scholarly journals Investigating Surface Effects on Thermomechanical Behavior of Embedded Circular Curved Nanosize Beams

2016 ◽  
Vol 2016 ◽  
pp. 1-11 ◽  
Author(s):  
Farzad Ebrahimi ◽  
Mohsen Daman
Keyword(s):  
Natural Frequency ◽  
Surface Properties ◽  
Nonlocal Parameter ◽  
Surface Elasticity ◽  
Surface Effects ◽  
Buckling Load ◽  
Opening Angle ◽  
Governing Equations ◽  
Critical Buckling Load ◽  
Elastic Foundations

To investigate the surface effects on thermomechanical vibration and buckling of embedded circular curved nanosize beams, nonlocal elasticity model is used in combination with surface properties including surface elasticity, surface tension, and surface density for modeling the nanoscale effect. The governing equations are determined via the energy method. Analytically Navier method is utilized to solve the governing equations for simply supported nanobeam at both ends. Solving these equations enables us to estimate the natural frequency and critical buckling load for circular curved nanobeam including Winkler and Pasternak elastic foundations and under the effect of a uniform temperature change. The results determined are verified by comparing the results with available ones in literature. The effects of various parameters such as nonlocal parameter, surface properties, Winkler and Pasternak elastic foundations, temperature, and opening angle of circular curved nanobeam on the natural frequency and critical buckling load are successfully studied. The results reveal that the natural frequency and critical buckling load of circular curved nanobeam are significantly influenced by these effects.

scholarly journals Nonlocal vibration and buckling of two-dimensional layered quasicrystal nanoplates embedded in an elastic medium

2021 ◽  
Author(s):  
Tuoya Sun ◽  
Junhong Guo ◽  
E. Pan
Keyword(s):  
Elastic Medium ◽  
Vibration Frequency ◽  
Surrounding Medium ◽  
Nonlocal Parameter ◽  
Buckling Load ◽  
Width Ratio ◽  
Two Dimensional ◽  
Coating Materials ◽  
Decagonal Quasicrystal ◽  
Critical Buckling Load

AbstractA mathematical model for nonlocal vibration and buckling of embedded two-dimensional (2D) decagonal quasicrystal (QC) layered nanoplates is proposed. The Pasternak-type foundation is used to simulate the interaction between the nanoplates and the elastic medium. The exact solutions of the nonlocal vibration frequency and buckling critical load of the 2D decagonal QC layered nanoplates are obtained by solving the eigensystem and using the propagator matrix method. The present three-dimensional (3D) exact solution can predict correctly the nature frequencies and critical loads of the nanoplates as compared with previous thin-plate and medium-thick-plate theories. Numerical examples are provided to display the effects of the quasiperiodic direction, length-to-width ratio, thickness of the nanoplates, nonlocal parameter, stacking sequence, and medium elasticity on the vibration frequency and critical buckling load of the 2D decagonal QC nanoplates. The results show that the effects of the quasiperiodic direction on the vibration frequency and critical buckling load depend on the length-to-width ratio of the nanoplates. The thickness of the nanoplate and the elasticity of the surrounding medium can be adjusted for optimal frequency and critical buckling load of the nanoplate. This feature is useful since the frequency and critical buckling load of the 2D decagonal QCs as coating materials of plate structures can now be tuned as one desire.

Analysis of Residual Stresses on the Vibration of a Circular Sensor Diaphragm with Surface Effects

2016 ◽  
Vol 33 (3) ◽  
pp. 323-329 ◽  
Author(s):  
S.-S. Zhou ◽  
S.-J. Zhou ◽  
A.-Q. Li ◽  
B.-L. Wang
Keyword(s):  
Residual Stresses ◽  
Natural Frequency ◽  
Flexural Rigidity ◽  
Plate Theory ◽  
Surface Elasticity ◽  
Surface Effects ◽  
Transition Range ◽  
Biochemical Sensors ◽  
Tension Parameter ◽  
Wide Range

AbstractResonant micro-biochemical sensors play important roles in a wide range of emerging applications to detect biochemical molecules. As the resonators of micro-biochemical sensors, the vibration characteristics of circular sensor diaphragms are important for the design of diaphragm-based resonant micro-biochemical sensors. In this paper, the influence of residual stresses on the vibration of a circular sensor diaphragm with surface effects is analyzed. Based on the Kirchhoff's plate theory and surface elasticity theory, the governing equation is presented. The material characteristic lengths for different surface effects are obtained. The influences of residual stresses on the effective flexural rigidity and natural frequency of the diaphragm with surface effects are discussed. Results show that the influence of residual stresses on the effective flexural rigidity becomes obvious with the increasing of residual stresses. The first order natural frequency increases rapidly when the tension parameter is larger than 30 for the stiffened surfaces, while for the softened surfaces the value is 10. Moreover, surface effects can influence the transition range of diaphragm from the plate behavior to membrane behavior in terms of the tension parameter. The transition range can be enlarged by the stiffened surface and be shortened by the softened surface. The analysis and results are helpful for the design of sensor diaphragm-based resonant micro-biochemical sensors and some related researches.

Buckling analysis of functionally graded annular sector plates resting on elastic foundations

2010 ◽  
Vol 225 (2) ◽  
pp. 312-325 ◽  
Author(s):  
A Naderi ◽  
A R Saidi
Keyword(s):  
Boundary Conditions ◽  
Elastic Foundation ◽  
Buckling Analysis ◽  
Functionally Graded ◽  
Buckling Load ◽  
Critical Buckling Load ◽  
Elastic Foundations ◽  
Annular Sector ◽  
Sector Plate ◽  
Annular Sector Plate

In this study, an analytical solution for the buckling of a functionally graded annular sector plate resting on an elastic foundation is presented. The buckling analysis of the functionally graded annular sector plate is investigated for two typical, Winkler and Pasternak, elastic foundations. The equilibrium and stability equations are derived according to the Kirchhoff's plate theory using the energy method. In order to decouple the highly coupled stability equations, two new functions are introduced. The decoupled equations are solved analytically for a plate having simply supported boundary conditions on two radial edges. Satisfying the boundary conditions on the circular edges of the plate yields an eigenvalue problem for finding the critical buckling load. Extensive results pertaining to critical buckling load are presented and the effects of boundary conditions, volume fraction, annularity, plate thickness, and elastic foundation are studied.

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.

scholarly journals Surface Effects on the Vibration and Buckling of Double-Nanobeam-Systems

2011 ◽  
Vol 2011 ◽  
pp. 1-7 ◽  
Author(s):  
Dong-Hui Wang ◽  
Gang-Feng Wang
Keyword(s):  
Natural Frequency ◽  
Surface Elasticity ◽  
Surface Effects ◽  
Nanoelectromechanical Systems ◽  
Beam Model ◽  
Cross Sectional ◽  
Axial Buckling ◽  
Cross Sectional Size ◽  
Euler Bernoulli Beam ◽  
Deformation Modes

Surface effects on the transverse vibration and axial buckling of double-nanobeam-system (DNBS) are examined based on a refined Euler-Bernoulli beam model. For three typical deformation modes of DNBS, we derive the natural frequency and critical axial load accounting for both surface elasticity and residual surface tension, respectively. It is found that surface effects get quite important when the cross-sectional size of beams shrinks to nanometers. No matter for vibration or axial buckling, surface effects are just the same in three deformation modes and usually enhance the natural frequency and critical load. However, the interaction between beams is clearly distinct in different deformation modes. This study might be helpful for the design of nano-optomechanical systems and nanoelectromechanical systems.

scholarly journals Bending and Vibration Analysis of Curved FG Nanobeams via Nonlocal Timoshenko Model

2018 ◽  
Vol 2 (2) ◽  
Author(s):  
Seyyed Amirhosein Hosseini ◽  
Omid Rahmani
Keyword(s):  
Nonlocal Parameter ◽  
Beam Theory ◽  
Opening Angle ◽  
Governing Equations ◽  
Timoshenko Model ◽  
Simply Supported ◽  
Significant Parameter ◽  
Nonlocal Timoshenko Beam Theory ◽  
Fg Nanobeam ◽  
Power Law Index

The bending and vibration behavior of a curved FG nanobeam using the nonlocal Timoshenko beam theory is analyzed in this paper. It is assumed that the material properties vary through the radius direction.  The governing equations were obtained using Hamilton principle based on the nonlocal Timoshenko model of curved beam. An analytical approach for a simply supported boundary condition is conducted to analyze the vibration and bending of curved FG nanobeam. In the both mentioned analysis, the effect of significant parameter such as opening angle, the power law index of FGM, nonlocal parameter, aspect ratio and mode number are studied. The accuracy of the solution is examined by comparing the results obtained with the analytical and numerical results published in the literatures.

scholarly journals Bending and Vibration Analysis of Curved FG Nanobeams via Nonlocal Timoshenko Model

2018 ◽  
Author(s):  
Seyyed Amirhosein Hosseini ◽  
Omid Rahmani
Keyword(s):  
Nonlocal Parameter ◽  
Beam Theory ◽  
Opening Angle ◽  
Governing Equations ◽  
Timoshenko Model ◽  
Simply Supported ◽  
Significant Parameter ◽  
Nonlocal Timoshenko Beam Theory ◽  
Fg Nanobeam ◽  
Power Law Index

The bending and vibration behavior of a curved FG nanobeam using the nonlocal Timoshenko beam theory is analyzed in this paper. It is assumed that the material properties vary through the radius direction.  The governing equations were obtained using Hamilton principle based on the nonlocal Timoshenko model of curved beam. An analytical approach for a simply supported boundary condition is conducted to analyze the vibration and bending of curved FG nanobeam. In the both mentioned analysis, the effect of significant parameter such as opening angle, the power law index of FGM, nonlocal parameter, aspect ratio and mode number are studied. The accuracy of the solution is examined by comparing the results obtained with the analytical and numerical results published in the literatures.

Natural Frequency and Buckling of Orthotropic Nanoplates Resting on Two-Parameter Elastic Foundations with Various Boundary Conditions

2014 ◽  
Vol 30 (5) ◽  
pp. 443-453 ◽  
Author(s):  
M. Sobhy
Keyword(s):  
Boundary Conditions ◽  
Natural Frequency ◽  
Plate Theory ◽  
Equations Of Motion ◽  
Nonlocal Parameter ◽  
Nonlocal Elasticity Theory ◽  
Graphene Sheets ◽  
Elastic Foundations ◽  
Various Boundary Conditions ◽  
Mechanics Of Composite Materials

AbstractIn this article, the analyses of the natural frequency and buckling of orthotopic nanoplates, such as single-layered graphene sheets, resting on Pasternak's elastic foundations with various boundary conditions are presented. New functions for midplane displacements are suggested to satisfy the different boundary conditions. These functions are examined by comparing their results with the results obtained by using the functions suggested by Reddy (Reddy JN. Mechanics of Composite Materials and Structures: Theory and Analysis. Boca Raton, FL: CRC Press; 1997). Moreover, these functions are very simple comparing with Reddy's functions, leading to ease of calculations. The equations of motion of the nonlocal model are derived using the sinusoidal shear deformation plate theory (SPT) in conjunction with the nonlocal elasticity theory. The present SPT are compared with other plate theories. Explicit solution for buckling loads and vibration are obtained for single-layered graphene sheets with isotropic and orthotropic properties; and under biaxial loads. The formulation and the method of the solution are firstly validated by executing the comparison studies for the isotropic nanoplates with the results being in literature. Then, the influences of nonlocal parameter and the other parameters on the buckling and vibration frequencies are investigated.

Effect of the Casimir Force on Buckling of a Double-Nanowire System with Surface Effects

2018 ◽  
Vol 18 (10) ◽  
pp. 1850118 ◽  
Author(s):  
J. Zou ◽  
X.-F. Li
Keyword(s):  
Surface Tension ◽  
Carrying Capacity ◽  
Critical Loads ◽  
Casimir Force ◽  
Surface Elasticity ◽  
Surface Effects ◽  
Load Carrying Capacity ◽  
Governing Equations ◽  
Simply Supported ◽  
Load Carrying

Structural stability of a double-nanowire system with surface effects subjected to axial compressive forces is analyzed. Taking into account the Casimir force between the two nanowires, two coupled governing equations for buckling of a double-nanowire system are derived. For four typical end supports including simply-supported, clamped, cantilevered, and clamped-pinned double-nanowire systems, the characteristic equations are derived and the critical loads are determined for the out-of-phase in-plane buckling. Numerical results indicate that positive surface elasticity enhances the load-carrying capacity of the nanowires, and the reverse is also true. The Casimir force and residual surface tension always increase the critical loads.

scholarly journals Multiobjective Design Optimization of Reentrant Auxetic Model Using Lichtenberg Algorithm Based on Metamodel

2022 ◽  
Author(s):  
Matheus Brendon Francisco ◽  
João Luiz Junho Pereira ◽  
Lucas Antonio de Oliveira ◽  
Sebastião Da Cunha ◽  
Guilherme Ferreira Gomes
Keyword(s):  
Natural Frequency ◽  
Performance Optimization ◽  
Poisson’S Ratio ◽  
Failure Load ◽  
Buckling Load ◽  
Poisson's Ratio ◽  
Critical Buckling Load ◽  
Compression Performance ◽  
Multi Objective ◽  
Multiobjective Design

Abstract The optimization of five different responses of an auxetic model was considered: mass; critical buckling load under compression effort; natural frequency; Poisson’s ratio; and failure load. The Response Surface Methodology was applied, and a new meta-heuristic of optimization called the Multi-Objective Lichtenberg Algorithm was used to find the optimized configuration of the model. It was possible to increase the failure load by 26,75% in compression performance optimization. Furthermore, in the optimization of modal performance, it was possible to increase the natural frequency by 37.43%. Finally, all 5 responses analyzed simultaneously were optimized. In this case, it was possible to increase the critical buckling load by 42.55%, the failure load by 28.70% and reduce the mass and Poisson’s ratio by 15.97% and 11%, respectively. This paper shows something unprecedented in the literature to date when evaluating in a multi-objective optimization problem, the compression and modal performance of an auxetic reentrant model.

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