Sharif Digital Repository

A nonlinear fluid–structure interaction (FSI) model is presented for nonlinear vibration analysis of sandwich cylindrical shells subjected to an external compressible flow by considering the curvature nonlinearity in impermeability condition and bending. The sandwich shells are made of two face sheets and a central core of advanced materials including functionally graded (FG), metal foam, and anisogrid lattice composite. Based on the Kirchhoff–love hypotheses with the geometric nonlinearities in the normal strain and curvature of mid-surface, one decoupled nonlinear integral–differential equation is obtained for axisymmetric bending vibration of sandwich cylindrical shells. For the first... 

A novel non-classical continuum model for pull-in analysis of multilayer graphene sheets (MLGSs) is developed to consider the effect of shear interaction between layers based on the nonlocal elasticity theory. The equation governing the motion and corresponding boundary conditions of electrostatically actuated MLGSs are obtained based on the nonlocal shear multiplate theory. The Galerkin method along with the first mode shapes for clamped and cantilever MLGSs together with the method of parameter expansion is used to obtain closed-form expressions of the normalized frequency and time history response. In addition, molecular dynamics (MD) simulations are carried out to validate the pull-in... 

In this study, the nodal discontinuous Galerkin method is formulated in three-dimensions and applied to simulate three-dimensional non-cavitating/cavitating flows. For this aim, the three-dimensional preconditioned Navier-Stokes equations based on the artificial compressibility approach considering appropriate source terms to model cavitating phenomena are used. The spatial derivative terms in the resulting equations are discretized by utilizing the nodal discontinuous Galerkin method on tetrahedral elements and the derivative of the solution vector with respect to the artificial time is discretized by applying an explicit time integration method. An artificial viscosity method is formulated... 

Analytical frequency analysis of a nonlinear viscoelastic microcantilever is performed based on strain gradient theory. The Kelvin–Voigt scheme is utilized to model the viscoelasticity effect. Due to the microcantilever shortening effect via Euler–Bernoulli inextensibility condition, geometric, inertia, stiffness, and inherent damping nonlinearities are considered. The equation of motion is derived from Hamilton’s principle, and discretized using Galerkin method. The multiple timescale perturbation method is performed to solve the time response equation. Implying steady-state condition, the nonlinear relation between detuning parameter and amplitude of the vibration of a nonlinear... 

Based on the first-order shear deformation (FSD) model and nonlocal elasticity theory, the simultaneous effects of shear and small scale on the nonlinear vibration behavior of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) beams are investigated for the first time. To this end, the governing equations of bending and stretching with von Kármán geometric nonlinearity are decoupled into one fourth-order partial differential equation in terms of transverse deflection. A closed-form solution of the nonlinear natural frequency, which can be used in conceptual design and optimization algorithms of FG- CNTRC beams with different boundary conditions, is developed using a hybrid... 

Based on the linear fluid-solid interaction (FSI) model and classical shell theories, vibration behavior of sandwich cylindrical shells subjected to external incompressible or compressible fluid flow is investigated. The sandwich shell includes the same outer and inner face sheets made of carbon nanotube (CNT) reinforced composites and a metal foam core. The effective mechanical properties of CNT reinforced composites are obtained using the extended rule of mixture. Also, the porosity distribution through the foam thickness is assumed to be in the form of a trigonometric function. Equations of motion and corresponding boundary conditions are derived according to the Donnell's, Love's and... 

In this paper, we investigate the local and global existence, asymptotic behavior, and blow-up of solutions to the Cauchy problem for Choquard-type equations involving the p(x)-Laplacian operator. As a particular case, we study the following initial value problem [Formula presented] where p,q,V:RN→R and α:RN×RN→R are continuous functions that satisfy some conditions which will be stated later on, and u0:RN→R is the initial function. Under some appropriate conditions, we prove the local and global existence of solutions for the above Cauchy problem by employing the abstract Galerkin approximation. Moreover, the blow-up of solutions and large-time behavior are also investigated. © 2021... 

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... 

This paper analytically studies the effect of functionally graded materials (FGMs) on the primary resonances of large amplitude flexural vibration of in-extensional rotating shafts with nonlinear curvature as well as nonlinear inertia. The constituent material is assumed to vary along the radial direction according to a power-law gradation. The governing differential equations and the corresponding boundary conditions are derived employing the variational approach. Then, the Galerkin method and the multiple scales perturbation method are utilized to obtain the frequency–response equation. In a numerical case study, the effects of the power-law index on the steady-state responses and locus of... 

Based on the classical Donnell's and Love's shell theories, free vibration behavior of variable-thickness thin cylindrical shells rotating with a constant angular velocity is analyzed. The equations of motion and corresponding boundary conditions of rotating homogenous cylindrical shells with axisymmetric variation of thickness are derived using Hamilton's principle. This formulation includes effects of initial hoop tension due to the centrifugal force as well as Coriolis and centrifugal accelerations. Considering the variation of stiffness coefficients in axial direction, the classical Love's theory results in a coupled system of two second-order and one fourth-order partial differential... 

A viscoelastic microcantilever beam is analytically analyzed based on the modified strain gradient theory. Kelvin-Voigt scheme is used to model beam viscoelasticity. By applying Euler-Bernoulli inextensibility of the centerline condition based on Hamilton's principle, the nonlinear equation of motion and the related boundary conditions are derived from shortening effect theory and discretized by Galerkin method. Inner damping, nonlinear curvature effect, and nonlinear inertia terms are also taken into account. In the present study, the generalized derived formulation allows modeling any nonlinear combination such as nonlinear terms that arise due to inertia, damping, and stiffness, as well... 

In this paper, we are concerned with existence, uniqueness and numerical approximation of the solution process to an initial value problem for stochastic fractional differential equation of Riemann-Liouville type. We propose and analyze a Petrov-Galerkin finite element method based on fractional (non-polynomial) Jacobi polyfractonomials as basis and test functions. Error estimates in L2 norm are derived and numerical experiments are provided to validate the theoretical results. As an illustrative application, we generate sample paths of the Riemann-Liouville fractional Brownian motion which is of importance in many applications ranging from geophysics to traffic flow in telecommunication... 

In this paper, we are concerned with existence, uniqueness and numerical approximation of the solution process to an initial value problem for stochastic fractional differential equation of Riemann-Liouville type. We propose and analyze a Petrov-Galerkin finite element method based on fractional (non-polynomial) Jacobi polyfractonomials as basis and test functions. Error estimates in L2 norm are derived and numerical experiments are provided to validate the theoretical results. As an illustrative application, we generate sample paths of the Riemann-Liouville fractional Brownian motion which is of importance in many applications ranging from geophysics to traffic flow in telecommunication... 

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... 

In this paper, the stability of pipes conveying fluid with viscoelastic fractional foundation is investigated. The pipe is fixed at the beginning while the pipe end is constrained with two lateral and rotational springs. The fluid flow effect is modeled as a lateral distributed force, containing the fluid inertia, Coriolis and centrifugal forces. The pipe is modeled using the Euler-Bernoulli beam theory and a fractional Kelvin-Voigt model is employed to describe the viscoelastic foundation. The equation of motion is derived using the extended Hamilton's principle. Presenting the derived equation in Laplace domain and applying the Galerkin method, a set of algebraic equations is extracted.... 

Stability analysis of a cantilevered pipe with an inclined terminal nozzle as well as simultaneous internal and external fluid flows is investigated in this study. The pipe is embedded in an aerodynamic cover with negligible mass and stiffness simply to streamline the external flow and avoid vortex induced vibrations. The structure of pipe is modeled as an Euler–Bernoulli beam and effects of internal fluid flow including flow-induced inertia, Coriolis and centrifugal forces and the follower force induced by the exhausting jet are taken into account. In addition, neglecting the compressibility effect and using the unsteady Wagner model, aerodynamic loading is determined as a distributed... 

Dynamical instability characteristics of sandwich truncated conical shell are investigated. The three-layered shell is composed of advanced grid stiffened core and laminated composite skins. The core maybe made of three different fiber paths. The conical shell with simply-supported ends is subjected to two different types of time-dependent axial compressions. The equations of motion and compatibility are derived by considering Kirchhoff-Love assumptions and von Karman relations. The solution procedure is divided to two steps. First, the terms consisting of spatial derivatives are eliminated by applying a stress function and following the Galerkin method. Second, the terms with temporal... 

This paper deals with the small-scale effects on the thermoelastic damping (TED) in microplates. The coupled equations of motion and heat conduction are provided utilizing the strain gradient theory (SGT) and the dual-phase-lag (DPL) heat conduction model. Solving these equations and adopting the Galerkin method, the real and imaginary parts of frequency are extracted. The complex frequency approach is then employed to present a size-dependent expression for evaluating TED in thin plates. An analytical expression for TED incorporating small-scale effects is also derived on the basis of the energy dissipation approach. To survey the effect of different continuum theories on TED, the results... 

In this study, a high-order accurate numerical method is applied and examined for the simulation of the inviscid/viscous cavitating flows by solving the preconditioned multiphase Euler/Navier-Stokes equations on triangle elements. The formulation used here is based on the homogeneous equilibrium model considering the continuity and momentum equations together with the transport equation for the vapor phase with applying appropriate mass transfer terms for calculating the evaporation/condensation of the liquid/vapor phase. The spatial derivative terms in the resulting system of equations are discretized by the nodal discontinuous Galerkin method (NDGM) and an implicit dual-time stepping... 

In this work, a high-order nodal discontinuous Galerkin method (NDGM) is developed and assessed for the simulation of 2D incompressible flows on triangle elements. The governing equations are the 2D incompressible Navier–Stokes equations with the artificial compressibility method. The discretization of the spatial derivatives in the resulting system of equations is made by the NDGM and the time integration is performed by applying the implicit dual-time stepping method. Three numerical fluxes, namely, the local Lax–Friedrich, Roe and AUSM+-up are formulated and applied to assess and compare their accuracy and performance in the simulation of incompressible flows using the NDGM. Several...