• Structural Engineering and Mechanics
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• 제69권2호
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• pp.205-219
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• 2019

This paper analyzes nonlinear free vibration of the circular nano-tubes made of functionally graded materials in the framework of nonlocal strain gradient theory in conjunction with a refined higher order shear deformation beam model. The effective material properties of the tube related to the change of temperature are assumed to vary along the radius of tube based on the power law. The refined beam model is introduced which not only contains transverse shear deformation but also satisfies the stress boundary conditions where shear stress cancels each other out on the inner and outer surfaces. Moreover, it can degenerate the Euler beam model, the Timoshenko beam model and the Reddy beam model. By incorporating this model with Hamilton's principle, the nonlinear vibration equations are established. The equations, including a material length scale parameter as well as a nonlocal parameter, can describe the size-dependent in linear and nonlinear vibration of FGM nanotubes. Analytical solution is obtained by using a two-steps perturbation method. Several comparisons are performed to validate the present analysis. Eventually, the effects of various physical parameters on nonlinear and linear natural frequencies of FGM nanotubes are analyzed, such as inner radius, temperature, nonlocal parameter, strain gradient parameter, scale parameter ratio, slenderness ratio, volume indexes, different beam models.

• 유체기계공업학회:학술대회논문집
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• 유체기계공업학회 2002년도 유체기계 연구개발 발표회 논문집
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• pp.447-452
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• 2002

An honeycomb/smooth land seal alternating with the honeycomb seal is suggested for structural enhancement in high pressure turbomachinery. Governing equations are derived for an honeycomb/smooth land annular gas seal based on Hirs' lubrication theory and Moody's friction factor model for smooth land and empirical friction factor model for honeycomb land. By using a perturbation analysis and a numerical integration method, the governing equations are solved to yield leakage and the corresponding dynamic coefficients developed by the seal. Theoretical results show that leakage is increasing and rotordynamic stability is decreasing as increasing the length of smooth land part in the honeycomb/smooth land seal.

• 한국유체기계학회 논문집
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• 제5권4호
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• pp.40-46
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• 2002

An honeycomb/smooth land seal alternating with the honeycomb seal is suggested for structural enhancement in high pressure turbomachinery. Governing equations are derived for an honeycomb/smooth land annular gas seal based on Hirs' lubrication theory and Moody's friction factor model for smooth land and empirical friction factor model for honeycomb land. By using a perturbation analysis and a numerical integration method, the governing equations are solved to yield leakage and the corresponding dynamic coefficients developed by the seal. Theoretical results show that the leakage increases and rotordynamic stability decreases as increasing the length of smooth land part in the honeycomb/smooth land seal.

• Structural Engineering and Mechanics
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• 제47권3호
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• pp.345-359
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• 2013

For the purpose of investigating the free vibration response of the spatial curved beams, the governing equations are derived in matrix formats, considering the variable curvature and torsion. The theory includes all the effects of rotary inertia, shear and axial deformations. Frobenius' scheme and the dynamic stiffness method are then applied to solve these equations. A computer program is coded in Mathematica according to the proposed method. As a special case, the dynamic stiffness and further the natural frequencies of a cylindrical helical spring under fixed-fixed boundary condition are carried out. Comparison of the present results with the FEM results using body elements in I-DEAS shows good accuracy in computation and validity of the model. Further, the present model is used for reciprocal spiral rods with different boundary conditions, and the comparison with FEM results shows that only a limited number of terms in the resultant provide a relatively accurate solution.

• Structural Engineering and Mechanics
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• 제66권6호
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• pp.693-701
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• 2018

This paper develops a nonlocal strain gradient plate model for vibration analysis of graphene sheets under thermal environments. For more accurate analysis of graphene sheets, the proposed theory contains two scale parameters related to the nonlocal and strain gradient effects. Graphene sheet is modeled via a two-variable shear deformation plate theory needless of shear correction factors. Governing equations of a nonlocal strain gradient graphene sheet on elastic substrate are derived via Hamilton's principle. Differential quadrature method (DQM) is implemented to solve the governing equations for different boundary conditions. Effects of different factors such as temperature rise, nonlocal parameter, length scale parameter, elastic foundation and aspect ratio on vibration characteristics a graphene sheets are studied. It is seen that vibration frequencies and critical buckling temperatures become larger and smaller with increase of strain gradient and nonlocal parameter, respectively.

• Structural Engineering and Mechanics
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• 제70권6호
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• pp.661-669
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• 2019

Buckling analysis of shape memory alloy (SMA) rectangular plates subjected to uniform and linearly distributed inplane loads is the main objective in the present paper. Brinson's model is developed to express the constitutive characteristics of SMA plate. Using the classical plate theory and variational approach, stability equations are derived. In addition to external inplane mechanical loads, the plate is subjected to the pre-stresses caused by the recovery stresses that are generated during martensitic phase transformation. Ritz method is used for solving the governing stability equations. Finally, the effects of conditions on the edges, thickness, aspect ratio, temperature and pre-strains on the critical buckling loads of SMA plate are investigated in details.

• Structural Engineering and Mechanics
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• 제71권3호
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• pp.257-269
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• 2019

This paper develops a nonlocal strain gradient plate model for damping vibration analysis of smart magneto-electro-viscoelastic nanoplates resting on visco-Pasternak medium. For more accurate analysis of nanoplate, the proposed theory contains two scale parameters related to the nonlocal and strain gradient effects. Viscoelastic effect which is neglected in all previous papers on magneto-electro-viscoelastic nanoplates is considered based on Kelvin-Voigt model. Governing equations of a nonlocal strain gradient smart nanoplate on viscoelastic substrate are derived via Hamilton's principle. Galerkin's method is implemented to solve the governing equations. Effects of different factors such as viscoelasticity, nonlocal parameter, length scale parameter, applied voltage and magnetic potential on damping vibration characteristics of a nanoplate are studied.

• Structural Engineering and Mechanics
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• 제70권4호
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• pp.407-420
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• 2019

In the present work, an attempt is made to explore the effects of shear in-plane preload on the wave propagation response of small-scale plates containing nanofibers. The small-scale system is assumed to be embedded in an elastic matrix. The nonlocal elasticity is utilized in order to develop a size-dependent model of plates. The proposed plate model is able to describe both nanofiber effects and the influences of being at small-scales on the wave propagation response. The size-dependent differential equations are derived for motions along all directions. The size-dependent coupled equations are solved analytically to obtain the phase and group velocities of the small-scale plate under a shear in-plane preload. The effects of this shear preload in conjunction with nanofiber and size effects as well as the influences of the elastic matrix on the wave propagation response are analyzed in detail.

• Structural Engineering and Mechanics
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• 제82권2호
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• pp.225-232
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• 2022

In this paper, the physical neutral surface concept is applied to study the wave propagation of functionally graded (FG) circular plate, the wave equation is derived by Hamiltonian variational principle and the first-order shear deformation plate model. Then, we convert the equations to dimensionless equations. The exact solution of wave propagation problem is obtained by Laplace integral transformation, the first order Hankel integral transformation and the zero order Hankel integral transformation. The results obtained by the current model are very close to those obtained in the existing literature, which indicates the correctness and reliability of this study. Moreover, the effects of the functionally graded index parameters and pore volume fraction on the wave propagation are also discussed in detail.

• Structural Engineering and Mechanics
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• 제87권2호
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• pp.129-136
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• 2023

In this paper, dynamic buckling of truncated conical shell made of carbon nanotubes (CNTs) composite is studied. In aerospace industries, this category of structures is utilized extensively due to wide range of engineering applications. To calculate the effective material properties of the nanocomposite, The Mori-Tanaka model is applied. Also, the motion equations are derived with the assistance of the first order shear deformation theory (FSDT), Hamilton's principle and energy method. Besides, In order to solve motion equations and analyze dynamic instability region (DIR) of the structure, mixed model of differential quadrature method (DQM) and Bolotin's method is used. Moreover, investigation of the different parameters effects such as geometrical parameters and volume fraction of CNTs on the analysis of the DIR of the structure is done. In accordance with the obtained results, the DIR will occur at higher frequencies by increasing the volume fraction of CNTs.