scholarly journals The Size-Dependent Thermoelastic Vibrations of Nanobeams Subjected to Harmonic Excitation and Rectified Sine Wave Heating

Mathematics ◽  
2020 ◽  
Vol 8 (7) ◽  
pp. 1128 ◽  
Author(s):  
Ahmed E. Abouelregal ◽  
Marin Marin
Keyword(s):  
External Force ◽  
Nonlocal Parameter ◽  
Generalized Thermoelasticity ◽  
Nonlocal Elasticity Theory ◽  
Sine Wave ◽  
Harmonic Excitation ◽  
Angular Frequency ◽  
Small Scale ◽  
Length Scale ◽  
Wave Heating

In this article, a nonlocal thermoelastic model that illustrates the vibrations of nanobeams is introduced. Based on the nonlocal elasticity theory proposed by Eringen and generalized thermoelasticity, the equations that govern the nonlocal nanobeams are derived. The structure of the nanobeam is under a harmonic external force and temperature change in the form of rectified sine wave heating. The nonlocal model includes the nonlocal parameter (length-scale) that can have the effect of the small-scale. Utilizing the technique of Laplace transform, the analytical expressions for the studied fields are reached. The effects of angular frequency and nonlocal parameters, as well as the external excitation on the response of the nanobeam are carefully examined. It is found that length-scale and external force have significant effects on the variation of the distributions of the physical variables. Some of the obtained numerical results are compared with the known literature, in which they are well proven. It is hoped that the obtained results will be valuable in micro/nano electro-mechanical systems, especially in the manufacture and design of actuators and electro-elastic sensors.

scholarly journals Double mode model of size-dependent chaotic vibrations of nanoplates based on the nonlocal elasticity theory

2021 ◽  
Author(s):  
Jan Awrejcewicz ◽  
Grzegorz Kudra ◽  
Olga Mazur
Keyword(s):  
Elasticity Theory ◽  
Nonlocal Elasticity ◽  
Scale Effects ◽  
Plate Theory ◽  
Nonlocal Parameter ◽  
Nonlocal Elasticity Theory ◽  
Phase Portraits ◽  
Small Scale ◽  
Governing System ◽  
Account Due

AbstractIn this paper vibrations of the isotropic micro/nanoplates subjected to transverse and in-plane excitation are investigated. The governing equations of the problem are based on the von Kármán plate theory and Kirchhoff–Love hypothesis. The small-size effect is taken into account due to the nonlocal elasticity theory. The formulation of the problem is mixed and employs the Airy stress function. The two-mode approximation of the deflection and application of the Bubnov–Galerkin method reduces the governing system of equations to the system of ordinary differential equations. Varying the load parameters and the nonlocal parameter, the bifurcation analysis is performed. The bifurcations diagrams, the maximum Lyapunov exponents, phase portraits as well as Poincare maps are constructed based on the numerical simulations. It is shown that for some excitation conditions the chaotic motion may occur in the system. Also, the small-scale effects on the character of vibrating regimes are illustrated and discussed.

Forced Flexural Vibrations in a Thin Nonlocal Rectangular Plate with Kirchhoff’s Thin Plate Theory

2020 ◽  
Vol 20 (09) ◽  
pp. 2050107
Author(s):  
Iqbal Kaur ◽  
Parveen Lata ◽  
Kulvinder Singh
Keyword(s):  
Rectangular Plate ◽  
Thin Plate ◽  
Plate Theory ◽  
Nonlocal Parameter ◽  
Generalized Thermoelasticity ◽  
Transversely Isotropic ◽  
Small Scale ◽  
Concentrated Load ◽  
Thin Rectangular Plate ◽  
Flexural Vibrations

This study deals with a novel model of forced flexural vibrations in a transversely isotropic thermoelastic thin rectangular plate (TRP) due to time harmonic concentrated load. The mathematical model is prepared for the thin plate in a closed form with the application of Kirchhoff’s love plate theory for nonlocal generalized thermoelasticity with Green–Naghdi (GN)-III theory of thermoelasticity. The nonlocal thin plate has a nonlocal parameter to depict small-scale effect. The double finite Fourier transform technique has been used to find the expressions for lateral deflection, thermal moment and temperature distribution for simply supported (SS) thin rectangular plate in the transformed domain. The effect of classical thermoelasticity (CTE) theory of thermoelasticity and nonlocal parameters has been shown on the computed quantities. Few particular cases have also been deduced.

scholarly journals Thermo-Electro-Mechanical Vibrations of Porous Functionally Graded Piezoelectric Nanoshells

Nanomaterials ◽  
2019 ◽  
Vol 9 (2) ◽  
pp. 301 ◽  
Author(s):  
Yun Fei Liu ◽  
Yan Qing Wang
Keyword(s):  
Boundary Conditions ◽  
Volume Fraction ◽  
Nonlocal Parameter ◽  
Nonlocal Elasticity Theory ◽  
Functionally Graded ◽  
Small Scale ◽  
Love’S Shell Theory ◽  
Small Scale Effect ◽  
Functionally Graded Piezoelectric ◽  
The Galerkin Method

In this work, we aim to study free vibration of functionally graded piezoelectric material (FGPM) cylindrical nanoshells with nano-voids. The present model incorporates the small scale effect and thermo-electro-mechanical loading. Two types of porosity distribution, namely, even and uneven distributions, are considered. Based on Love’s shell theory and the nonlocal elasticity theory, governing equations and corresponding boundary conditions are established through Hamilton’s principle. Then, natural frequencies of FGPM nanoshells with nano-voids under different boundary conditions are analyzed by employing the Navier method and the Galerkin method. The present results are verified by the comparison with the published ones. Finally, an extensive parametric study is conducted to examine the effects of the external electric potential, the nonlocal parameter, the volume fraction of nano-voids, the temperature rise on the vibration of porous FGPM cylindrical nanoshells.

Effect of External Moving Torque on Dynamic Stability of Carbon Nanotube

2020 ◽  
Vol 61 ◽  
pp. 118-135 ◽  
Author(s):  
Seyyed Amirhosein Hosseini ◽  
Farshad Khosravi ◽  
Majid Ghadiri
Keyword(s):  
Boundary Condition ◽  
Carbon Nanotube ◽  
Aspect Ratio ◽  
Natural Frequency ◽  
Nonlocal Parameter ◽  
Nonlocal Elasticity Theory ◽  
Small Scale ◽  
Torsional Mode ◽  
Angular Displacements ◽  
The Galerkin Method

In nano-dimension, the strength of the material is considerable, and the failure is unavoidable in a torsional mode. Because of this reason, the free and forced torsional vibrations of single-walled carbon nanotube (SWCNT) are investigated in this paper. For dynamic analysis, the moving harmonic torsional load is exerted to SWCNT. The related boundary condition and equation of motion are derived by Hamilton’s principle, and the equation is discretized by the Galerkin method. In order to demonstrate the nonlocality and small–scale effect, Eringen’s theory based on nonlocal elasticity theory is applied. A clamped-clamped (C-C) boundary condition is fitted for the end supports. The influences of the aspect ratio and mode number on the free natural frequency are investigated. Furthermore, the dynamic effects of nonlocal parameter, velocity, thickness, length, and excitation-to-natural frequencies on dimensional and nondimensional angular displacements are indicated. Moreover, the natural frequency was investigated due to the variation of the aspect ratio.

Nonlinear vibration and stability analysis of a size-dependent viscoelastic cantilever nanobeam with axial excitation

2020 ◽  
pp. 095440622095910
Author(s):  
Mohammad Noroozi ◽  
Majid Ghadiri
Keyword(s):  
Steady State ◽  
Bifurcation Point ◽  
Nonlocal Parameter ◽  
Nonlocal Elasticity Theory ◽  
Multiple Scale ◽  
Harmonic Excitation ◽  
Steady State Response ◽  
Size Dependent ◽  
State Response ◽  
Point Types

In the present paper, nonlinear forced vibrations of an axial moving nanobeam which is vertically influenced by an external harmonic excitation and gravity is analyzed by considering the effects of linear damping. Considering certain assumptions, a nonlinear Euler-Bernoulli beam theory is developed. With the implementation of the nonlocal elasticity theory, the governing integro-partial-differential equation is obtained by using the Hamilton principle. The multiple scale method is employed to obtain a steady-state response for the size-dependent viscoelastic nanobeam with fixed-free boundary conditions. Subsequently, the trivial and non-trivial steady-state response and the bifurcation point types are examined. Finally, the effects of damping coefficient and nonlocal parameter on stability and bifurcation of trivial and non-trivial solutions are studied. It is found that the effect of nonlocal parameter on the steady-state response and the bifurcation point types is quite important.

scholarly journals A Perturbation Approach for Lateral Excited Vibrations of a Beam-like Viscoelastic Microstructure Using the Nonlocal Theory

2021 ◽  
Vol 12 (1) ◽  
pp. 40
Author(s):  
Cheng Li ◽  
Chengxiu Zhu ◽  
Suihan Sui ◽  
Jianwei Yan
Keyword(s):  
Lateral Displacement ◽  
Nonlocal Parameter ◽  
Nonlinear Partial Differential Equation ◽  
Excitation Amplitude ◽  
Nonlocal Theory ◽  
Harmonic Excitation ◽  
Small Scale ◽  
Perturbation Approach ◽  
Stress Theory ◽  
Excited Vibration

In this paper, we investigate the lateral vibration of fully clamped beam-like microstructures subjected to an external transverse harmonic excitation. Eringen’s nonlocal theory is applied, and the viscoelasticity of materials is considered. Hence, the small-scale effect and viscoelastic properties are adopted in the higher-order mathematical model. The classical stress and classical bending moments in mechanics of materials are unavailable when modeling a microstructure, and, accordingly, they are substituted for the corresponding effective nonlocal quantities proposed in the nonlocal stress theory. Owing to an axial elongation, the nonlinear partial differential equation that governs the lateral motion of beam-like viscoelastic microstructures is derived using a geometric, kinematical, and dynamic analysis. In the next step, the ordinary differential equations are obtained, and the time-dependent lateral displacement is determined via a perturbation method. The effects of external excitation amplitude on excited vibration are presented, and the relations between the nonlocal parameter, viscoelastic damping, detuning parameter, and the forced amplitude are discussed. Some dynamic phenomena in the excited vibration are revealed, and these have reference significance to the dynamic design and optimization of beam-like viscoelastic microstructures.

Size-Dependent Buckling and Postbuckling Analyses of First-Order Shear Deformable Magneto-Electro-Thermo Elastic Nanoplates Based on the Nonlocal Elasticity Theory

2017 ◽  
Vol 17 (01) ◽  
pp. 1750014 ◽  
Author(s):  
R. Ansari ◽  
R. Gholami
Keyword(s):  
Boundary Conditions ◽  
Elasticity Theory ◽  
Shear Deformation ◽  
Nonlocal Elasticity ◽  
Nonlocal Parameter ◽  
Nonlocal Elasticity Theory ◽  
Small Scale ◽  
First Order ◽  
Size Dependent ◽  
Shear Deformable

This paper presents a nonlocal nonlinear first-order shear deformable plate model for investigating the buckling and postbuckling of magneto-electro-thermo elastic (METE) nanoplates under magneto-electro-thermo-mechanical loadings. The nonlocal elasticity theory within the framework of the first-order shear deformation plate theory along with the von Kármán-type geometrical nonlinearity is used to derive the size-dependent nonlinear governing partial differential equations and associated boundary conditions, in which the effects of shear deformation, small scale parameter and thermo-electro-magneto-mechanical loadings are incorporated. The generalized differential quadrature (GDQ) method and pseudo arc-length continuation algorithm are used to determine the critical buckling loads and postbuckling equilibrium paths of the METE nanoplates with various boundary conditions. Finally, the influences of the nonlocal parameter, boundary conditions, temperature rise, external electric voltage and external magnetic potential on the critical buckling load and postbuckling response are studied.

scholarly journals Nonlinear magneto-thermo-elastic vibration of mass sensor armchair carbon nanotube resting on an elastic substrate

2020 ◽  
Vol 7 (1) ◽  
pp. 153-165
Author(s):  
Rajendran Selvamani ◽  
M. Mahaveer Sree Jayan ◽  
Rossana Dimitri ◽  
Francesco Tornabene ◽  
Farzad Ebrahimi
Keyword(s):  
Carbon Nanotube ◽  
Mechanical Response ◽  
Scale Effects ◽  
Nonlocal Elasticity Theory ◽  
Wave Dispersion ◽  
Elastic Vibration ◽  
Ultrasonic Waves ◽  
Small Scale ◽  
Dimensionless Frequency ◽  
Mass Sensors

AbstractThe present paper aims at studying the nonlinear ultrasonic waves in a magneto-thermo-elastic armchair single-walled (SW) carbon nanotube (CNT) with mass sensors resting on a polymer substrate. The analytical formulation accounts for small scale effects based on the Eringen’s nonlocal elasticity theory. The mathematical model and its differential equations are solved theoretically in terms of dimensionless frequencies while assuming a nonlinear Winkler-Pasternak-type foundation. The solution is obtained by means of ultrasonic wave dispersion relations. A parametric work is carried out to check for the effect of the nonlocal scaling parameter, together with the magneto-mechanical loadings, the foundation parameters, the attached mass, boundary conditions and geometries, on the dimensionless frequency of nanotubes. The sensitivity of the mechanical response of nanotubes investigated herein, could be of great interest for design purposes in nano-engineering systems and devices.

scholarly journals Parametric vibrations of graphene sheets based on the double mode model and the nonlocal elasticity theory

2021 ◽  
Author(s):  
Jan Awrejcewicz ◽  
Grzegorz Kudra ◽  
Olga Mazur
Keyword(s):  
Elasticity Theory ◽  
Nonlocal Elasticity ◽  
Nonlinear Oscillations ◽  
Scale Effects ◽  
Equations Of Motion ◽  
Nonlocal Elasticity Theory ◽  
Small Scale ◽  
Largest Lyapunov Exponent ◽  
Graphene Sheets ◽  
Parametric Vibrations

AbstractParametric vibrations of the single-layered graphene sheet (SLGS) are studied in the presented work. The equations of motion govern geometrically nonlinear oscillations. The appearance of small effects is analysed due to the application of the nonlocal elasticity theory. The approach is developed for rectangular simply supported small-scale plate and it employs the Bubnov–Galerkin method with a double mode model, which reduces the problem to investigation of the system of the second-order ordinary differential equations (ODEs). The dynamic behaviour of the micro/nanoplate with varying excitation parameter is analysed to determine the chaotic regimes. As well the influence of small-scale effects to change the nature of vibrations is studied. The bifurcation diagrams, phase plots, Poincaré sections and the largest Lyapunov exponent are constructed and analysed. It is established that the use of nonlocal equations in the dynamic analysis of graphene sheets leads to a significant alteration in the character of oscillations, including the appearance of chaotic attractors.

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