Wave Propagation Analysis of Piezoelectric Nanoplates Based on the Nonlocal Theory

2018 ◽  
Vol 18 (04) ◽  
pp. 1850060 ◽  
Author(s):  
Li-Hong Ma ◽  
Liao-Liang Ke ◽  
Yi-Ze Wang ◽  
Yue-Sheng Wang
Keyword(s):  
Wave Propagation ◽  
Electric Potential ◽  
Mechanical Load ◽  
Tensile Force ◽  
Nonlocal Parameter ◽  
Nonlocal Theory ◽  
Wave Number ◽  
Small Scale ◽  
Axial Tensile ◽  
Propagation Analysis

Based on the nonlocal theory, this paper develops the Kirchhoff nanoplate and Mindlin nanoplate models for the wave propagation analysis of piezoelectric nanoplates. The effects of small scale parameter and thermo-electro-mechanical loads are incorporated in the nanoplate models. The Hamilton’s principle is employed to derive the governing equations of the nanoplate, which are solved analytically to obtain the dispersion relation for piezoelectric nanoplates. The results show that the nonlocal parameter, temperature change, mechanical load and external electric potential have significant influence on the wave propagation characteristics of the piezoelectric nanoplates. The cut-off wave number is observed to exist for piezoelectric nanoplates subjected to positive electric potential, axial tensile force and temperature rise.

Wave Propagation in a Piezoelectric Coupled Solid Medium

2002 ◽  
Vol 69 (6) ◽  
pp. 819-824 ◽  
Author(s):  
Q. Wang
Keyword(s):  
Wave Propagation ◽  
Wave Velocity ◽  
Electric Potential ◽  
Solid Medium ◽  
Electric Displacement ◽  
Piezoelectric Medium ◽  
Wave Number ◽  
Mode Shapes ◽  
Coupled Structures ◽  
Shear Horizontal

Shear horizontal (SH) wave propagation in a semi-infinite solid medium surface bonded by a layer of piezoelectric material abutting the vacuum is investigated in this paper. The dispersive characteristics and the mode shapes of the deflection, the electric potential, and the electric displacements in the thickness direction of the piezoelectric layer are obtained theoretically. Numerical simulations show that the asymptotic phase velocities for different modes are the Bleustein surface wave velocity or the shear horizontal wave velocity of the pure piezoelectric medium. Besides, the mode shapes of the deflection, electric potential, and electric displacement show different distributions for different modes and different wave number. These results can be served as a benchmark for further analyses and are significant in the modeling of wave propagation in the piezoelectric coupled structures.

Nonlocal Modeling and Behavior of Carbon Nanotube-Based Sensors in Thermal Environment

2018 ◽  
Author(s):  
Seyedeh Sepideh Ghaffari ◽  
Samantha Ceballes ◽  
Abdessattar Abdelkefi
Keyword(s):  
Carbon Nanotube ◽  
Thermal Effects ◽  
Thermal Environment ◽  
Nonlocal Parameter ◽  
Nonlocal Theory ◽  
Small Scale ◽  
Mass Sensor ◽  
Buckling Behavior ◽  
Mass Detector ◽  
And Behavior

An exact solution that investigates the pre-buckling characteristics of nonlocal carbon nanotube (CNT)-based mass sensor subjected to thermal load under clamped-clamped boundary condition is determined. The uniform temperature rise is utilized to study thermal effects on the sensitivity of the mechanical resonator in pre-buckling configuration. Using Eringen’s nonlocal theory, along with the Hamilton’s principle, the governing equations considering small scale and geometric nonlinearity are derived. The influences of important parameters including nonlocal parameter, temperature change, length, and diameter of the CNT on the pre-buckling behavior and frequency shift of the CNT-based mass detector are also studied. Results show that these parameters have significant impact on the dynamic characteristics of the CNT-mass sensor.

Wave Propagation Analysis in Anisotropic Plate Using Wavelet Spectral Element Approach

2008 ◽  
Vol 75 (1) ◽  
Author(s):  
Mira Mitra ◽  
S. Gopalakrishnan
Keyword(s):  
Finite Element ◽  
Wave Propagation ◽  
Differential Equations ◽  
Laminated Composite ◽  
Composite Plates ◽  
Spectral Element ◽  
Wave Number ◽  
Frequency Wave ◽  
Propagation Analysis ◽  
Spectral Finite Element

In this paper, a 2D wavelet-based spectral finite element (WSFE) is developed for a anisotropic laminated composite plate to study wave propagation. Spectral element model captures the exact inertial distribution as the governing partial differential equations (PDEs) are solved exactly in the transformed frequency-wave-number domain. Thus, the method results in large computational savings compared to conventional finite element (FE) modeling, particularly for wave propagation analysis. In this approach, first, Daubechies scaling function approximation is used in both time and one spatial dimensions to reduce the coupled PDEs to a set of ordinary differential equations (ODEs). Similar to the conventional fast Fourier transform (FFT) based spectral finite element (FSFE), the frequency-dependent wave characteristics can also be extracted directly from the present formulation. However, most importantly, the use of localized basis functions in the present 2D WSFE method circumvents several limitations of the corresponding 2D FSFE technique. Here, the formulated element is used to study wave propagation in laminated composite plates with different ply orientations, both in time and frequency domains.

scholarly journals Dynamic Behavior of Multi-Layered Viscoelastic Nanobeam System Embedded in a Viscoelastic Medium with a Moving Nanoparticle

2016 ◽  
Vol 33 (5) ◽  
pp. 559-575 ◽  
Author(s):  
Sh. Hosseini Hashemi ◽  
H. Bakhshi Khaniki
Keyword(s):  
Dynamic Behavior ◽  
Viscoelastic Medium ◽  
Scale Effects ◽  
Nonlocal Parameter ◽  
Nonlocal Theory ◽  
Function Technique ◽  
Small Scale ◽  
Transform Method ◽  
Damping Parameter ◽  
Moving Nanoparticle

AbstractIn this paper, dynamic behavior of multi-layered viscoelastic nanobeams resting on a viscoelastic medium with a moving nanoparticle is studied. Eringens nonlocal theory is used to model the small scale effects. Layers are coupled by Kelvin-Voigt viscoelastic medium model. Hamilton's principle, eigen-function technique and the Laplace transform method are employed to solve the governing differential equations. Analytical solutions for transverse displacements of double-layered is presented for both viscoelastic nanobeams embedded in a viscoelastic medium and without it while numerical solution is achieved for higher layered nanobeams. The influences of the nonlocal parameter, stiffness and damping parameter of medium, internal damping parameter and number of layers are studied while the nanoparticle passes through. Presented results can be useful in analysing and designing nanocars, nanotruck moving on surfaces, racing nanocars etc.

Analytical modeling of wave propagation in viscoelastic functionally graded carbon nanotubes reinforced piezoelectric microplate under electro-magnetic field

2016 ◽  
Vol 231 (1) ◽  
pp. 17-33 ◽  
Author(s):  
Ali Ghorbanpour Arani ◽  
Majid Jamali ◽  
Mohammad Mosayyebi ◽  
Reza Kolahchi
Keyword(s):  
Carbon Nanotubes ◽  
Wave Propagation ◽  
Scale Parameter ◽  
Three Dimensional ◽  
Functionally Graded ◽  
Small Scale ◽  
Dimensionless Frequency ◽  
Propagation Analysis ◽  
Electro Magnetic ◽  
Functionally Graded Carbon Nanotubes

Wave propagation analysis of a functionally graded carbon nanotubes reinforced piezoelectric composite (FG-CNTRPC) microplate is the major main of the present research. In order to present a realistic model, the material properties of the system are assumed viscoelastic and the Kelvin–Voigt model is applied. The viscoelastic FG-CNTRPC microplate is subjected to longitudinal magnetic and three-dimensional electric fields. The distribution of carbon nanotubes in FG-CNTRPC microplate is supposed as uniform distribution and surrounding circumference is simulated as Visco-Pasternak foundation. The original formulation of the quasi-three-dimensional sinusoidal shear deformation plate theory is here extended to the wave propagation analysis and the size effects are considered based on Eringen’s nonlocal theory. In order to calculate the dimensionless frequency, cut-off and escape frequencies analytical solution is applied. In this article, the influences of the volume fraction of carbon nanotubes, electro-magnetic fields and elastic medium on the dimensionless frequency of viscoelastic FG-CNTRPC microplate are investigated. Furthermore, the effect of small-scale parameter on the cut-off and escape frequencies of the system will be studied. Results demonstrate that the dimensionless cut-off and escape frequencies decrease with increasing the magnitude of small-scale parameter. In addition, the imposed magnetic field and external voltage are significant parameters for controlling wave propagation of the viscoelastic FG-CNTRPC microplate. Results of this investigation can be helpful for the study and design of composite systems based on smart control and sensor applications.

Wave dispersion analysis of magnetic-electrically affected fluid-conveying nanotubes in thermal environment

2019 ◽  
Vol 233 (19-20) ◽  
pp. 7116-7131 ◽  
Author(s):  
M Dehghan ◽  
F Ebrahimi ◽  
M Vinyas
Keyword(s):  
Wave Propagation ◽  
Elasticity Theory ◽  
Knudsen Number ◽  
Scale Effects ◽  
Fluid Velocity ◽  
Nonlocal Parameter ◽  
Small Scale ◽  
Governing Equations ◽  
Slip Boundary ◽  
Physical Fields

In this paper, the wave propagation analysis of fluid-conveying Magneto-Electro-Elastic (MEE) nanotube subjected to multi-physical fields is investigated via nonlocal strain gradient elasticity theory (NSGT). To take into account the small-scale effects, the nonlocal elasticity theory of Eringen is employed. Nonlocal governing equations of MEE nanotube have been derived utilizing Hamilton’s principle. The results of this study have been verified by checking them of antecedent investigations. An analytical solution of governing equations is used to acquire wave frequencies and phase velocities. The Knudsen number is considered to study the slip boundary wall of nanotube and flow. The effects of various parameters such as multi-physical fields, the Knudsen number, different mode, length parameter, nonlocal parameter, fluid velocity, fluid effect and the slip boundary condition on wave propagation characteristics of fluid-conveying MEE nanotube are investigated in detail.

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.

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