scholarly journals Nonlocal FEM Formulation for Vibration Analysis of Nanowires on Elastic Matrix with Different Materials

2019 ◽  
Vol 24 (2) ◽  
pp. 38 ◽  
Author(s):  
Büşra Uzun ◽  
Ömer Civalek
Keyword(s):  
Boundary Conditions ◽  
Nonlocal Elasticity Theory ◽  
Silver Nanowire ◽  
Small Scale ◽  
Weighted Residual Method ◽  
Simply Supported ◽  
Scale Parameters ◽  
Various Boundary Conditions ◽  
Winkler Elastic Foundation ◽  
Foundation Model

In this study, free vibration behaviors of various embedded nanowires made of different materials are investigated by using Eringen’s nonlocal elasticity theory. Silicon carbide nanowire (SiCNW), silver nanowire (AgNW), and gold nanowire (AuNW) are modeled as Euler–Bernoulli nanobeams with various boundary conditions such as simply supported (S-S), clamped simply supported (C-S), clamped–clamped (C-C), and clamped-free (C-F). The interactions between nanowires and medium are simulated by the Winkler elastic foundation model. The Galerkin weighted residual method is applied to the governing equations to gain stiffness and mass matrices. The results are given by tables and graphs. The effects of small-scale parameters, boundary conditions, and foundation parameters on frequencies are examined in detail. In addition, the influence of temperature change on the vibrational responses of the nanowires are also pursued as a case study.

LINEAR BENDING ANALYSIS OF INHOMOGENEOUS VARIABLE-THICKNESS ORTHOTROPIC PLATES UNDER VARIOUS BOUNDARY CONDITIONS

2007 ◽  
Vol 04 (03) ◽  
pp. 417-438 ◽  
Author(s):  
A. M. ZENKOUR ◽  
M. N. M. ALLAM ◽  
D. S. MASHAT
Keyword(s):  
Boundary Conditions ◽  
Variable Thickness ◽  
Flexural Rigidity ◽  
Approximate Solutions ◽  
Rectangular Plates ◽  
Orthotropic Plates ◽  
Simply Supported ◽  
Various Boundary Conditions ◽  
Thickness Parameter ◽  
Space Concept

An exact solution to the bending of variable-thickness orthotropic plates is developed for a variety of boundary conditions. The procedure, based on a Lévy-type solution considered in conjunction with the state-space concept, is applicable to inhomogeneous variable-thickness rectangular plates with two opposite edges simply supported. The remaining ones are subjected to a combination of clamped, simply supported, and free boundary conditions, and between these two edges the plate may have varying thickness. The procedure is valuable in view of the fact that tables of deflections and stresses cannot be presented for inhomogeneous variable-thickness plates as for isotropic homogeneous plates even for commonly encountered loads because the results depend on the inhomogeneity coefficient and the orthotropic material properties instead of a single flexural rigidity. Benchmark numerical results, useful for the validation or otherwise of approximate solutions, are tabulated. The influences of the degree of inhomogeneity, aspect ratio, thickness parameter, and the degree of nonuniformity on the deflections and stresses are investigated.

scholarly journals Modeling of smart magnetically affected flexoelectric/piezoelectric nanostructures incorporating surface effects

2017 ◽  
Vol 7 ◽  
pp. 184798041771310 ◽  
Author(s):  
Farzad Ebrahimi ◽  
Mohammad Reza Barati
Keyword(s):  
Boundary Conditions ◽  
Elastic Foundation ◽  
Nonlocal Elasticity ◽  
Nonlocal Parameter ◽  
Surface Elasticity ◽  
Nonlocal Elasticity Theory ◽  
Surface Effects ◽  
Geometrical Parameters ◽  
Various Boundary Conditions ◽  
Buckling Behavior

In this article, electromechanical buckling behavior of size-dependent flexoelectric/piezoelectric nanobeams is investigated based on nonlocal and surface elasticity theories. Flexoelectricity represents the coupling between the strain gradients and electrical polarizations. Flexoelectric/piezoelectric nanostructures can tolerate higher buckling loads compared with conventional piezoelectric ones, especially at lower thicknesses. Nonlocal elasticity theory of Eringen is applied for analyzing flexoelectric/piezoelectric nanobeams for the first time. The flexoelectric/piezoelectric nanobeams are assumed to be in contact with a two-parameter elastic foundation which consists of infinite linear springs and a shear layer. The residual surface stresses which are usually neglected in modeling of flexoelectric nanobeams are incorporated into nonlocal elasticity to provide better understanding of the physics of the problem. Applying an analytical method which satisfies various boundary conditions, the governing equations obtained from Hamilton’s principle are solved. The reliability of the present approach is verified by comparing the obtained results with those provided in literature. Finally, the influences of nonlocal parameter, surface effects plate geometrical parameters, elastic foundation, and boundary conditions on the buckling characteristics of the flexoelectric/piezoelectric nanobeams are explored in detail.

Free and Forced Vibration of Coupled Beam Systems Resting on Variable Viscoelastic Foundations

2020 ◽  
Vol 20 (12) ◽  
pp. 2050141
Author(s):  
Jinpeng Su ◽  
Kun Zhang ◽  
Qiang Zhang ◽  
Ying Tian
Keyword(s):  
Boundary Conditions ◽  
Forced Vibration ◽  
Dynamic Properties ◽  
Least Square ◽  
Weighted Residual Method ◽  
Transient Vibration ◽  
Various Boundary Conditions ◽  
Beam System ◽  
Interface Potential ◽  
Forced Vibration Analysis

This paper presents a modified variational method for free and forced vibration analysis of coupled beam systems resting on various viscoelastic foundations. Non-uniform as well as uniform curved and straight Timoshenko beam components are considered in the coupled beam system. Using proper coordinate transformations, interactions among the beam components of the coupled beam system are accommodated by combining Lagrange multiplier method and least-square weighted residual method. Interface potential energy for various boundary conditions including the elastic ones is simultaneously formulated. Thus, the proposed method allows flexible choice of the admissible functions, regardless of the boundary conditions. Based on the proposed energy method, Winkler, Pasternak or even variable foundations distributed in a parabolic or sinusoidal manner can be easily introduced into the coupled beam systems. Two kinds of damping, namely the proportional and viscous damping, are also employed to model the energy dissipation of the viscoelastic foundations. Corresponding finite element (FE) simulations are performed where possible and good agreement is observed. Thus, great efficiency and accuracy of the present approach are demonstrated for free, steady-state and transient vibration of the coupled beam systems. The influences of the parameters of the variable viscoelastic foundations on the dynamic properties of the coupled beam system are also examined.

scholarly journals A nonlocal sinusoidal plate model for micro/nanoscale plates

2014 ◽  
Vol 228 (14) ◽  
pp. 2652-2660 ◽  
Author(s):  
Huu-Tai Thai ◽  
Thuc P Vo ◽  
Trung-Kien Nguyen ◽  
Jaehong Lee
Keyword(s):  
Boundary Conditions ◽  
Shear Deformation ◽  
Transverse Shear ◽  
Plate Theory ◽  
Equations Of Motion ◽  
Nonlocal Elasticity Theory ◽  
Small Scale ◽  
Plate Model ◽  
Proposed Model ◽  
Small Scale Effect

A nonlocal sinusoidal plate model for micro/nanoscale plates is developed based on Eringen’s nonlocal elasticity theory and sinusoidal shear deformation plate theory. The small-scale effect is considered in the former theory while the transverse shear deformation effect is included in the latter theory. The proposed model accounts for sinusoidal variations of transverse shear strains through the thickness of the plate, and satisfies the stress-free boundary conditions on the plate surfaces, thus a shear correction factor is not required. Equations of motion and boundary conditions are derived from Hamilton’s principle. Analytical solutions for bending, buckling, and vibration of simply supported plates are presented, and the obtained results are compared with the existing solutions. The effects of small scale and shear deformation on the responses of the micro/nanoscale plates are investigated.

Investigation of Vibration and Thermal Buckling of Nanobeams Embedded in An Elastic Medium Under Various Boundary Conditions

2015 ◽  
Vol 32 (3) ◽  
pp. 277-287 ◽  
Author(s):  
D. S. Mashat ◽  
A. M. Zenkour ◽  
M. Sobhy
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Equations Of Motion ◽  
Thermal Buckling ◽  
Governing Equations ◽  
Linear Temperature ◽  
Simply Supported ◽  
Various Boundary Conditions ◽  
Dynamic Version ◽  
Beam Theories

AbstractAnalyses of free vibration and thermal buckling of nanobeams using nonlocal shear deformation beam theories under various boundary conditions are precisely illustrated. The present beam is restricted by vertically distributed identical springs at the top and bottom surfaces of the beam. The equations of motion are derived using the dynamic version of Hamilton's principle. The governing equations are solved analytically when the edges of the beam are simply supported, clamped or free. Thermal buckling solution is formulated for two types of temperature change through the thickness of the beam: Uniform and linear temperature rise. To validate the accuracy of the results of the present analysis, the results are compared, as possible, with solutions found in the literature. Furthermore, the influences of nonlocal coefficient, stiffness of Winkler springs and span-to-thickness ratio on the frequencies and thermal buckling of the embedded nanobeams are examined.

Torsional Vibration of Cracked Nanobeam Based on Nonlocal Stress Theory with Various Boundary Conditions: An Analytical Study

2015 ◽  
Vol 07 (03) ◽  
pp. 1550036 ◽  
Author(s):  
Omid Rahmani ◽  
S. A. H. Hosseini ◽  
M. H. Noroozi Moghaddam ◽  
I. Fakhari Golpayegani
Keyword(s):  
Boundary Conditions ◽  
Torsional Vibration ◽  
Analytical Study ◽  
Nonlocal Parameter ◽  
Nonlocal Elasticity Theory ◽  
Stress Theory ◽  
Various Boundary Conditions ◽  
Crack Location ◽  
Nonlocal Stress ◽  
Torsional Spring

In this paper, the torsional vibration of cracked nanobeam was studied based on a nonlocal elasticity theory. The location of the crack is simulated by a torsional spring which links segments of nanobeam together. Also, different boundary conditions, including clamped–free, clamped–clamped and clamped–torsional spring, were considered. Furthermore, a detailed parametric study was conducted to investigate the influence of crack location, nonlocal parameter, length of nanobeam, spring constant and end supports on the torsional vibration.

Strain Gradient Finite Element Analysis on the Vibration of Double-Layered Graphene Sheets

2016 ◽  
Vol 13 (03) ◽  
pp. 1650011 ◽  
Author(s):  
Wei Xu ◽  
Lifeng Wang ◽  
Jingnong Jiang
Keyword(s):  
Finite Element ◽  
Boundary Conditions ◽  
Scale Effect ◽  
Strain Gradient ◽  
Virtual Work ◽  
Gradient Elasticity ◽  
Kirchhoff Plate ◽  
Small Scale ◽  
Graphene Sheets ◽  
Simply Supported

A nonlocal Kirchhoff plate model with the van der Waals (vdW) interactions taken into consideration is developed to study the vibration of double-layered graphene sheets (DLGS). The dynamic equations of multi-layered Kirchhoff plate are derived based on strain gradient elasticity. An explicit formula is derived to predict the natural frequency of the DLGS with all edges simply supported. Then a 4-node 24-degree of freedom (DOF) Kirchhoff plate element is developed to discretize the higher order partial differential equations with the small scale effect taken into consideration by the theory of virtual work. It can be directly used to predict the scale effect on the vibrational DLGS with different boundary conditions. A good agreement between finite element method (FEM) results and theoretical natural frequencies of the vibration simply supported double-layered graphene sheet (DLGS) validates the reliability of the FEM. Finally, this new FEM is used to investigate the effect of vdW coefficients, sizes, nonlocal parameters, vibration mode and boundary conditions on the vibration behaviors of DLGS.

Size-Dependent Pull-In Instability of Hydrostatically and Electrostatically Actuated Circular Microplates

2012 ◽  
Vol 8 (2) ◽  
Author(s):  
R. Ansari ◽  
R. Gholami ◽  
V. Mohammadi ◽  
M. Faghih Shojaei
Keyword(s):  
Boundary Conditions ◽  
Governing Equation ◽  
Couple Stress Theory ◽  
Gradient Elasticity ◽  
Modified Couple Stress Theory ◽  
Distributed Model ◽  
Length Scale ◽  
Scale Parameters ◽  
Various Boundary Conditions ◽  
Size Dependent

This article is concerned with the development of a distributed model based on the modified strain gradient elasticity theory (MSGT), which enables us to investigate the size-dependent pull-in instability of circular microplates subjected to the uniform hydrostatic and nonuniform electrostatic actuations. The model developed herein accommodates models based on the classical theory (CT) and modified couple stress theory (MCST), when all or two material length scale parameters are set equal to zero, respectively. On the basis of Hamilton's principle, the higher-order nonlinear governing equation and corresponding boundary conditions are obtained. In order to linearize the nonlinear equation, a step-by-step linearization scheme is implemented, and then the linear governing equation is discretized along with different boundary conditions using the generalized differential quadrature (GDQ) method. In the case of CT, it is indicated that the presented results are in good agreement with the existing data in the literature. Effects of the length scale parameters, hydrostatic and electrostatic pressures, and various boundary conditions on the pull-in voltage and pull-in hydrostatic pressure of circular microplates are thoroughly investigated. Moreover, the results generated from the MSGT are compared with those predicted by MCST and CT. It is shown that the difference between the results from the MSGT and those of MCST and CT is considerable when the thickness of the circular microplate is on the order of length scale parameter.

Vibration of a Fluid Conveying Pipe Carrying a Discrete Mass

1974 ◽  
Vol 96 (4) ◽  
pp. 268-272 ◽  
Author(s):  
T. T. Wu ◽  
P. P. Raju
Keyword(s):  
Dynamic Response ◽  
Boundary Conditions ◽  
Flow Velocity ◽  
General Expression ◽  
Normal Modes ◽  
Critical Value ◽  
Numerical Results ◽  
Simply Supported ◽  
Various Boundary Conditions ◽  
Discrete Mass

This paper presents a method to predict the dynamic response of a fluid conveying pipe carrying a discrete mass when the flow velocity is less than its critical value. A general expression for the normal modes of a vibrating pipe with various boundary conditions is newly derived herein. Also presented for a particular case are the numerical results of eigenfunctions and eigenvalues which can be used to calculate the dynamic response of a simply-supported pipe with an attached discrete mass at its mid-span.

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