A non-classical model for first-ordershear deformation circular cylindrical thin shells incorporating microstructure and surface energy effects

Critical velocities and middle-surface displacements of anisotropic axisymmetric cylindrical shells (tubes) under a uniform internal pressure moving at a constant velocity are derived in closed-form expressions by using the Love–Kirchhoff thin shell theory incorporating the rotary inertia and material anisotropy. The formulation is based on the general three-dimensional constitutive relations for orthotropic elastic materials and provides a unified treatment of orthotropic, transversely isotropic, cubic and isotropic tubes, which can represent various composite and metallic tubes. Closed-form formulas are first obtained for the general case with both the rotary inertia and radial stress effects, which are then reduced to the special cases without the rotary inertia effect and/or radial stress effect. It is shown that when the rotary inertia effect is suppressed and the radial normal stress is neglected, the newly derived formulas for the critical velocities of orthotropic and isotropic tubes recover the two existing ones for thin tubes as special cases. An example for an isotropic tube is provided to illustrate the new formulas, which give the values of the critical velocity and dynamic amplification factor that agree well with those obtained experimentally and computationally by others.

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“…are the Cauchy stress resultants through the shell thickness. The kinetic energy of the shell has the form [25,26]:…”

Section: Orthotropic Cylindrical Shell Model With the Rotary Inertia ...mentioning

confidence: 99%

Critical velocities and displacements of anisotropic tubes under a moving pressure

Gao

Littlefield

2022

Mathematics and Mechanics of Solids

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“…The size effect induces distinct mechanical properties in microstructures compared to macrostructures. Currently, many high-order theories are proposed to describe the size effect [35][36][37][38][39][40][41][42][43][44], such as the couple stress theory [45], strain gradient theory [46], non-local elasticity theory [47], surface elasticity theory [48], and reformulated strain gradient elasticity theory [49][50][51]. Utilizing the couple stress theory, Yang et al established the modified couple stress theory (MCST), which specifically accounts for the symmetric curvature tensor with one additional material parameter for isotropic material.…”

Section: Model and Formulationmentioning

confidence: 99%

Size and Temperature Effects on Band Gap Analysis of a Defective Phononic Crystal Beam

Yao,

Wang,

Hong

et al. 2024

Crystals

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In this paper, a new defective phononic crystal (PC) microbeam model in a thermal environment is developed with the application of modified couple stress theory (MCST). By using Hamilton’s principle, the wave equation and complete boundary conditions of a heated Bernoulli–Euler microbeam are obtained. The band structures of the perfect and defective heated PC microbeams are solved by employing the transfer matrix method and supercell technology. The accuracy of the new model is validated using the finite element model, and the parametric analysis is conducted to examine the influences of size and temperature effects, as well as defect segment length, on the band structures of current microbeams. The results indicate that the size effect induces microstructure hardening, while the increase in temperature has a softening impact, decreasing the band gap frequencies. The inclusion of defect cells leads to the localization of elastic waves. These findings have significant implications for the design of microdevices, including applications in micro-energy harvesters, energy absorbers, and micro-electro-mechanical systems (MEMS).

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“…where u x , u θ and u z are, respectively, the x-, θ -and z-components of the displacement vector u of a point (x, θ , z) in the shell at time t, and u and w are, respectively, the x-and z-displacement components of the corresponding point (x, θ , 0) on the shell middle surface at time t. Note that u θ is identically zero and there is no dependence on θ for all kinematic and kinetic quantities in such an axisymmetric problem (e.g., [11,14]), which differ from those in general deformations of circular cylindrical shells (e.g., [37,40]). From Eq.…”

Section: Axisymmetric Circular Cylindrical Shell Model With the Rotar...mentioning

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 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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A non-classical model for first-ordershear deformation circular cylindrical thin shells incorporating microstructure and surface energy effects

Cited by 18 publications

References 58 publications

Critical velocities and displacements of anisotropic tubes under a moving pressure

Critical velocities and displacements of anisotropic tubes under a moving pressure

Size and Temperature Effects on Band Gap Analysis of a Defective Phononic Crystal Beam

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

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