On vibration behavior of rotating functionally graded double-tapered beam with the effect of porosities

Ebrahimi, Farzad; Hashemi, Mahmud

doi:10.1177/0954410015619647

Cited by 28 publications

(6 citation statements)

References 45 publications

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“…Considering exponential through-thickness material gradation, Ebrahimi and Mokhtari 27 studied the free vibration behavior of rotating FGM Timoshenko beam. Ebrahimi and Hashemi 28 performed the free vibration analysis of rotating double-tapered FGM Euler–Bernoulli beams for even and uneven distribution of porosities. Based on Euler–Bernoulli beam theory and Lagrange’s method, Maganti and Nalluri 29,30 reported the free vibration analysis of rotating double-tapered FGM beams for flap-wise and chord-wise motions.…”

Section: Introductionmentioning

confidence: 99%

A tangent stiffness–based approach to study free vibration of shear-deformable functionally graded material rotating beam through a geometrically non-linear analysis

Pal

Das

2017

The Journal of Strain Analysis for Engineering Design

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An improved mathematical model to study the free vibration behavior of rotating functionally graded material beam is presented, considering non-linearity up to second order for the normal and transverse shear strains. The study is carried out considering thermal loading due to uniform temperature rise and using temperature-dependent material properties. Power law variation is assumed for through-thickness symmetric functional gradation of ceramic-metal functionally graded beam. The effects of shear deformation and rotary inertia are considered in the framework of Timoshenko beam theory. First, the rotating beam configuration under time-invariant centrifugal loading and thermal loading is obtained through a geometrically non-linear analysis, employing minimum total potential energy principle. Then, the free vibration analysis of the deformed beam is performed using the tangent stiffness of the deformed beam configuration, and employing Hamilton's principle. The Coriolis effect is considered in the free vibration problem, and the governing equations are transformed to the state-space to obtain the eigenvalue problem. The solution of the governing equations is obtained following Ritz method. The validation is performed with the available results, and also with finite element software ANSYS. The analysis is carried out for clamped-free beam and for clamped-clamped beam with immovably clamped ends. The results for the first two modes of chord-wise and flap-wise vibration in non-dimensional speed-frequency plane are presented for different functionally graded material compositions, material profile parameters, root offset parameters and operating temperatures.

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Section: Introductionmentioning

confidence: 99%

A tangent stiffness–based approach to study free vibration of shear-deformable functionally graded material rotating beam through a geometrically non-linear analysis

Pal

Das

2017

The Journal of Strain Analysis for Engineering Design

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“…However, in the case of uneven distribution porosities exist only in the middle zone where ceramic and metal phases become mixed. The equations used to compute the effective properties of FGM plates with porosity inclusions are given below [24,53]:…”

Section: Geometric Configuration and Effective Materials Properties O...mentioning

confidence: 99%

Thermo‐mechanical nonlinear stability analysis of geometrically imperfect functionally graded plates with microstructural defects using logarithmic structure kinematics: An unified expression

Rajput

Gupta

2022

Z Angew Math Mech

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In the present paper, thermo‐mechanical stability analysis of geometrically imperfect porous functionally graded plates (FGP) with geometric nonlinearity is presented. The equilibrium, stability, and compatibility equations are derived using Logarithmic structural kinematics in conjunction with the von‐Karman type of geometric nonlinearity. A logarithmic‐based shear‐strain function has been used for the first time for the buckling response of functionally graded material (FGM) plates. Generic imperfection function has been implemented to incorporate the various imperfection modes like sin‐type or global type in the formulation. The effective materials properties of the plates with porosity inclusion have been computed using modified power law. The plate is subjected to uniaxial and biaxial compression as well as combined compression and tension along with thermal loading. An exact expression for the critical buckling load and critical buckling thermal load of geometrically imperfect porous FGM plate for each loading case has been developed. After confirming the excellent accuracy of the current exact solutions, the effect of geometric imperfection, porosity inclusion, and geometric configurations on the nonlinear stability of the FGM plate have been discussed extensively. The results presented in this paper will be used as a benchmark for future research.

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“…Free vibration studies of rotating macro-size beams have been an important research field for many years, and different researchers had addressed this problem employing classical theory (independent of size-effect). Some of those studies are found in 10–16 dealing with homogeneous beams and in 17–22 dealing with FGM beams. It is worthwhile to mention that investigations on free vibration of rotating micro-size beams have also gained attention from the researchers over the past few years.…”

Section: Introductionmentioning

confidence: 99%

Study on free vibration behavior of rotating bidirectional functionally graded nano-beams based on Eringen’s nonlocal theory

Malik

Das

2020

Proceedings of the Institution of Mechanical Engineers, Part L:

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Free vibration behavior of rotating bidirectional functionally graded nano-beams is studied based on Eringen’s nonlocal theory. The beam material consists of ceramic and metal constituents, and the material is graded across the length and thickness directions. The mathematical formulation is framed on Euler–Bernoulli beam theory, and the system of governing equations is derived in variational form using Hamilton’s principle. The governing equations are discretized and transformed to an eigen value problem using Ritz method. The model is formulated to study the flapping and lead-lag motions due to free vibration. The model is verified with the available numerical results. The numerical results are presented in non-dimensional frequency-speed plane to study the influence of normalized nonlocal parameter, length gradient parameter, thickness gradient parameter, root radius parameter, and section aspect ratio. Some normalized mode shapes are presented to illustrate the mode switching phenomenon. The mathematical model of a nonlocal rotating bidirectional functionally graded material nano-beam is presented for the first time through this work and the reported results are new of its kind.

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On vibration behavior of rotating functionally graded double-tapered beam with the effect of porosities

Cited by 28 publications

References 45 publications

A tangent stiffness–based approach to study free vibration of shear-deformable functionally graded material rotating beam through a geometrically non-linear analysis

A tangent stiffness–based approach to study free vibration of shear-deformable functionally graded material rotating beam through a geometrically non-linear analysis

Thermo‐mechanical nonlinear stability analysis of geometrically imperfect functionally graded plates with microstructural defects using logarithmic structure kinematics: An unified expression

Study on free vibration behavior of rotating bidirectional functionally graded nano-beams based on Eringen’s nonlocal theory

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