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Journal ArticleDOI: 10.1080/17455030.2019.1584420

A nonlocal strain gradient theory for vibration and flutter instability analysis in rotary SWCNT with conveying viscous fluid

04 Mar 2021-Waves in Random and Complex Media (Informa UK Limited)-Vol. 31, Iss: 2, pp 305-330
Abstract: In this article, the influence of flow velocity and rotational speed on instability and free vibration analysis of a rotating viscoelastic single wall carbon nanotube (SWCNT) conveying viscous flui...

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Topics: Viscous liquid (57%), Viscoelasticity (55%), Flow velocity (52%) ... show more
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7 results found


Journal ArticleDOI: 10.1007/S00366-020-01123-7
Xuping Zhu1, Zhangxian Lu1, Zhengliang Wang1, Lixin Xue1  +1 moreInstitutions (1)
Abstract: As a first attempt, the vibration and stability analysis of magnetically embedded spinning axially functionally graded (AFG) nanotubes conveying fluid under axial loads is performed based on the nonlocal strain gradient theory (NSGT). A detailed parametric investigation is conducted to elucidate the influence of key factors such as material distribution type and size-dependent parameters on the divergence and flutter instability borders. Also, a comparative study is conducted to evaluate the available theories in the modeling of nanofluidic systems. The material characteristics of the system are graded along the longitudinal direction based on the power-law and exponential distribution functions. To accurate model and formulate the system, the no-slip boundary condition is considered. Adopting the Laplace transform and Galerkin discretization technique, the governing size-dependent dynamical equations of the system are solved. The backward and forward natural frequencies, as well as critical fluid and spin velocities of the system, are extracted. Besides, an analytical approach is applied to identify the instability thresholds of the system. Dynamical configurations, Campbell diagrams, and stability maps are analyzed. Meanwhile, it is concluded that, in contrast to the influence of nonlocal and density gradient parameters, the increment of strain gradient and elastic modulus gradient parameters expands the stability regions and alleviate the destabilizing effect of the axial compressive load.

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Topics: Instability (52%), Axial symmetry (51%), Laplace transform (51%) ... show more

12 Citations


Open accessJournal ArticleDOI: 10.1016/J.DT.2020.01.007
Farzad Ebrahimi1, Ali Dabbagh2Institutions (2)
01 Feb 2021-Defence Technology
Abstract: The vibration problem of a fluid conveying cylindrical shell consisted of newly developed multi-scale hybrid nanocomposites is solved in the present manuscript within the framework of an analytical solution. The consistent material is considered to be made from an initial matrix strengthened via both macro- and nano-scale reinforcements. The influence of nanofillers’ agglomeration, generated due to the high surface to volume ratio in nanostructures, is included by implementing Eshelby-Mori-Tanaka homogenization scheme. Afterwards, the equivalent material properties of the carbon nanotube reinforced (CNTR) nanocomposite are coupled with those of CFs within the framework of a modified rule of mixture. On the other hand, the influences of viscous flow are covered by extending the Navier-Stokes equation for cylinders. A cylindrical coordinate system is chosen and mixed with the infinitesimal strains of first-order shear deformation theory of shells to obtain the motion equations on the basis of the dynamic form of principle of virtual work. Next, the achieved governing equations will be solved by Galerkin’s method to reach the natural frequency of the structure for both simply supported and clamped boundary conditions. Presenting a set of illustrations, effects of each parameter on the dimensionless frequency of nanocomposite shells will be shown graphically.

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Topics: Cylindrical coordinate system (53%), Galerkin method (52%), Homogenization (chemistry) (51%) ... show more

8 Citations


Journal ArticleDOI: 10.1080/15397734.2020.1819310
Abstract: This article is a comprehensive investigation into the equations of the size-dependent free vibration of a special type of fluid-conveying nanotubes, i.e., double-walled boron nitride nanotubes, in...

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Topics: Boron nitride (62%)

7 Citations


Open accessJournal ArticleDOI: 10.22034/JSM.2020.1895313.1561
Abstract: The free vibration behavior of two fluid-conveying vertically-aligned single-walled boron nitride nanotubes are studied in the present paper via the nonlocal strain gradient piezoelectric theory in conjunction with the first-order shear deformation shell assumption in thermal environments. It is supposed that the two adjacent boron nitride nanotubes are coupled with each other in the context of linear deformation by van der Waals interaction according to Lennard–Jones potential function. To achieve a more accurate modeling for low-scale structures, both hardening and softening effects of materials are considered in the nonlocal strain gradient approach. The motion equations and associated boundary conditions are derived by means of Hamilton’s variational principle, then solved utilizing differential quadrature method. Numerical studies are done to reveal the effect of different boundary conditions, size scale parameters, aspect ratio, inter-tube distance, and temperature change on the variations of dimensionless eigenfrequency and critical flow velocity.

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Topics: Boundary value problem (54%), Boron nitride (53%), Shell (structure) (51%) ... show more

3 Citations


Journal ArticleDOI: 10.1140/EPJP/S13360-021-01785-2
Wenyong Weng1, Yin Lu, Vahid Borjalilou2Institutions (2)
Abstract: In this article, size-dependent modeling and analysis of thermoelastic coupling effect on the oscillations of Timoshenko nanobeams are carried out. Small-scale effect on the nanostructure and heat conduction is taken into account with the aid of nonlocal strain gradient theory (NSGT) together with dual-phase-lag (DPL) heat conduction model. In order to illustrate the influence of nonclassical scale parameters on the coefficients of governing equations, the normalized forms of size-dependent equations of motion and heat conduction are established by definition of some dimensionless parameters. These coupled differential equations are then solved in the Laplace domain to attain the analytical thermoelastic responses of a simply supported Timoshenko nanobeam subjected to a dynamic load. Through several numerical examples, a detailed parametric study is performed to illuminate the decisive role of nonlocal, strain gradient and phase lag parameters in thermoelastic behavior of Timoshenko nanobeams. Furthermore, comparing the results corresponding to various relative magnitudes of nonlocal and strain gradient length scale parameters confirms the potential of NSGT for covering both hardening and softening characteristic of nanoscale structures.

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3 Citations


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75 results found


Journal ArticleDOI: 10.1063/1.332803
Abstract: Integropartial differential equations of the linear theory of nonlocal elasticity are reduced to singular partial differential equations for a special class of physically admissible kernels. Solutions are obtained for the screw dislocation and surface waves. Experimental observations and atomic lattice dynamics appear to support the theoretical results very nicely.

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3,440 Citations


Journal ArticleDOI: 10.1016/S0022-5096(03)00053-X
David Chuen Chun Lam1, Fan Yang2, Fan Yang1, Arthur C.M. Chong1  +3 moreInstitutions (2)
Abstract: Conventional strain-based mechanics theory does not account for contributions from strain gradients. Failure to include strain gradient contributions can lead to underestimates of stresses and size-dependent behaviors in small-scale structures. In this paper, a new set of higher-order metrics is developed to characterize strain gradient behaviors. This set enables the application of the higher-order equilibrium conditions to strain gradient elasticity theory and reduces the number of independent elastic length scale parameters from five to three. On the basis of this new strain gradient theory, a strain gradient elastic bending theory for plane-strain beams is developed. Solutions for cantilever bending with a moment and line force applied at the free end are constructed based on the new higher-order bending theory. In classical bending theory, the normalized bending rigidity is independent of the length and thickness of the beam. In the solutions developed from the higher-order bending theory, the normalized higher-order bending rigidity has a new dependence on the thickness of the beam and on a higher-order bending parameter, bh. To determine the significance of the size dependence, we fabricated micron-sized beams and conducted bending tests using a nanoindenter. We found that the normalized beam rigidity exhibited an inverse squared dependence on the beam's thickness as predicted by the strain gradient elastic bending theory, and that the higher-order bending parameter, bh, is on the micron-scale. Potential errors from the experiments, model and fabrication were estimated and determined to be small relative to the observed increase in beam's bending rigidity. The present results indicate that the elastic strain gradient effect is significant in elastic deformation of small-scale structures.

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Topics: Bending stiffness (70%), Pure bending (68%), Plastic bending (67%) ... show more

2,091 Citations


Journal ArticleDOI: 10.1016/0020-7683(65)90006-5
Raymond D. Mindlin1Institutions (1)
Abstract: In this paper there is formulated a linear theory of deformation of an elastic solid in which the potential energy-density is a function of the strain and its first and second gradients. This is a theory in which cohesive force and surface-tension are intrinsic. A solution is given for the strain and surface-tension, or surface-energy per unit area, resulting from separation of a solid along a plane; and a comparison is made with an analogous lattice model. Also presented are a general solution of the displacement-equation of equilibrium in terms of stress functions and the particular solution for the concentrated force. The special case of a liquid is considered and the solutions are given for the surface-tensions at plane and spherical surfaces.

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Topics: Linear elasticity (60%), Stress functions (57%), Surface stress (56%) ... show more

1,523 Citations


Open accessBook
14 Jan 2000-
Abstract: Application of Differential Quadrature to Engineering ProblemsApplication of Differential Quadrature to the Analysis of Structural ComponentsTsinghua Science and TechnologyApplication of Differential Quadrature Method to the Analysis of Delamination Buckling of Laminated CompositesDifferential Quadrature and Differential Quadrature Based Element MethodsApplication of the Differential Quadratire Method to Problems in Engineering MechanicsProceedings of the International Conference on Advances in Computational Mechanics 2017Advanced Differential Quadrature MethodsA Differential Quadrature Hierarchical Finite Element MethodLaminated Composite Doubly-Curved Shell StructuresRecent Advances in Mathematics for EngineeringComputer Modeling in Engineering & SciencesMeshfree Approximation Methods with MatlabApplication of Differential Quadrature to the Analysis of Static Aeroelastic PhenomenaApplication of the Differential Quadrature Method to the Plane Elasticity ProblemMathematical Methods in Interdisciplinary SciencesDiQuMaSPABWave Propagation in Materials for Modern ApplicationsDifferential Quadrature Methods and Its ApplicationsA Generalization and Application of the Differential Quadrature MethodApplication of the Differential Quadrature Method to the Buckling Analysis of Cylindrical Shells and TanksBoundary Elements and Other Mesh Reduction Methods XXXVDifferential Quadrature and Its Application in EngineeringDifferential Quadrature Method in Computational MechanicsUse of Differential Quadrature in a Recursive FilterApplication of Differential Quadrature to Nuclear Engineering ProblemsMathematical PhysicsStructural Dynamics of Earthquake EngineeringDeterministic Flexibility AnalysisHandbook of Research on Computational Science and Engineering: Theory and PracticeNonlinear DynamicsInternational Petroleum Conference & Exhibition of MexicoVibration Analysis of Non-uniform Beams Using the Differential Quadrature MethodApplication of Differential Quadrature Method to the Analysis of Delamination Buckling of Laminated CompositesMechanical Vibration: Where Do We Stand?Scientific and Technical Aerospace ReportsA New Differential Quadrature Method Based on Bernstein PolynomialsA Primer on Radial Basis Functions with Applications to the GeosciencesMechanics of laminated Composite doubly-curvel shell structuresProceedings of the Sixth International Colloguium on Differential Equations

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Topics: Gauss–Jacobi quadrature (83%), Adaptive quadrature (75%), Quadrature (mathematics) (62%) ... show more

1,340 Citations


Journal ArticleDOI: 10.1016/0021-9991(72)90089-7
Abstract: The numerical solution of nonlinear partial differential equations plays a prominent role in numerical weather forecasting, optimal control theory, radiative transfer, and many other areas of physics, engineering, and biology. In many cases all that is desired is a moderately accurate solution at a few points which can be calculated rapidly. In this paper we wish to present a simple direct technique which can be applied in a large number of cases to circumvent the difficulties of programming complex algorithms for the computer, as well as excessive use of storage and computer time. We illustrate this technique with the solution of some partial differential equations arising in various simplified models of fluid flow and turbulence.

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1,146 Citations


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