Vibration Analysis of Axially Functionally Graded Timoshenko Beams with Non-uniform Cross-section

Chen, Wei‐Ren

doi:10.1590/1679-78256434

Cited by 7 publications

(3 citation statements)

References 31 publications

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“…The dynamic of sandwich beams with a viscoelastic core subjected to a moving load is investigated using the finite element method in [18]. The natural frequencies of non-uniform axially functionally graded beams were investigated using the Chebyshev collocation method in [19].…”

Section: Introductionmentioning

confidence: 99%

Stochastic Higher-order Finite Element Model for the Free Vibration of a Continuous Beam resting on Elastic Support with Uncertain Elastic Modulus

Hien

Diem²,

Tan³

et al. 2023

Eng. Technol. Appl. Sci. Res.

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This paper deals with a continuous beam resting on elastic support with elastic modulus derived from a random process. Governing equations of the stochastic higher-order finite element method of the free vibration of the continuous beam were derived from Hamilton's principle. The random process of elastic modulus was discretized by averaging random variables in each element. A solution for the stochastic eigenvalue problem for the free vibration of the continuous beam was obtained by using the perturbation technique, in conjunction with the finite element method. Spectral representation was used to generate a random process and employ the Monte Carlo simulation. A good agreement was obtained between the results of the first-order perturbation technique and the Monte Carlo simulation.

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Section: Introductionmentioning

confidence: 99%

Stochastic Higher-order Finite Element Model for the Free Vibration of a Continuous Beam resting on Elastic Support with Uncertain Elastic Modulus

Hien

Diem²,

Tan³

et al. 2023

Eng. Technol. Appl. Sci. Res.

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“…(Kumar et al, 2015) analyzed the geometrically nonlinear free vibration of axially FG taper beams. (Chen, 2021) studied the vibration analysis of axially FG Timoshenko beams with non-uniform sectioncross. (Huang et al, 2013) examined the free vibration of axially functionally graded Timoshenko beam with non-uniform cross section.…”

Section: Introductionmentioning

confidence: 99%

Dynamic Control of Non-Linearly Tapering FGM Beams

HARTI¹,

SAADANI²,

Miloud³

2022

EPSTEM

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This work presents the dynamics and active vibration control of a non-uniform functionally graded beam. Thanks to the strong use of beams and specifically with non-uniform section, in the different industrial applications, such as helicopter rotor blades, wind turbines, space and marine structures, we present in this article, a comparison of linearly and non-linearly tapering beams. The FGM beam is equipped with four layers of piezoelectric materials as sensors and actuators, bonded on the upper and lower surfaces of the main structure, on different finite elements to see the influence of its location on the dynamics and active control. In this study, the Timoshenko beam’s theory combined with FEM is applied to a beam divided into a finite number of elements. Hamilton's principle is applied to generate the equation of motion. The structure is modeled analytically and numerically and the simulation results are presented at the end. The optimal LQG control with Kalman filtering is applied.

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“…The transverse vibration of four types (two metals and two Ceramics) of Timoshenko beams (non-uniform axially functionally graded with cross-sectional and material properties varying in the beam length direction) based on the Chebyshev collocation method has been investigated. 14 Depending on the values of taper ratios (increasing height and width taper ratios) boundary conditions, the natural frequencies of AFGM beams may decrease or increase. The natural frequencies are dependent mainly on height taper ratio than the width taper ratio except for the fundamental frequencies of clamped-free beams.…”

Section: Introductionmentioning

confidence: 99%

Comparative modal analysis on fishing rod made of functionally graded composite material using finite element analysis

Asiri

2022

Journal of Applied Biomaterials & Functional Materials

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The use of smart and advanced composite materials instead of conventional metals is foreseen in material sciences due to the development of novel manufacturing techniques. In this regard, a novel type of composite materials “functionally graded materials (FGM)” has attained great attention owing to their intrinsic mechanical characteristics. FGM have been the focus for researchers for analytical formulation, static structural (large deformation, material nonlinearity) analysis as well as for dynamic analysis on simple beams and on structure having non-uniform tapered rectangular profile considering different boundary conditions. No focus is made to thin structure having non-uniform circular cross-sections. This study aims to deal with analyzing the “dynamic behavior of thin circular non-uniform truncated conical section” which is mostly used for manufacturing of fishing rod. This works primarily compares the static, modal, and harmonic analysis under the application of loads of 50 N acting on fishing rod made up of conventional steel, composite (carbon fiber) steel, and functionally graded material (FGM) with the help of ANSYS®. Firstly, static analysis performed to analyze the structural behavior under the application of static loadings. After that modal analysis performed and first five modes selected for Steel; from 0 to 600 Hz, for Carbon Fiber; from 0 to 850 Hz and for FGM; from 0 to 900 Hz for harmonic analysis. Maximum defection at resonance for steel is 7.94 mm, for composite is 74.4 mm, and for FGM is just 0.032 mm. The comparison of these results clearly depicts that FGM is having excellent vibration suppression performance as compared to other two materials under consideration. This confirms that thin structure (non-uniform circular profile) made of FGM can be used efficiently for the intended applications in future.

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Vibration Analysis of Axially Functionally Graded Timoshenko Beams with Non-uniform Cross-section

Cited by 7 publications

References 31 publications

Stochastic Higher-order Finite Element Model for the Free Vibration of a Continuous Beam resting on Elastic Support with Uncertain Elastic Modulus

Stochastic Higher-order Finite Element Model for the Free Vibration of a Continuous Beam resting on Elastic Support with Uncertain Elastic Modulus

Dynamic Control of Non-Linearly Tapering FGM Beams

Comparative modal analysis on fishing rod made of functionally graded composite material using finite element analysis

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