Effect of piezoelectric patch on natural frequencies of Timoshenko beam made of functionally graded material

Abstract

The present paper addresses developing the Dynamic Stiffness Method (DSM) for natural frequency analysis of functionally graded beam with piezoelectric patch based on the Timoshenko beam theory and power law of material grading. Governing equations and general solution of free vibration are conducted for the beam element with piezoelectric layer that is modelled as a homogeneous Timoshenko beam. The obtained solution allows establishing dynamic stiffness matrix for modal analysis of FGM beam with bonded piezoelectric distributed sensors/actuators. Effect of thickness and position of the smart sensors/actuators and material parameters on natural frequencies is studied with the aim for dynamic testing and health monitoring of FGM structures. The theoretical developments are validated and illustrated by numerical examples.

Modal analysis of cracked beam with a piezoelectric layer

“…, C 6 } T is vector of arbitrary constants and α j = −k j (ω 2 I 12 + k 2 j B 12 )/(ω 2 I 11 + k 2 j B 11 ), j = 1, 2, 3. For example, using expression (24), a particular solution denoted by z 1 (x, ω) = {U 1 (x, ω) , W 1 (x, ω)} T , satisfying conditions…”

“…Wang and Quek [23] used the sandwich beam model for modal analysis of a Euler-Bernoulli beam embedded with piezoelectric layers and they found that natural frequency of the sandwich beam is function of stiffness and thickness of the piezoelectric layers. Nguyen Tien Khiem et al [24] investigated effect of piezoelectric patch on natural frequencies of beam made of functionally graded material. Recently, dynamics of cracked structures with piezoelectric patches [25,26] has attracted a special attention of researchers to develop an efficient method for crack identification using piezoelectric material.…”

Vibrations of cracked functionally graded beams: General solution and application – A review

“…[45]. The established model of crack in FGM has been employed for vibration analysis of cracked functionally graded beams [46][47][48] and the beams with piezoelectric layer [49,50]. Moreover, the obtained general solution for vibration mode of cracked FGM beam allows one to develop the well-known transfer matrix method and dynamic stiffness method for vibration analysis of cracked FGM beam-like structures.…”

Crack identification of functionally graded beam using distributed piezoelectric sensor

“…In both the latter works mode shapes of FGM structures are employed for crack identification instead of natural frequencies. Functionally graded beams with piezoelectric layer have been investigated in Khorramabadi and Nezamabadi (2010), Rafiee et al (2013), and Khiem et al (2020). However, studies on vibration of cracked functionally graded beam with piezoelectric layer or crack detection in functionally graded beams using distributed piezoelectric sensor, to the author's knowledge, have not been reported in the literature.…”