Critical velocities of anisotropic tubes under a moving pressure incorporating transverse shear and rotary inertia effects

Gao, X.-L.

doi:10.1007/s00707-022-03284-6

Cited by 7 publications

(2 citation statements)

References 45 publications

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“…3 are listed in Table 1, where they are also compared to the values of V cr0 for the same composite tube computationally determined in Simkins [29] by plotting the dispersion curves, which read A comparison of the values of V cr0 summarized in Table 1 with the values of V cr1 -V cr3 listed in Eq. ( 83) for the two-layer composite tube shows that V cr0 is much smaller than V cr1 , V cr2 or V cr3 , which is consistent with what was found for the single-layer isotropic steel tube without the orthotropic outer layer [10,11].…”

Section: Examplesupporting

confidence: 83%

“…Efforts have been made to determine critical velocities of single-layer, homogeneous tubes of materials with various types of symmetry, including isotropic, cubic, transversely isotropic and orthotropic (e.g., [10,11,15,27,30,35,36]). However, for composite tubes containing two or more cylindrical layers of dissimilar materials (e.g., [20,21,29]), very few studies have been conducted to find their critical velocities.…”

Section: Introductionmentioning

confidence: 99%

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Critical velocities of a two-layer composite tube under a moving internal pressure

Gao

2023

Acta Mech

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Critical velocities of a two-layer composite tube under a uniform internal pressure moving at a constant velocity are analytically determined. The formulation is based on a Love–Kirchhoff thin shell theory that incorporates the rotary inertia and material anisotropy. The composite tube consists of two perfectly bonded axisymmetric circular cylindrical layers of dissimilar materials, which can be orthotropic, transversely isotropic, cubic or isotropic. Closed-form expressions for the critical velocities and radial displacement of the two-layer composite tube are first derived for the general case by including the effects of material anisotropy, rotary inertia and radial stress. The formulas for composite tubes without the rotary inertia effect and/or the radial stress effect and with various types of material symmetry for each layer are then obtained as special cases. In addition, it is shown that the model for single-layer, homogeneous tubes can be recovered from the current model as a special case. To illustrate the new model, a composite tube with an isotropic inner layer and an orthotropic outer layer is analyzed as an example. All four critical velocities of the composite tube are calculated using the newly derived closed-form formulas. Six values of the lowest critical velocity of the two-layer composite tube are computed using three sets of the new formulas, which compare fairly well with existing results.

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Section: Examplesupporting

confidence: 83%

Section: Introductionmentioning

confidence: 99%

Critical velocities of a two-layer composite tube under a moving internal pressure

Gao

2023

Acta Mech

Self Cite

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Critical velocities of a two-layer composite tube incorporating the effects of transverse shear, rotary inertia and material anisotropy

Gao

2023

Z. Angew. Math. Phys.

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Critical velocities of a two-layer composite tube subjected to a uniform internal pressure moving at a constant velocity are analytically derived by using a first-order shear deformation shell theory incorporating the transverse shear, rotary inertia and material anisotropy. The composite tube consists of two perfectly bonded axisymmetric circular cylindrical layers of dissimilar materials, which can be orthotropic, transversely isotropic, cubic or isotropic. Closed-form expressions for four critical velocities are first derived for the general case by including the effects of transverse shear, rotary inertia, material orthotropy and radial stress. The formulas for composite tubes without the transverse shear, rotary inertia or radial stress effect and with simpler anisotropy are then obtained as special cases. In addition, it is shown that the model for a single-layer, homogeneous tube is included in the current model as a special case. To illustrate the newly derived closed-form formulas, a composite tube with an isotropic inner layer and an orthotropic outer layer is analyzed as an example. The numerical values of the lowest critical velocity of the two-layer composite tube predicted by the new formulas compare well with existing data.

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New analytical model for thermomechanical responses of multi-layered structures with imperfect interfaces

Shaat,

Gao,

et al. 2023

Acta Mech

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A new analytical model is developed for thermomechanical responses of multi-layered structures with an arbitrary number of layers and subjected to general thermal and mechanical loading. The formulation is based on an extended Bernoulli–Euler beam theory and a slip-interface model. The former includes Poisson’s effect and covers both the plane stress and plane strain deformations, and the latter allows slipping between two adjacent layers but no jump in the normal displacement or traction. An analytical solution for a multi-layered structure under general thermomechanical loading is derived by using a new approach that first determines one interfacial shear stress and the curvature of the deformed structure. To illustrate the newly developed model, three example problems for two-, three- and five-layer structures respectively are analytically solved by directly applying the new model. In all three cases, the solutions are obtained in closed-form expressions by considering both temperature changes and mechanical loads including body forces, distributed normal and shear stresses on the top and bottom surfaces, and normal forces, transverse shear forces and bending moments at the two ends, unlike existing ones. It is shown that the current solution for two-layer structures recovers an existing solution without considering Poisson’s effect and mechanical loading and the classical solution of Timoshenko for perfectly bonded bi-metal thermostats as two special cases. The closed-form solution for five-layer structures with imperfect interfaces is derived here for the first time. In addition, numerical results are provided for five- and seven-layer transistor stacks to quantitatively demonstrate the new model. It is found that the current results for the five-layer transistor stack agree well with those obtained by others, thereby further validating the new model.

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Critical velocities of anisotropic tubes under a moving pressure incorporating transverse shear and rotary inertia effects

Cited by 7 publications

References 45 publications

Critical velocities of a two-layer composite tube under a moving internal pressure

Critical velocities of a two-layer composite tube under a moving internal pressure

Critical velocities of a two-layer composite tube incorporating the effects of transverse shear, rotary inertia and material anisotropy

New analytical model for thermomechanical responses of multi-layered structures with imperfect interfaces

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