求解方法，数值方法对此类结构的研究也甚少，而关于预应力波导结构的波动特性研究更为鲜见，严重制约着超声导波技术在此类结构中的推广应用。
为究明诸如板条类等异性截面波导结构中超声导波的波动频散特性和预应力结构的波动特性及导波各模态的声弹应力敏感性，本文在连续体振动理论有限元分析的基础上，建立一种能够适应任意截面波导结构频散特性分析的方法。应用该方法研究板条类波导结构中超声导波的传播特性，并发展该方法应用于预应力结构的波动特性分析，实现超声导波声弹敏感模态与激励频散的优化选取。通过在超声导波声弹理论分析的基础上，探讨试验影响因素；搭建声弹试验系统；以钢杆和矩形管为研究对象，对纵向模态和SH0模态的声弹常数进行了试验测试，论证了超声导波声弹试验系统的可靠性和该方法的可行性。主要研究工作如下：
(1)提出了一种适合求解截面沿轴向一致波导结构频散特性分析的有限元特征频率法，分析了收敛性要求所必需的网格单元尺寸与模型长度。用此方法计算了几种典型波导结构与两类特殊波导结构中各个模态的波动频散特性。实例分析结果表明：可利用适合的边界条件降低求解自由度数且能实现单一种类模态的频散计算；对于复杂波导结构与在高频段的频散计算较为困难。
(2)研究分析了板条结构中导波的频散特性与板条宽度边界的影响。结果表明：同阶低次模态会叠加形成高次模态，产生的新模态截止频率由边界尺寸决定；发展无限单元法用于超声导波无损检测领域，并用于模拟板条结构中的Lamb波传播特性，验证了在板条结构中可激励出SH0与A0模态，其余Lamb波模态不容易被激励与识别；同时，以工程板条类结构矩形管、H型钢和椭圆管为研究对象，分析了此类结构的频散特性；发现此类结构各模态在截止频率处，受边界约束影响明显；最容易激励的是反对称类模态（弯曲模态），局部模态分析可由板条结构替代。
(3)发展有限元特征频率法应用于预应力波导结构频散特性分析。提出利用声弹常数频散曲线表征超声导波的声弹性效应，得到了适合杆、板、圆管与板条结构中应力检测时，声弹性效应较敏感的模态与所对应的激励频率。发现导波多数模态存在无声弹性效应的频率盲点；对于不同结构中频散特性相同的模态具有相同的声弹性效应。
(4)阐明了材料组分、三阶弹性常数和织构效应对声弹性效应的影响，并对三阶弹性常数的各个参量通过正交分析方法得到了影响纵向模态声弹性效应的主次因素与显著性水平。同时，对温度效应、拉伸应变、泊松效应带来的影响进行了分析，并对时延估计方法的精度进行了评估。结果表明：泊松效应可不予考虑，互相关函数法最适合用于声弹的时延估计。最后，通过试验标定的方法对测量系统的工作参数给出了建议。
(5)搭建了超声导波声弹试验测试系统，以杆结构与矩形管为检测对象，对纵向模态与SH0模态的声弹特性进行了试验研究。结果表明：在低应力区域得到的声弹常数误差普遍较大，说明超声导波声弹常数标定应选在高应力区域。通过频率与模态对声弹性效应影响的试验研究论证了超声导波声弹试验系统的可靠性与理论声弹计算方法的可行性。而SH0模态的初步声弹试验结果表明该方法对矩形管等板条类结构的应力检测具有可行性，但需要完善的试验测量技术。
As an efficient nondestructive testing method, Ultrasonic guided wavetechnology can detect concurrently defects and stress, it has a potential advantage thatthe main components of steel structure (e.g., rectangular tube, h-beam, steel rod, etc.)are detected. However, because of the complexity of cross section shape, the wavecharacteristics of steel structures are difficult solved by the traditional wave theory,the numerical method is also less, and the research of prestressed waveguide structureis more rare.
To investigate wave characteristics of the special section waveguideds andprestressed structures, a finite element eigenfrequency method is established toanalysis dispersion of arbitrary cross-section waveguideds base on continuum theoryof vibration. The propagaton characteristics of plate strip are studied by this method,and it is applied to analysis wave motion of prestressed structure, the optimal modesand excitation frequencies are obtained for stress measurement. On the basis oftheoretical analysis, the effect factors are study, and acoustoelastic experiment systemis constructed. With steel bar and rectangular tube as the research object, theacoustoelastic effect of longitudinal modes and SH0mode are studied, demonstratesreliability of acoustoelastic experimental system and feasibility of this method. Themain work is as follows:
(1) The finite element eigenfrequency method is put forward to solve dispersioncharacteristic which cross section is consistent along the axial, the convergence isanalysed for mesh size and length of the model. The dispersion of common structuresand two kinds of special waveguide structures are calculated. The results show thatfree degree numbers and type of model can be choosed by the suitable boundaryconditions. It is difficult that the dispersion is calculated for complex waveguidestructure and high frequency band.
(2) The wave characteristics of plate strip are studied, and the affect of widthboundary is analyzed for dispersion. The results show that the low order mode canform high order modal by in-order superposition, the cutoff frequency is determinedby the boundary dimensions for new mode. A0and SH0mode can be generated inplate strip by numerical simulation combined with the infinite element method, therest of the Lamb wave modes is not easy to be incentive and recognition, the reason is explained that S0mode is difficult to excitate. The engineering structure, rectangulartube, h-beam and elliptical tube as the research object, the dispersion characteristicsare analyzed, it is found that the boundary constraint is obvious in cutoff frequency.The antisymmetric mode is easiest generated, the local modal analysis can besubsituted for plate strip.
(3) The prestressed waveguide structure is analysed by finite elementeigenfrequency method. It is presented that acoustoelastic effect is described byacoustoelastic constant dispersion curve. The acoustoelastic effect sensitive mode andexcitation frequency are obtained for plate, rod, pipe and plate strip. The frequencyblind spot is existent that no acoustoelatic effect. It is provided with the sameacoustoelasticity effect for the same dispersion in different structures.
(4) The affect of acoutoelstic effect is clarify for material composition,third-order elastic constants and texture effect, the secondary factors and thesignificance level of third-order elastic constants is obtained by orthogonal analysismethod for longitudinal modes. the temperature effect, the effects of tensile strain,poisson's effect is analyzed, and the precision of time delay estimation method areevaluated. The results show that the poisson effect can be ignored, thecross-correlation method is best suited for time delay estimation. Finally, themeasuring system is calibrated.
(5) The acoustoelastic test system is established. The acoustoelstic effect oflongitudinal modes and SH0mode were studied with rod and rectangular tube astesting object. The results show that: the error of acoustoelastic constant is bigger inlow stress areas. The reliability of experimental system and the feasible of theorymethod are demonstrated. The SH0mode test results show that the method is adaptivefor rectangular tube, but it is prerequisite to improve experiment technology.
为究明诸如板条类等异性截面波导结构中超声导波的波动频散特性和预应力结构的波动特性及导波各模态的声弹应力敏感性，本文在连续体振动理论有限元分析的基础上，建立一种能够适应任意截面波导结构频散特性分析的方法。应用该方法研究板条类波导结构中超声导波的传播特性，并发展该方法应用于预应力结构的波动特性分析，实现超声导波声弹敏感模态与激励频散的优化选取。通过在超声导波声弹理论分析的基础上，探讨试验影响因素；搭建声弹试验系统；以钢杆和矩形管为研究对象，对纵向模态和SH0模态的声弹常数进行了试验测试，论证了超声导波声弹试验系统的可靠性和该方法的可行性。主要研究工作如下：
(1)提出了一种适合求解截面沿轴向一致波导结构频散特性分析的有限元特征频率法，分析了收敛性要求所必需的网格单元尺寸与模型长度。用此方法计算了几种典型波导结构与两类特殊波导结构中各个模态的波动频散特性。实例分析结果表明：可利用适合的边界条件降低求解自由度数且能实现单一种类模态的频散计算；对于复杂波导结构与在高频段的频散计算较为困难。
(2)研究分析了板条结构中导波的频散特性与板条宽度边界的影响。结果表明：同阶低次模态会叠加形成高次模态，产生的新模态截止频率由边界尺寸决定；发展无限单元法用于超声导波无损检测领域，并用于模拟板条结构中的Lamb波传播特性，验证了在板条结构中可激励出SH0与A0模态，其余Lamb波模态不容易被激励与识别；同时，以工程板条类结构矩形管、H型钢和椭圆管为研究对象，分析了此类结构的频散特性；发现此类结构各模态在截止频率处，受边界约束影响明显；最容易激励的是反对称类模态（弯曲模态），局部模态分析可由板条结构替代。
(3)发展有限元特征频率法应用于预应力波导结构频散特性分析。提出利用声弹常数频散曲线表征超声导波的声弹性效应，得到了适合杆、板、圆管与板条结构中应力检测时，声弹性效应较敏感的模态与所对应的激励频率。发现导波多数模态存在无声弹性效应的频率盲点；对于不同结构中频散特性相同的模态具有相同的声弹性效应。
(4)阐明了材料组分、三阶弹性常数和织构效应对声弹性效应的影响，并对三阶弹性常数的各个参量通过正交分析方法得到了影响纵向模态声弹性效应的主次因素与显著性水平。同时，对温度效应、拉伸应变、泊松效应带来的影响进行了分析，并对时延估计方法的精度进行了评估。结果表明：泊松效应可不予考虑，互相关函数法最适合用于声弹的时延估计。最后，通过试验标定的方法对测量系统的工作参数给出了建议。
(5)搭建了超声导波声弹试验测试系统，以杆结构与矩形管为检测对象，对纵向模态与SH0模态的声弹特性进行了试验研究。结果表明：在低应力区域得到的声弹常数误差普遍较大，说明超声导波声弹常数标定应选在高应力区域。通过频率与模态对声弹性效应影响的试验研究论证了超声导波声弹试验系统的可靠性与理论声弹计算方法的可行性。而SH0模态的初步声弹试验结果表明该方法对矩形管等板条类结构的应力检测具有可行性，但需要完善的试验测量技术。
As an efficient nondestructive testing method, Ultrasonic guided wavetechnology can detect concurrently defects and stress, it has a potential advantage thatthe main components of steel structure (e.g., rectangular tube, h-beam, steel rod, etc.)are detected. However, because of the complexity of cross section shape, the wavecharacteristics of steel structures are difficult solved by the traditional wave theory,the numerical method is also less, and the research of prestressed waveguide structureis more rare.
To investigate wave characteristics of the special section waveguideds andprestressed structures, a finite element eigenfrequency method is established toanalysis dispersion of arbitrary cross-section waveguideds base on continuum theoryof vibration. The propagaton characteristics of plate strip are studied by this method,and it is applied to analysis wave motion of prestressed structure, the optimal modesand excitation frequencies are obtained for stress measurement. On the basis oftheoretical analysis, the effect factors are study, and acoustoelastic experiment systemis constructed. With steel bar and rectangular tube as the research object, theacoustoelastic effect of longitudinal modes and SH0mode are studied, demonstratesreliability of acoustoelastic experimental system and feasibility of this method. Themain work is as follows:
(1) The finite element eigenfrequency method is put forward to solve dispersioncharacteristic which cross section is consistent along the axial, the convergence isanalysed for mesh size and length of the model. The dispersion of common structuresand two kinds of special waveguide structures are calculated. The results show thatfree degree numbers and type of model can be choosed by the suitable boundaryconditions. It is difficult that the dispersion is calculated for complex waveguidestructure and high frequency band.
(2) The wave characteristics of plate strip are studied, and the affect of widthboundary is analyzed for dispersion. The results show that the low order mode canform high order modal by in-order superposition, the cutoff frequency is determinedby the boundary dimensions for new mode. A0and SH0mode can be generated inplate strip by numerical simulation combined with the infinite element method, therest of the Lamb wave modes is not easy to be incentive and recognition, the reason is explained that S0mode is difficult to excitate. The engineering structure, rectangulartube, h-beam and elliptical tube as the research object, the dispersion characteristicsare analyzed, it is found that the boundary constraint is obvious in cutoff frequency.The antisymmetric mode is easiest generated, the local modal analysis can besubsituted for plate strip.
(3) The prestressed waveguide structure is analysed by finite elementeigenfrequency method. It is presented that acoustoelastic effect is described byacoustoelastic constant dispersion curve. The acoustoelastic effect sensitive mode andexcitation frequency are obtained for plate, rod, pipe and plate strip. The frequencyblind spot is existent that no acoustoelatic effect. It is provided with the sameacoustoelasticity effect for the same dispersion in different structures.
(4) The affect of acoutoelstic effect is clarify for material composition,third-order elastic constants and texture effect, the secondary factors and thesignificance level of third-order elastic constants is obtained by orthogonal analysismethod for longitudinal modes. the temperature effect, the effects of tensile strain,poisson's effect is analyzed, and the precision of time delay estimation method areevaluated. The results show that the poisson effect can be ignored, thecross-correlation method is best suited for time delay estimation. Finally, themeasuring system is calibrated.
(5) The acoustoelastic test system is established. The acoustoelstic effect oflongitudinal modes and SH0mode were studied with rod and rectangular tube astesting object. The results show that: the error of acoustoelastic constant is bigger inlow stress areas. The reliability of experimental system and the feasible of theorymethod are demonstrated. The SH0mode test results show that the method is adaptivefor rectangular tube, but it is prerequisite to improve experiment technology.
引文
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