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This paper aims at investigating free vibrations and stability of double-walled carbon nanotube (DWCNT)-based spinning nanobearings. The so-called nanobearing consists of two coaxial carbon nanotubes (CNTs) where either of the two CNTs can be a rotor while the other takes the role of stator. Euler–Bernoulli beam model along with the Eringen’s nonlocal theory of elasticity are employed to obtain governing equations of transverse vibrations for the CNTs. The coupling of the two CNTs originates from the van-der-Waals (vdW) forcing present in the interface of the two CNTs. The coupling is taken into account as distributed spring foundation with an equivalent elastic stiffness. Based on the... 

This work studies the nonlinear oscillations of an elastic rotating shaft with acceleration to pass through the critical speeds. A mathematical model incorporating the Von-Karman higher-order deformations in bending is developed to investigate the nonlinear dynamics of rotors. A flexible shaft on flexible bearings with springs and dampers is considered as rotor system for this work. The shaft is modeled as a beam and the Euler-Bernoulli beam theory is applied. The kinetic and strain energies of the rotor system are derived and Lagrange method is then applied to obtain the coupled nonlinear differential equations of motion for 6 degrees of freedom. In order to solve these equations... 

This work studies the nonlinear oscillations of an elastic rotating shaft with acceleration to pass through the critical speeds. A mathematical model incorporating the Von-Karman higher-order deformations in bending is developed and analyzed to investigate the nonlinear dynamics of rotors. A flexible shaft on flexible bearings with springs and dampers is considered as rotor system for the present work. The shaft is modeled as a beam with a circular cross-section and the Euler Bernoulli beam theory is applied. The kinetic and strain energies of the rotor system are derived and Lagrange method is then applied to obtain the coupled nonlinear differential equations of motion for 6° of freedom.... 

This paper presents a numerical scheme for stability analysis of the aeroelastic systems in the Laplace domain. The proposed technique, which is called the PP method, is proposed for when the aerodynamic model is represented in the Laplace domain and includes complicated transcendental expressions in terms of the Laplace variable. This method utilizes a matrix iterative procedure to find the eigenvalues of the system and generalizes the other methods such as the P and PK methods for prediction of the flutter conditions. The major advantage of this technique over the other approximate methods is true prediction of subcritical damping and frequency values of the aeroelastic modes. To examine... 

This research aims to investigate the dynamic response of a dual rotor-bearing system for passing through critical speeds. The Newmark-β method for solving the nonlinear lateral vibration of rotor-bearing systems is approached and the effects of various parameters including shaft crack, unbalanced mass, shaft bow, and support parameters are shown. A model, including shaft cracks, rotor unbalance, and shaft bow, is established using the finite element method with six degrees of freedom per node. The results provide a detailed feature analysis of the support parameters in a dual rotor-bearing system when it is coupled with various faults to pass through the critical speeds. © The Author(s)... 

This paper aims to revisit the effect of sloshing on the flutter characteristics of a partially liquid-filled cylinder. A computational fluid-structure interaction model within the framework of the finite element method is developed to capture fluid-structure interactions arising from the sloshing of the internal fluid and the flexibility of its containing structure exposed to an external supersonic airflow. The internal liquid sloshing is represented by a more sophisticated model, referred to as the liquid sloshing model, and the shell structure is modeled by Sanders' shell theory. The aerodynamic pressure loading is approximated by the first-order piston theory. The initial geometric... 

Interactive vibrations and buckling of double current-carrying strips (DCCS) are investigated in this study. Considering the rotational and transverse deformation of the strip, four coupled equations of motion are obtained using Hamilton’s principle. Using the Galerkin method, mass and stiffness matrices are extracted and the stability of the system is determined by solving the eigenvalue problem. Effects of pretension and elevated temperature on the stability of DCCS are studied for three types of materials and various arrangements. Finally, the effect of horizontal or vertical distance between strips on the critical current value is investigated. According to the results, the effects of... 

Interactive vibrations and buckling of double current-carrying strips (DCCS) are investigated in this study. Considering the rotational and transverse deformation of the strip, four coupled equations of motion are obtained using Hamilton’s principle. Using the Galerkin method, mass and stiffness matrices are extracted and the stability of the system is determined by solving the eigenvalue problem. Effects of pretension and elevated temperature on the stability of DCCS are studied for three types of materials and various arrangements. Finally, the effect of horizontal or vertical distance between strips on the critical current value is investigated. According to the results, the effects of... 

The present study aims at the investigation of free vibration analysis of thin cylindrical shells surrounded by an elastic medium, which is distributed over a particular length of the shell. The Love’s shell theory is utilized along with the Winkler foundation to obtain the governing equations of motion. An exact series expansion method of solution is employed for any arbitrary boundary conditions. The excellent accuracy of the obtained results is validated by comparing to the available literature. Moreover, several case studies are performed to provide an insight into the influence of some practically important parameters on free vibrations of circular cylindrical shells, including... 

A fast and efficient reduced order formulation is presented for the first time to study dynamics and stability of conical/cylindrical shells with internal fluid flows. The structural and fluid formulations are developed based on general assumptions to avoid any deficiency due to modeling. Their respective solutions and the final solution to the coupled field problem are also developed in a way to be capable of capturing any desirable set of boundary conditions. In addition to the flexibility provided by the solution methodology and generalization provided by the formulation, current solution proposes an additional advantage over others which is the minimal computational cost due to the... 

Carbon nanoropes (CNRs) are of interest for a wide variety of nanotechnological applications. Since little attention has been paid to mechanical properties of CNRs, their axial elastic modulus is explored herein. Molecular dynamics (MDs) simulations are adopted for analysis of Young's modulus of CNRs. It is also shown that increase in the initial helical angle decreases Young's modulus; however, by increase in the number of CNTs and strands, different influence on Young's modulus emerges. Therefore, the highest value of Young's modulus obtained at the lower value of initial helical angle and consequently, Young's modulus of bundle of straight CNTs is higher than CNRs with hierarchical... 

Stability and dynamics of rotating coaxial cylindrical shells conveying incompressible and inviscid fluid are investigated. The interior shell is assumed to be flexible while the exterior cylinder is rigid. Using Sander's-Koiter theory assumptions and following Hamilton's principle, governing equations of motion are determined in their integral form. Employing the extended Galerkin method of solution, the integral equations of motion are projected to their equivalent system of algebraic equations. Fluid equations are fundamentally based on the linearized inviscid Navier-Stokes equations. Impermeability condition on the fluid and structure interface as well as the zero radial velocity... 

This work studies the natural frequencies and modes of liquid sloshing in a rectangular 3D tank with the slotted baffles in middle. A new vibrational model incorporating the pressure difference between the two sides of the baffle, using a transmission function in Laplace space is presented. To this end, a part of the baffle that includes the wall and the slot is modeled in Fluent software, to express this pressure difference as a function of the fluid velocity passing through the baffle. Then, using the boundary element method, and boundary conditions, the equations of the fluid domain are developed. In this research, the rigid baffle is surrounded by a three-dimensional irrotational... 

This study aims to investigate the nonlinear dynamic characteristics of annular cylinders coupled with a fluid medium to identify the effective parameters on stability margins at different rotation speeds. To achieve this, stability and nonlinear vibrations of rotating cylindrical shells containing incompressible annular fluid are considered. The fluid medium is bounded by a rigid external cylinder. Sanders–Koiter kinematic assumptions are utilized to determine the geometrically nonlinear structural equations of motion. These equations are then used to investigate finite amplitude vibrations of various fluid-loaded shells at different states. A penalty approach is introduced by using... 

In order to study the interaction of sloshing and structural vibrations of baffled tanks, a reduced order model based on modal analysis of structure model and boundary element method for fluids motion is developed. For this purpose, the governing equations of elastic structure and incompressible flow are used to derive simple models to simulate both fields. Using the modal analysis technique, the structural motions are applied to the fluid model and on the other hand by using boundary element method, the fluid loads are applied to the structural model. Based on this formulation, a code is developed which is applicable to an arbitrary elastic tank with arbitrary arrangement of baffles. The... 

Sloshing, or liquid free surface oscillation, in containers has many important applications in a variety of engineering fields. The modal method can be used to solve linear sloshing problems and is the most efficient reduced order method that has been used during the previous decade. In the present article, the modal method is used to solve a nonlinear sloshing problem. The method is based on a potential flow solution that implements a two-phase analysis on sloshing in a rectangular container. According to this method, the solution to the mass conservation equation, with a nonpenetration condition at the tank walls, results in velocity potential expansion; this is similar to the mode shapes... 

The effect of elastic foundation on the free vibration characteristics of embedded nanocones is investigated in this paper. The nanocone is modeled as a thin shell and the nonlocal elasticity theory is used to derive the governing equations of motion. Also the elastic medium is simulated using Winkler and Pasternak foundation models. Based on the modal analysis technique and applying the Galerkin method the governing equations are solved to obtain the natural frequencies. The drawn results emphasis the effects of geometry and small-scale parameter on the natural frequencies of nanocone. Also the effect of elastic foundation modulus on the resonance frequencies of the nanocones are studied... 

This paper undertakes to facilitate appraisal of aeroelastic interaction of a locally distributed, flap-type control surface with aircraft wings operating in a subsonic potential flow field. The extended Hamilton's principle serves as a framework to ascertain the Euler-Lagrange equations for coupled bending-torsional-flap vibration. An analytical solution to this boundary-value problem is then accomplished by assumed modes and the extended Galerkin's method. The developed aeroelastic model considers both the inherent flexibility of the control surface displaced on the wing and the inertial coupling between these two flexible bodies. The structural deformations also obey the Euler-Bernoulli... 

In this paper, the static stability of the variable cross section columns, subjected to distributed axial force, is considered. The presented solution is based on the singular perturbation method of Wentzel-Kramers-Brillouin and the column is modeled using Euler-Bernoulli beam theory. Closed-form solutions are obtained for calculation of buckling loads and the corresponding mode shapes. The obtained results are compared with the results in the literature to verify the present approach. Using numerous examples, it is shown that the represented solution has a very good convergence and accuracy for determination of the instability condition  

In the present study, the mechanical properties of vertically aligned carbon nanotube (VACNT) arrays in the most general case of anisotropic elasticity is studied. To quantify the elastic stiffness coefficients, continuum mechanics is employed, in which the constitutive relation is formulized in terms of the interatomic potential obtained via molecular dynamics (MDs) simulations. Detailed investigations into elastic stiffness coefficients with different geometrical parameters are performed and, consequently, their sensitivity on length and radius parameters is hereby studied. With such study it would be possible to tune the mechanical properties of VACNTs. © 2019, Società Italiana di Fisica...