On modal analysis of axially functionally graded material beam under hygrothermal effect

Sharma, Pankaj; Singh, Rahul; Hussain, Muzamal

doi:10.1177/0954406219888234

Cited by 39 publications

(5 citation statements)

References 70 publications

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“…Additionally, they used COMSOL Multiphysics to perform a finite element simulation, which has the benefit of defining material properties as analytical functions. Sharma et al [168] investigated the modal analysis of an axially functionally graded material beam under hygrothermal effect. The material constants of the beam were supposed to be graded smoothly along the axial direction under both power law and sigmoid law distribution.…”

Section: Commercial Softwarementioning

confidence: 99%

Optimal Design of Functionally Graded Parts

Nayak

Armani

2022

Metals

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Several additive manufacturing processes are capable of fabricating three-dimensional parts with complex distribution of material composition to achieve desired local properties and functions. This unique advantage could be exploited by developing and implementing methodologies capable of optimizing the distribution of material composition for one-, two-, and three-dimensional parts. This paper is the first effort to review the research works on developing these methods. The underlying components (i.e., building blocks) in all of these methods include the homogenization approach, material representation technique, finite element analysis approach, and the choice of optimization algorithm. The overall performance of each method mainly depends on these components and how they work together. For instance, if a simple one-dimensional analytical equation is used to represent the material composition distribution, the finite element analysis and optimization would be straightforward, but it does not have the versatility of a method which uses an advanced representation technique. In this paper, evolution of these methods is followed; noteworthy homogenization approaches, representation techniques, finite element analysis approaches, and optimization algorithms used/developed in these studies are described; and most powerful design methods are identified, explained, and compared against each other. Also, manufacturing techniques, capable of producing functionally graded materials with complex material distribution, are reviewed; and future research directions are discussed.

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Section: Commercial Softwarementioning

confidence: 99%

Optimal Design of Functionally Graded Parts

Nayak

Armani

2022

Metals

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“…Here, Galerkin’s method is used to solve the CNT problem of differential equations in an efficient and comprehensive way [71–79]. The analysis of vibration of SWCNTs as a theoretical work is very necessary before their practical applications.…”

Section: Theoretical Formulationsmentioning

confidence: 99%

Mass density effect on vibration of zigzag and chiral SWCNTs: A theoretical study

Hussain

2020

Jnl of Sandwich Structures & Materials

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Carbon nanotubes fascinate new materials with astonishing mechanical, optical, and electrical properties. In fact, carbon nanotubes are kinds of rolled graphene sheets, and the rolling manner shows the basic properties of the tube, and that is actually the main reason for the extraordinary feature of the carbon nanotubes. This paper aims to presents formulation of Love’s shell theory for single-wall carbon nanotubes (SWCNTs) using Galerkin’s method. For this system, the governing equation is developed with proposed method. It is assumed that C–C and C–F support conditions are applied on the edge of carbon nanotube. Zigzag and chiral structures are considered for the vibrational analysis to investigate the effect of different mode and in-plane rigidity with end conditions. Moreover, the influence of mass density per unit lateral area on the same structure is also developed. It is also concluded that the fundamental frequencies of chiral tubes are lower than that of zigzag tubes frequencies. By increasing values of in-plane rigidity, resulting frequencies also increase and frequencies decrease on increasing mass density per unit lateral area. Though the trends of frequency values of both mass density per unit lateral area and in-plane rigidity are converse to each other. It is shown that variation in mass density has a significant effect on the vibration of SWCNTs. To generate the fundamental natural frequencies and for better accuracy and effectiveness, the computer software MATLAB is used. Tube dynamical equations for the present problem are taken in the integral form energy expressions for a carbon nanotube. The axial modal deformations are approximated by making use of the beam functions. The proposed model is continuum-model for getting the dynamic character of SWCNTs and to validate the results by earlier methods.

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“…Several studies are available in the literature to describe the vibration behavior of AFG non-prismatic beams using different numerical techniques, that is, finite element analysis (Shahba et al, 2011; Shahba and Rajasekaran, 2012), Rayleigh–Ritz method (Akgoz and Civalek, 2013), modified Chebyshev spectral method (Zhao et al, 2017), Galerkin method (Ghayesh, 2018a, 2018b, 2018c, 2019a, 2019b), asymptotic development method (Cao and Gao, 2019), isogeometric approach (Chen et al, 2019), Jacobi polynomial (Zhang et al, 2019), and variational iteration method (Chen et al, 2020). The vibration analysis of FGM beam with piezoelectric effect using the generalized differential quadrature (GDQ) method is available with Parashar and Sharma (2016), Sharma and Parashar (2016a, 2016b), and Sharma (2018, 2019, 2020), and vibration of FGM structures is available with Sharma et al (2020), Sharma and Singh (2021), Singh and Sharma (2019), and Sharma and Singh (2020). It is observed from the literature that in most of the articles pertaining to vibration analysis of AFG beam, the temperature is assumed to be varied in the thickness direction only.…”

Section: Introductionmentioning

confidence: 99%

Vibration analysis of an axially functionally graded material non-prismatic beam under axial thermal variation in humid environment

Singh

Sharma

2021

Journal of Vibration and Control

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The vibration analysis of an axially functionally graded material non-prismatic Timoshenko beam under axial thermal variation in humid environment is carried out using the harmonic differential quadrature method. In this modeling, the length and width of the beam remains constant whereas thickness of the beam is linearly varied along the axis of the beam. The material properties are temperature dependent and are assumed to be varied continuously along the axial direction according to power law distribution. Three types of temperature variations are considered in this study, that is, uniform temperature rise, linear temperature rise, and non-linear temperature rise. The temperature of the beam remains constant under uniform temperature rise condition and it is varied linearly and nonlinearly along the length of beam for rest of the conditions. The beam is subjected to uniform moisture concentration to impose humidity. Hamiltonian’s approach is used to derive the governing equations of motion. The resultant governing equations are then solved using the harmonic differential quadrature method to obtain the natural frequencies of the axially functionally graded material non-prismatic beam. The results obtained using the harmonic differential quadrature method are compared with results obtained for special cases. The effects of thermal variation, humidity, non-homogeneity parameter, and end conditions on natural frequencies of the non-prismatic beam are reported.

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On modal analysis of axially functionally graded material beam under hygrothermal effect

Cited by 39 publications

References 70 publications

Optimal Design of Functionally Graded Parts

Optimal Design of Functionally Graded Parts

Mass density effect on vibration of zigzag and chiral SWCNTs: A theoretical study

Vibration analysis of an axially functionally graded material non-prismatic beam under axial thermal variation in humid environment

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