Nonlinear buckling and resonances of functionally graded fluid-conveying pipes with initial geometric imperfection

Ding, Hao-Xuan; She, Gui-Lin; Zhang, Yiwen

doi:10.1140/epjp/s13360-022-03570-1

Cited by 11 publications

(2 citation statements)

References 34 publications

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“…To address this gap, Li and Qiao [37] studied the static behavior of beams featuring an initial curvature, analyzing the factors influencing the buckling behavior of the system under different boundary conditions. Ding et al [38] studied the dynamic characteristics of functionally graded pipes with initial geometric defects. Further, they analyzed the influence of temperature variation and other factors on the nonlinear dynamic characteristics.…”

Section: Introductionmentioning

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: Introductionmentioning

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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“…has come into being recently. While for pipe structure, accessories such as connector [24] and restrained clip [25], complex spatial configuration [26][27], the material is functionally gradient [28][29][30][31], altered geometric shape [32][33] etc. are some research hotspots in recent years.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of a cantilevered fluid-conveying straight pipe with centrosymmetric rib plates installed at its fixed end

Zhao,

Cai,

et al. 2023

Preprint

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Rib plates are often used for improving load-bearing capacity, to study the influences of centrosymmetric rib plates installed at the fixed end on the dynamics of a cantilevered fluid-conveying straight pipe, the governing equation is deduced based on D’Alembert principle at first, during this process, the centrosymmetric rib plates are equivalently replaced by the combination of a series of linear and torsional springs whose stiffness coefficients are formulated according to thin plate bending theory. Then Galerkin method is used to discretize the above governing equation, where the shape functions are just the mode functions of cantilevered Euler-Bernoulli straight beam deduced by differential transformation method, the expressions of eigenfunction for flow-induced vibration and steady-state displacement response for forced vibration are obtained subsequently. Numerical experiments of a real water-supplying pipe are carried out, some conclusions never mentioned in published literatures are drawn. The same dynamic problems for other kinds of straight pipes and for curved pipes possessing one clamped end are also discussed. The investigation has reference meaning for optimal design of rib plates in aspects of geometric sizes and materials, also for optimal design of supporting formats of fluid-conveying pipes.

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Parametric resonance of axially functionally graded pipes conveying pulsating fluid

Jing,

Mao,

Ding

et al. 2024

Appl. Math. Mech.-Engl. Ed.

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Based on the generalized Hamilton’s principle, the nonlinear governing equation of an axially functionally graded (AFG) pipe is established. The non-trivial equilibrium configuration is superposed by the modal functions of a simply supported beam. Via the direct multi-scale method, the response and stability boundary to the pulsating fluid velocity are solved analytically and verified by the differential quadrature element method (DQEM). The influence of Young’s modulus gradient on the parametric resonance is investigated in the subcritical and supercritical regions. In general, the pipe in the supercritical region is more sensitive to the pulsating excitation. The nonlinearity changes from hard to soft, and the non-trivial equilibrium configuration introduces more frequency components to the vibration. Besides, the increasing Young’s modulus gradient improves the critical pulsating flow velocity of the parametric resonance, and further enhances the stability of the system. In addition, when the temperature increases along the axial direction, reducing the gradient parameter can enhance the response asymmetry. This work further complements the theoretical analysis of pipes conveying pulsating fluid.

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Nonlinear buckling and resonances of functionally graded fluid-conveying pipes with initial geometric imperfection

Cited by 11 publications

References 34 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

Dynamics of a cantilevered fluid-conveying straight pipe with centrosymmetric rib plates installed at its fixed end

Parametric resonance of axially functionally graded pipes conveying pulsating fluid

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