Vibration of spinning functionally graded nanotubes conveying fluid
TL;DR: In this paper, 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).
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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TL;DR: In this article, the impact of the nonlinear modal analysis of axially functionally graded (AFG) truncated conical micro-scale tube including the thermal loading for the different type of cross sections such as uniform section, linear tapered section, convex section, the exponential section are studied that are applicable for various application, for example, the micro-thermal fins, macro-/micro-fluid-flow diffuser, fluid-flow nozzle, micro-sensor, etc.
Abstract: In this paper, to improve the vibrational response of microstructures, the impact of the nonlinear modal analysis of axially functionally graded (AFG) truncated conical micro-scale tube including the thermal loading for the different type of cross sections such as uniform section, linear tapered section, convex section, the exponential section are studied that are applicable for various application, for example, the micro-thermal fins, macro-/micro-fluid-flow diffuser, fluid-flow nozzle, fluid-flow throat, micro-sensor, etc. The nonlinear equations are obtained applying Hamilton’s principles based on the modified couple stress to determine the size effect and Euler–Bernoulli beam theory considering the von-Karman’s nonlinear strain. The material combination varies along the tube’s length, denouncing the AFG tube made by metal and ceramic phases. The nonlinear equations are solved by applying a couple of homotopy perturbation methods (HPM) to calculating the nonlinear results and the generalized differential quadrature method (GDQM) to providing the initial conditions. The linear and nonlinear results presented the effect of various cross sections and other parameters on the micro-tube frequency that are valuable to design and manufacture the micro-electro-mechanical systems (MEMS).
39 citations
TL;DR: The early studies on the dynamics of pipes conveying fluid by Feodos'ev, Housner, Benjamin and Païdoussis elucidated the basic dynamics of the system as mentioned in this paper .
15 citations
TL;DR: In this article, the frequency response of thermally pre/post buckled composite pipes reinforced with carbon nanotubes (CNTs) is analyzed using a higher-order shear deformation model and the von Karman assumption.
15 citations
TL;DR: In this paper, the coupled vibrations of nanobeams with axial and spinning motions under complex environmental changes are modeled, and a detailed parametric investigation is also performed to determine the effect of size-dependent parameters, boundary conditions, hygro-thermo-magnetic loads, axial, and spin velocities on the dynamical behavior and stability regions of the system.
Abstract: In this paper, based on the nonlocal strain gradient theory (NSGT), the coupled vibrations of nanobeams with axial and spinning motions under complex environmental changes are modeled. A detailed parametric investigation is also performed to determine the effect of size-dependent parameters, boundary conditions, hygro–thermo–magnetic loads, axial and spin velocities on the dynamical behavior and stability regions of the system. Adopting the Galerkin discretization technique, the eigenvalue problem is solved, and natural frequencies, divergence and flutter instability thresholds of the system are extracted accordingly. The acquired outcomes are compared with the reported results in the literature. Besides, the accuracy of the numerical method is compared with analytical approaches and a good agreement is observed. The obtained results demonstrate that considering the nonlocal and hygro–thermal effects in modeling has destabilizing impacts on the dynamical response of the system. While imposing the strain gradient term and magnetic field leads to the enhancement of vibrational frequencies and enlargement of stability areas. In addition, it is concluded that in hygro–thermal environments, by ascending the spin velocity, instead of the occurrence of divergence instability, the system experiences the flutter conditions. Meanwhile, the attained outcomes indicated that the variation of spin velocity does not affect the flutter instability threshold of the system.
14 citations
TL;DR: In this article, the authors established a thorough model for appraisal of size-dependent thermoelastic vibrations of Timoshenko nanobeams by capturing small-scale effect on both structural and thermal fields.
14 citations
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Book•
25 Feb 2014
TL;DR: In this article, the first volume of the Fluid-Structure Interaction (FSI) series, Volume 1 covers the fundamentals and mechanisms giving rise to flow-induced vibration, with a particular focus on the challenges associated with pipes conveying fluid.
Abstract: The first of two books concentrating on the dynamics of slender bodies within or containing axial flow, Fluid-Structure Interaction, Volume 1 covers the fundamentals and mechanisms giving rise to flow-induced vibration, with a particular focus on the challenges associated with pipes conveying fluid. This volume has been thoroughly updated to reference the latest developments in the field, with a continued emphasis on the understanding of dynamical behaviour and analytical methods needed to provide long-term solutions and validate the latest computational methods and codes. In this edition, Chapter 7 from Volume 2 has also been moved to Volume 1, meaning that Volume 1 now mainly treats the dynamics of systems subjected to internal flow, whereas in Volume 2 the axial flow is in most cases external to the flow or annular. * Provides an in-depth review of an extensive range of fluid-structure interaction topics, with detailed real-world examples and thorough referencing throughout for additional detail. * Organized by structure and problem type, allowing you to dip into the sections that are relevant to the particular problem you are facing, with numerous appendices containing the equations relevant to specific problems. * Supports development of long-term solutions by focusing on the fundamentals and mechanisms needed to understand underlying causes and operating conditions under which apparent solutions might not prove effective.
1,175 citations
TL;DR: In this paper, a higher-order non-local strain gradient elasticity model is proposed, which is based on the nonlocal effects of the strain field and first gradient strain field.
Abstract: In recent years there have been many papers that considered the effects of material length scales in the study of mechanics of solids at micro- and/or nano-scales There are a number of approaches and, among them, one set of papers deals with Eringen's differential nonlocal model and another deals with the strain gradient theories The modified couple stress theory, which also accounts for a material length scale, is a form of a strain gradient theory The large body of literature that has come into existence in the last several years has created significant confusion among researchers about the length scales that these various theories contain The present paper has the objective of establishing the fact that the length scales present in nonlocal elasticity and strain gradient theory describe two entirely different physical characteristics of materials and structures at nanoscale By using two principle kernel functions, the paper further presents a theory with application examples which relates the classical nonlocal elasticity and strain gradient theory and it results in a higher-order nonlocal strain gradient theory In this theory, a higher-order nonlocal strain gradient elasticity system which considers higher-order stress gradients and strain gradient nonlocality is proposed It is based on the nonlocal effects of the strain field and first gradient strain field This theory intends to generalize the classical nonlocal elasticity theory by introducing a higher-order strain tensor with nonlocality into the stored energy function The theory is distinctive because the classical nonlocal stress theory does not include nonlocality of higher-order stresses while the common strain gradient theory only considers local higher-order strain gradients without nonlocal effects in a global sense By establishing the constitutive relation within the thermodynamic framework, the governing equations of equilibrium and all boundary conditions are derived via the variational approach Two additional kinds of parameters, the higher-order nonlocal parameters and the nonlocal gradient length coefficients are introduced to account for the size-dependent characteristics of nonlocal gradient materials at nanoscale To illustrate its application values, the theory is applied for wave propagation in a nonlocal strain gradient system and the new dispersion relations derived are presented through examples for wave propagating in Euler–Bernoulli and Timoshenko nanobeams The numerical results based on the new nonlocal strain gradient theory reveal some new findings with respect to lattice dynamics and wave propagation experiment that could not be matched by both the classical nonlocal stress model and the contemporary strain gradient theory Thus, this higher-order nonlocal strain gradient model provides an explanation to some observations in the classical and nonlocal stress theories as well as the strain gradient theory in these aspects
1,085 citations
TL;DR: In this article, a nonlocal Bernoulli-Euler beam model is established based on the theory of nonlocal elasticity, which can be applied to modeling and characterization of size-dependent mechanical properties of micro- or nanoelectromechanical system (MEMS or NEMS) devices.
Abstract: In this paper, a nonlocal Bernoulli-Euler beam model is established based on the theory of nonlocal elasticity. Frequency equations and modal shape functions of beam structures with some typical boundary conditions are derived based on the model. The corresponding dynamic properties are presented and discussed in detail, which are shown to be very different from those predicted by classic elasticity theory when nonlocal effects are significant. The results can be applied to modeling and characterization of size-dependent mechanical properties of micro- or nanoelectromechanical system (MEMS or NEMS) devices.
406 citations
TL;DR: In this article, the small scaling parameter e0 of the nonlocal Timoshenko beam theory is calibrated for the free vibration problem of single-walled carbon nanotubes (SWCNTs).
Abstract: In this paper, the small scaling parameter e0 of the nonlocal Timoshenko beam theory is calibrated for the free vibration problem of single-walled carbon nanotubes (SWCNTs). The calibration exercise is performed by using vibration frequencies generated from molecular dynamics simulations at room temperature. It was found that the calibrated values of e0 are rather different from published values of e0. Instead of a constant value, the calibrated e0 values vary with respect to length-to-diameter ratios, mode shapes, and boundary conditions of the SWCNTs. In addition, the physical meaning of the scaling parameter is explored. The results show that scaling parameter assists in converting the kinetic energy to the strain energy, thus enabling the kinetic energy to be equal to the strain energy. The calibrated e0 presented herein should be useful for researchers who are using the nonlocal beam theories for analysis of micro and nano beams/rods/tubes.
341 citations
TL;DR: In this paper, the bending, buckling and vibration problems of axially functionally graded (FG) beams are solved by a generalized differential quadrature method, and the influence of power-law variation and size-dependent parameters on the axially FG beam behavior is investigated.
245 citations