The paper theoretically and experimentally analyzes free vibration characteristics of statically loaded moving boundary type curved beam considering rotary inertia and shear deformation effects. Effects of rotary inertia and shear deformation are observed for different thickness to span ratios of curved beam. The subject problem is decoupled into two interrelated problems: determining equilibrium configuration under static load and finding the corresponding free vibration frequency. The static problem is analyzed incrementally in body fitted curvilinear frame as it involves geometric nonlinearity due to generalized curvature, large deformation, and moving boundaries. Variational energy principle is employed to derive governing equation. The nonlinear governing equation associated with complicated boundary conditions is solved through iterative geometry updation. Once static problem is solved for current load step, governing equation for dynamic characteristics is derived using Hamilton’s principle. The governing equation gets linearized by using the static configuration, which finally yields a linear eigenvalue problem. Experiment is performed in a dedicated setup with two master leafs having different thickness to span ratios. The roller supported specimens are excited with an instrumented hammer and response signals are captured by accelerometers. The excitation and response signals are recorded using HBM-MX840B data acquisition system. Frequency response functions of the curved beam systems under different static loads are obtained from postprocessing of the dynamic signals in MATLAB®. First two natural frequencies of the specimens are noted from the experimental results and the corresponding theoretical results are generated. The specimens are also modeled in ABAQUS® CAE and finite element results are computed. Comparison between the theoretical, experimental, and finite element results validates the present model. The study also provides some meaningful observations on effects of rotary inertia and shear deformation. Based on the observations, more results are generated for different thickness to span ratios and findings are reported suitably.

中文翻译：

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结合转动惯量和剪切变形效应的大变形曲梁自由振动分析及试验验证

论文从理论和实验上分析了静载动边界型曲梁考虑转动惯量和剪切变形效应的自由振动特性。观察了不同弯梁厚跨比下转动惯量和剪切变形的影响。该主题问题被分解为两个相互关联的问题：确定静载荷下的平衡配置和找到相应的自由振动频率。由于广义曲率、大变形和移动边界，静态问题涉及几何非线性，因此在贴身曲线框架中逐步分析静态问题。利用变分能量原理推导出控制方程。通过几何迭代更新求解复杂边界条件下的非线性控制方程。一旦解决了当前载荷步的静态问题，就可以使用汉密尔顿原理推导出动态特性的控制方程。通过使用静态配置将控制方程线性化，最终产生线性特征值问题。实验是在专用设置中进行的，其中两个主叶片具有不同的厚度跨度比。滚筒支撑的样品用仪器锤激发，响应信号由加速度计捕获。使用 HBM-MX840B 数据采集系统记录激励和响应信号。曲线梁系统在不同静载荷下的频率响应函数是通过在 MATLAB® 中对动态信号进行后处理获得的。从实验结果中注意到试样的前两个固有频率并产生相应的理论结果。试样也在 ABAQUS® CAE 中建模并计算有限元结果。理论、实验和有限元结果之间的比较验证了本模型。该研究还对旋转惯性和剪切变形的影响提供了一些有意义的观察结果。根据观察结果，针对不同的厚度跨度比生成了更多结果，并适当地报告了结果。从实验结果中注意到试样的前两个固有频率并产生相应的理论结果。试样也在 ABAQUS® CAE 中建模并计算有限元结果。理论、实验和有限元结果之间的比较验证了本模型。该研究还对旋转惯性和剪切变形的影响提供了一些有意义的观察结果。根据观察结果，针对不同的厚度跨度比产生了更多结果，并适当地报告了结果。从实验结果中注意到试样的前两个固有频率并产生相应的理论结果。试样也在 ABAQUS® CAE 中建模并计算有限元结果。理论、实验和有限元结果之间的比较验证了本模型。该研究还对旋转惯性和剪切变形的影响提供了一些有意义的观察结果。根据观察结果，针对不同的厚度跨度比产生了更多结果，并适当地报告了结果。该研究还对旋转惯性和剪切变形的影响提供了一些有意义的观察结果。根据观察结果，针对不同的厚度跨度比产生了更多结果，并适当地报告了结果。该研究还对旋转惯性和剪切变形的影响提供了一些有意义的观察结果。根据观察结果，针对不同的厚度跨度比产生了更多结果，并适当地报告了结果。