A Comprehensive Review on Vibration Analysis of Functionally Graded Beams

Abstract

Beams and beam structures are structural components commonly used in mechanical, aerospace, nuclear, and civil engineering. To meet the different engineering design limitations such as operational conditions, weight, and vibrational characteristics, these components may be made of various materials such as functionally-graded materials (FGMs), composites, and homogeneous materials. Functionally-graded (FG) beams play a key role not only in classical structural applications, but also have vast applications in thermal, electric-structural and electric-thermal-structural systems, e.g. in the form of FG beam energy harvesters, sensors and actuators. In all these applications, using new materials like FGMs can greatly improve the efficiency of the structural components and systems. Since FG beams are mostly used as moving components in engineering structures, vibration analysis of these components has been studied by numerous researchers. In order to solve the governing equation and related boundary conditions of the FG beams, powerful numerical methods with a high level of accuracy and fast rate of convergence are often required. The differential quadrature method (DQM) is a powerful and reliable numerical method which has been extensively used by researchers to perform the vibration analyses of FG structures in the last decade. In this paper, firstly various mathematical models which have been used to express the material properties of FGMs are reviewed. Secondly different elasticity theories which have been applied in vibration analysis of FG beams are summarized. In addition, a review on the DQM and its applications is presented. At the next step, a comprehensive review on free vibration analyses of FG beams based on different elasticity theories and in particular those using the DQM is performed. In continue, a brief review on the application of other numerical methods in vibration analysis of FG beams is presented. Moreover, because of the importance of nonlinear vibration analysis of FG beams, a review on the application of various numerical methods and different elasticity theories on nonlinear vibration analysis of FG beams is performed. Finally, a brief review on linear and nonlinear vibration analysis of FG microbeams, as a special type of FG beams, is presented.

Fonksiyonel Derecelendirilmiş Kiriş Yapıların Eğilme Analizinde Homojenleştirme Modellerinin Etkisi

“…Özellikle malzeme fazları arasındaki yumuşak geçişleri tanımlamak amacıyla tercih edilir. Matematiksel olarak sigmoid fonksiyon, aşağıdaki formülle ifade edilir [39]:…”

Nonlinear dynamic analysis on centrifugal stiffening of rotating cracked tapered functionally graded beam for flap-wise vibrations

“…Cheng et al (2011) studied free vibration analysis of cracked rotating tapered beams using P-version FEM. Zahedinejad et al (2020) provided a complete review on vibration of FGM beams. Vibrational analysis of pre-twisted FGM tapered beams is done using Rayleigh–Ritz along with Kane’s method by Oh and Yoo (2016).…”

Vibration analysis of rotating porous functionally graded material beams using exact formulation

“…The FGMs are normally made from isotropic materials (metals and ceramics) and have remarkable properties such as high strength, low weight, long fatigue life and wear resistance. Therefore, these materials have extensively been used in different applications, and hence, various analyses (static, dynamics…) on the behaviour of structures made of FGMs have been carried out (Cong et al, 2018; Jin et al, 2019; Khaneh Masjedi et al, 2019; Lee and Lee, 2017; Pradhan and Chakraverty, 2013; Sarkar and Ganguli, 2014; Zahedinejad et al, 2020). The dynamic behaviour of FGM structures is an active research area and has attracted the interest of many researchers (Amoozgar et al, 2017; Giunta et al, 2011; Lü et al, 2008; Şimşek and Kocatürk, 2009; Sina et al, 2009; Vo et al, 2014).…”

“…The quasi-3D dynamic behaviour of functionally graded beams using Carrera unified beam formulation was studied by Jin et al (2019). Zahedinejad et al (2020) presented a comprehensive literature review of the research studies carried out on the vibration of FGM beams. More recently, Tian et al (2019) studied the effect of porosity and material grading on the fundamental frequencies of rotating FGM beams and showed that the rotational speed, hub radius and porosity affect the dynamics of the beam significantly.…”