WU Rujun，SUN Dianliang（1.Shanghai Dianji University，Shanghai 01306，China；.Shandong P&T Engineering Co.，LTD，Jinan 50001，China）



Error Analysis of FBG Sensors Bonded on LowModulus Host Materials*

WU Rujun1*，SUN Dianliang2
（1.Shanghai Dianji University，Shanghai 201306，China；2.Shandong P&T Engineering Co.，LTD，Jinan 250001，China）

FBG sensor has been widely used in measuring the strain of host material.The existing of FBG sensor af⁃fects strain distribution of the host material，and the host material does not contact the optical fiber.However，may result in a decrease of strain measurement accuracy.So，the strain relationship between the optical fiber and host material was needed to study to improve the measurement accuracy.A theoretical model of strain transfer was devel⁃oped to include the influence of FBG sensor.Subsequently，the theoretical predictions were validated by finite ele⁃ment analysis.The effect of parameters on strain transfer rate was discussed according to the current theoretical analysis.the error between theoretical solution and FEA was controlled within 3%.The theoretical model satisfied accuracy requirement of the FBG sensors，which is considered as a guidance for its practical application。

Fiber Bragg Grating（FBG）；strain transfer rate；theoretical analysis；shear stress

与传统电阻传感器相比，光纤布拉格光栅（FBG）传感器具有体积小、质量轻、抗电磁干扰等众多优点。根据安装方式的不同，可以分为表面粘贴式和埋入式两种，但是无论哪一种安装方式，测量应变和真实应变存在一定的误差，为进一步提高测量精度，建立测量应变与真实应变之间的关系至关重要［1］。

国内外众多学者针对该问题作了研究，Ansari等［2］假定光纤中心处的应变和基体应变相同，从而得到FBG传感器的应变分布规律。Duck G等［3］利用傅里叶变换得到光纤应变与基体应变之间的关系。李东升等［4-6］首次提出FBG传感器各层应变率相等的假设，得到更高精度的应变传递理论。周智等［7］假定各层中点处应变相等，进而得到光纤应变与基体应变之间的关系。Zhao等［8］对四层表面粘贴式FBG传感器应变传递理论进行了研究，得出各层应变分布规律。Wang等［9］对表面式FBG传感器应变传递问题进行了研究，得到与李东升等人相似的结论。Her和Huang［10］针对表面粘贴式FBG传感器应变传递问题进行了相关研究。Moradi M［11］建立了粘贴于薄板上的传感器测量应变与薄板应变之间的传递理论。Wu等［12］人研究了埋入式FBG传感器与基体之间的耦合作用；吴入军等［13］首次提出多项式形式的剪应力表达式，基于此建立应变传递方程，经验证具有较高精度。王花平等［14］针对纯沥青包裹的FBG传感器结构进行应变传递理论分析和实验验证工作。金秀梅等［15］推出了裸光纤、涂覆层和基体的剪应力在径向的分布，并通过有限元进行了验证。……