Abstract

The present paper addresses modal analysis of cracked Timoshenko beam bonded with piezoelectric layer. The host beam is made of functionally graded material with the power law and crack appeared in the host beam is modeled by a pair of axial and rotational springs with stiffness calculated from its depth. The piezoelectric layer is represented as a homogeneous Timoshenko beam. Governing equations and general solution for free vibration of the cracked double beam are conducted in the frequency domain. The obtained solution has been used for examining modal parameters of the coupled beam that include natural frequencies, mode shapes and so-called modal sensor charge in dependence on crack parameter, material gradient index and thickness of piezoelectric layer. Analysis of the modal sensor charge in dependence upon crack parameters provides a novel indicator that is expected to be more efficient than the traditional ones for crack detection in functionally graded beam using distributed smart sensors. The theoretical development is validated and illustrated by numerical analysis accomplished for simply supported beam.

摘要

本文讨论了与压电层粘合的裂纹 Timoshenko 梁的模态分析。主梁由具有幂律的功能梯度材料制成，主梁中出现的裂纹由一对轴向和旋转弹簧建模，其刚度根据其深度计算。压电层被表示为均匀的铁莫申科梁。裂纹双梁自由振动的控制方程和通解在频域中进行。所获得的解决方案已用于检查耦合梁的模态参数，包括固有频率、振型和依赖于裂纹参数、材料梯度指数和压电层厚度的所谓模态传感器电荷。根据裂纹参数对模态传感器电荷进行分析提供了一种新颖的指示器，预计该指示器比使用分布式智能传感器在功能梯度光束中进行裂纹检测的传统指示器更有效。通过对简支梁进行数值分析来验证和说明理论发展。