Stability analysis of cantilever functionally graded material nanotube under thermo-magnetic coupling effect

Tong, Guojun; Liu, Yongshou; Cheng, Qian; Dai, Jiayin

doi:10.1016/j.euromechsol.2019.103929

Cited by 21 publications

(5 citation statements)

References 24 publications

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“…, 2 The elastic modulus E(r), density ρ(r), viscosity coefficient η(r), shear modulus G(r), and thermal expansion coefficient α(r) of the FGV fluid-conveying pipe obey the following variation functions [42]:…”

Section: Mathematical Modelmentioning

confidence: 99%

Vibration Characteristics of a Functionally Graded Viscoelastic Fluid-Conveying Pipe with Initial Geometric Defects under Thermal–Magnetic Coupling Fields

Ma,

Wang

2024

Mathematics

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In this study, the Kevin–Voigt viscoelastic constitutive relationship is used to investigate the vibration characteristics and stability of a functionally graded viscoelastic(FGV) fluid-conveying pipe with initial geometric defects under thermal–magnetic coupling fields. First, the nonlinear dimensionless differential equations of motion are derived by applying Timoshenko beam theory. Second, by solving the equilibrium position of the system, the nonlinear term in the differential equations of motion is approximated as the sum of the longitudinal displacement at the current time and longitudinal displacement relative to the position, and the equations are linearized. Third, these equations are discretized using the Galerkin method and are numerically solved under simply supported conditions. Finally, the effects of dimensionless temperature field parameters, dimensionless magnetic field parameters, thermal–magnetic coupling, initial geometric defect types, and the power-law exponent on the complex frequency of the pipe are examined. Results show that increasing the magnetic field intensity enhances the critical velocity of first-order mode instability, whereas a heightened temperature variation reduces the critical velocity of first-order diverge instability. Under thermal–magnetic fields, when the magnetic field intensity and temperature difference are simultaneously increased, their effects on the complex frequency can partially offset each other. Increasing the initial geometric defect amplitude increases the imaginary parts of the complex frequencies; however, for different types of initial geometric defect tubes, it exhibits the most distinct influence only on a certain order.

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Section: Mathematical Modelmentioning

confidence: 99%

Vibration Characteristics of a Functionally Graded Viscoelastic Fluid-Conveying Pipe with Initial Geometric Defects under Thermal–Magnetic Coupling Fields

Ma,

Wang

2024

Mathematics

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“…According to thermoelastic theory, the thermal axial force generated by a temperature difference and the work done by the thermal axial force on the microtube can be written as [22]…”

Section: Governing Equationsmentioning

confidence: 99%

“…Therefore, owing to their excellent physical properties, functionally graded carbon nanotubes can be used in multiple physical fields, such as thermo-magnetic fields. Tong et al [22] established the dynamics equation for functionally graded cantilevered nanotubes under thermo-magnetic coupling. The influences of the external magnetic field and temperature on the stability of functionally graded material nanotubes were investigated.…”

Section: Introductionmentioning

confidence: 99%

Study on the Stability of Functionally Graded Simply Supported Fluid-Conveying Microtube under Multi-Physical Fields

2022

Micromachines

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The stability of functionally graded simply supported fluid-conveying microtubes under multiple physical fields was studied in this article. The strain energy of the fluid-conveying microtubes was determined based on strain gradient theory, and the governing equation of the functionally graded, simply supported, fluid-conveying microtube was established using Hamilton’s principle. The Galerkin method was used to solve the governing equation, and the effects of the dimensionless microscale parameters, temperature difference, and magnetic field intensity on the stability of the microtube were investigated. The results showed that the dimensionless microscale parameters have a significant impact on the stability of the microtube. The smaller the dimensionless microscale parameters were, the stronger the microscale effect of the material and the better the microtube stability became. The increase in the temperature difference decreased the eigenfrequency and critical velocity of the microtube and reduced the microtube stability. However, the magnetic field had the opposite effect. The greater the magnetic field intensity was, the greater the eigenfrequency and critical velocity were, and the more stable the microtube became.

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“…As for the influence of the external magnetic fields on carbon nanotubes, Sadeghi-Goughari et al [12] researched the microscale effects and transverse magnetic fields on the vibrational properties of cantilever carbon nanotubes. Based on the Euler-Bernoulli beam model, Tong et al [13] analyzed the effects of external magnetic fields and temperature fields on the stability of the functionally graded cantilever nanotubes under the effect of thermo-magnetic coupling.…”

Section: Introductionmentioning

confidence: 99%

Analysis of Nonlinear Vibration of Functionally Graded Simply Supported Fluid-Conveying Microtubes Subjected to Transverse Excitation Loads

2022

Micromachines

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This paper presents a nonlinear vibration analysis of functionally graded simply supported fluid-conveying microtubes subjected to transverse excitation loads. The development of the nonlinear equation of motion is based on the Euler–Bernoulli theory, Hamilton principle and Strain gradient theory. The nonlinear equation of motion is reduced to a second-order nonlinear ordinary differential equation by the Galerkin method. The Runge–Kutta method is adapted to solve the equation, and the effects of the dimensionless microscale parameters, the amplitude and frequency of excitation loads on the stability of the microtubes system are analyzed. It is found that when the microtube diameter is equal to the material length scale parameter, the microtube movement pattern is quasi-periodic. With the increase of the dimensionless microscale parameter, the microtube movement changes from quasi-periodic to chaos. The smaller the power-law index of volume fraction, the smaller the vibration displacement of microtubes and the better the stability. The larger the amplitude of excitation loads is, the larger the vibration displacement of the microtubes will be. When the frequency of excitation loads is equal to the natural frequency of the microtubes, it will have resonance and the vibration displacement will increase significantly.

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Stability analysis of cantilever functionally graded material nanotube under thermo-magnetic coupling effect

Cited by 21 publications

References 24 publications

Vibration Characteristics of a Functionally Graded Viscoelastic Fluid-Conveying Pipe with Initial Geometric Defects under Thermal–Magnetic Coupling Fields

Vibration Characteristics of a Functionally Graded Viscoelastic Fluid-Conveying Pipe with Initial Geometric Defects under Thermal–Magnetic Coupling Fields

Study on the Stability of Functionally Graded Simply Supported Fluid-Conveying Microtube under Multi-Physical Fields

Analysis of Nonlinear Vibration of Functionally Graded Simply Supported Fluid-Conveying Microtubes Subjected to Transverse Excitation Loads

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