Pull-In Analysis of a Nonlinear Viscoelastic Nanocomposite Microplate Under an Electrostatic Actuation

2012 ◽  
Vol 28 (1) ◽  
pp. 179-189 ◽  
Author(s):  
A. Jalali ◽  
S. E. Khadem
Keyword(s):  
Quality Factor ◽  
Natural Frequency ◽  
Plate Theory ◽  
Equations Of Motion ◽  
Viscoelastic Model ◽  
Electrostatic Actuation ◽  
Response Characteristics ◽  
Damping Characteristics ◽  
Nonlinear Viscoelastic ◽  
Nonlinear Equations Of Motion

ABSTRACTIn this paper, the deflection, natural frequency and damping quality factor of a viscoelastic microplate under an electrostatic actuation are investigated. The microplate is assumed as a CNT-reinforced nanocomposite microplate, and an electrostatic actuation is applied on it. The nonlinear equations of motion are derived using the Von-Karman plate theory, and the Kelvin-Voigt viscoelastic model. In order to obtain the material properties of the nanocomposite microplate, the Eshelby–Mori–Tanaka method is implemented. The static pull-in instability of the microplate is obtained. It is shown that the nanocomposite microplate can both increase the deflection and natural frequency of the micro devices. So, one may have a nanocomposite microplate with the same deflection of the SiO2 microplate, while its frequency would be 1.45 times of the SiO2 microplate. This characteristic is highly desirable in microswitches. Also, it is shown that the damping quality factor of the nanocomposite microplate is much greater than SiO2 microplate. This fact limits the implementation of a nanocomposite microplate as a vibrating element of the micro devises. So, there are great beneficial static and frequency response characteristics for nanocomposite microplates. But, it is not recommended for microresonators due to high damping characteristics.

On the Frequency Response of a Spinning Disk With Large Deformations

2010 ◽  
Author(s):  
Ramin M. H. Khorasany ◽  
Stanley G. Hutton
Keyword(s):  
Frequency Response ◽  
Plate Theory ◽  
Equations Of Motion ◽  
Rotating Disk ◽  
Nonlinear Frequency ◽  
Response Characteristics ◽  
Geometrical Nonlinear ◽  
Oscillation Frequencies ◽  
Multi Mode ◽  
Different Levels

In this paper, the effect of geometrical nonlinear terms, caused by a space fixed point force, on the frequencies of oscillations of a rotating disk with clamped-free boundary conditions is investigated. The nonlinear geometrical equations of motion are based on Von Karman plate theory. Using the eigenfunctions of a stationary disk as approximating functions in Galerkin’s method, the equations of motion are transformed into a set of coupled nonlinear Ordinary Differential Equations (ODEs). These equations are then used to find the equilibrium positions of the disk at different discrete blade speeds. At any given speed, the governing equations are linearized about the equilibrium solution of the disk under the application of a space fixed external force. These linearized equations are then used to find the oscillation frequencies of the disk considering the effect of large deformation. Using multi mode approximation and different levels of nonlinearity, the frequency response of the disk considering the effect of geometrical nonlinear terms are studied. It is found that at the linear critical speed, the nonlinear frequency of the corresponding mode is not zero. Results are presented that illustrate the effect of the magnitude of disk displacement upon the frequency response characteristics. It is also found that for each mode, including the effect of the geometrical nonlinear terms due to the applied load causes a separation in the frequency responses of its backward and forward traveling waves when the disk is stationary. This effect is similar to the effect of a space fixed constraint in the linear problem. In order to verify the numerical results, experiments are conducted and the results are presented.

scholarly journals Effect of Insertion Viscoelastic Damping Layer with Different Thicknesses on the Dynamic Response of Multi-layered Beam in Forced Vibration

2020 ◽  
Vol 65 (1) ◽  
pp. 1-9
Author(s):  
Messaoud Baali ◽  
Mohamed Nadir Amrane
Keyword(s):  
Finite Element ◽  
Forced Vibration ◽  
Sandwich Structure ◽  
Natural Frequencies ◽  
Equations Of Motion ◽  
Viscoelastic Model ◽  
Viscoelastic Layer ◽  
Thickness Variation ◽  
Vertical Displacements ◽  
Nonlinear Equations Of Motion

In this work, we study the effect of the thickness variation of viscoelastic layer inserted in a laminated multi-layer beam in forced vibration on the vertical displacements and on the natural frequencies. The new structure is a sandwich structure composed by two external layers (top and bottom facesheets) of aluminum and viscoelastic core of 3M ISD112 polymers. The viscoelastic model used to describe the behavior of the core is a four-parameter fractional derivative model. The finite element method including the viscoelastic model of fractional derivatives for modeling the sandwich structure is used. The system resolution of the nonlinear equations of motion of the sandwich structure is required to use a numerical integration method as the explicit method of Newmark to obtain the transient response. Also, ANSYS finite element modeling is applied to the sandwich structure to calculate the frequency response in harmonic vibration. The increase in the thickness of the viscoelastic layer leads to a decrease in the amplitudes of vibration. The natural frequencies found by the two methods are very close to the frequencies found experimentally in the literature.

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.

Static Pull-In Analysis of a Carbon Nano Tube (CNT)-Reinforced Microplate Under Electrostatic Actuation

2010 ◽  
Author(s):  
Amir Jalali ◽  
Siamak E. Khadem
Keyword(s):  
Galerkin Method ◽  
Equations Of Motion ◽  
Electrostatic Actuation ◽  
Simply Supported ◽  
Base Matrix ◽  
Viscoelastic Characteristics ◽  
Square Plate ◽  
Nonlinear Equations Of Motion ◽  
Carbon Nano Tube ◽  
Selection Of

In this paper, nonlinear vibration characteristics of a viscoelastic microplate under electrostatic actuation have been obtained. The microplate has been assumed as a CNT-reinforced simply supported square plate and an electrostatic actuation applied on it. The nonlinear equations of motion have been derived and solved, by using combined Galerkin method and indeterminate coefficient procedure. Static pull-in instability of the microplate has been also derived. It has been shown that the pull-in voltage, natural frequency and deflection of the system depend on the value of electrostatic actuation and viscoelastic characteristics of the microplate and differ from those obtained in elastic one. So, good selection of composite components (nanotube, base matrix) can result in better controlling of the microplate due to increasing/decreasing of the pull-in voltage.

Vibration Analysis of Nanoplate with the Effects of Surface Irregularity and Initial Stresses

2021 ◽  
Vol 16 (1) ◽  
pp. 48-53
Author(s):  
Mahmoud. M. Selim ◽  
Sherif A. El-Safty
Keyword(s):  
Natural Frequency ◽  
Vibration Analysis ◽  
Plate Theory ◽  
Equations Of Motion ◽  
Initial Stresses ◽  
Surface Irregularity ◽  
Closed Form Solutions ◽  
Stress Effects ◽  
Vibration Properties ◽  
Stress Parameters

Based on Kirchhoff plate theory, the vibration behavior of irregular nanoplate with consideration of initial compressive stress effects is investigated. The equations of motion are derived and the closed form solutions for the natural frequency of the nanoplate are obtained. The analytical solutions reveal that, the natural frequency of the nanoplate, are found to be significantly dependent on the irregularity and compressive initial stresses present in the nanoplate. Numerical results show that, the natural frequency of nanoplates increases with increase of surface irregularity and initial stress parameters. To the author best knowledge, the effects of surface irregularity and initial stresses on the vibration behaviour of nanoplates have not yet been studied, and the present work is an attempt to find out this effectiveness. The results of this work is expected to be useful to design and analyze the vibration properties of nanostructures and Devices in NEMS.

Bifurcation and Chaos of the Rectangular Moderate Thickness Cracked Plates on an Elastic Foundation

2006 ◽  
Vol 324-325 ◽  
pp. 399-402
Author(s):  
Yong Gang Xiao
Keyword(s):  
Elastic Foundation ◽  
Nonlinear Equations ◽  
External Load ◽  
Plate Theory ◽  
Equations Of Motion ◽  
Rectangular Plates ◽  
Bifurcation And Chaos ◽  
Periodic Load ◽  
Hamilton Variational Principle ◽  
Nonlinear Equations Of Motion

Based on Reissner plate theory and using Hamilton variational principle, the nonlinear equations of motion are derived for the moderate thickness rectangular plates with transverse surface penetrating crack on an elastic foundation under the action of periodic load. The suitable expressions of trial functions satisfied all boundary conditions and crack’s continuous conditions are proposed. By using the Galerkin method and the Runge-Kutta integration method, the nonlinear equations are solved. The possible bifurcation and chaos of the system are analyzed under the action of external load. In numerical calculation, the influences of the different location and depth of crack and external load on the bifurcation and chaos of the rectangular moderate thickness plates with freely supported boundary are discussed.

scholarly journals Vibration analysis of a sandwich cylindrical shell in hygrothermal environment

2021 ◽  
Vol 10 (1) ◽  
pp. 414-430
Author(s):  
Chunwei Zhang ◽  
Qiao Jin ◽  
Yansheng Song ◽  
Jingli Wang ◽  
Li Sun ◽  
...  
Keyword(s):  
Cylindrical Shell ◽  
Natural Frequency ◽  
Equations Of Motion ◽  
Single Layer ◽  
Functionally Graded ◽  
Sandwich Shell ◽  
Continuous Change ◽  
Multilayered Structures ◽  
Cylindrical Sandwich Shell ◽  
Vibrational Behavior

Abstract The sandwich structures are three- or multilayered structures such that their mechanical properties are better than each single layer. In the current research, a three-layered cylindrical shell including a functionally graded porous core and two reinforced nanocomposite face sheets resting on the Pasternak foundation is used as model to provide a comprehensive understanding of vibrational behavior of such structures. The core is made of limestone, while the epoxy is utilized as the top and bottom layers’ matrix phase and also it is reinforced by the graphene nanoplatelets (GNPs). The pattern of the GNPs dispersion and the pores distribution play a crucial role at the continuous change of the layers’ properties. The sinusoidal shear deformation shells theory and the Hamilton’s principle are employed to derive the equations of motion for the mentioned cylindrical sandwich shell. Ultimately, the impacts of the model’s geometry, foundation moduli, mode number, and deviatory radius on the vibrational behavior are investigated and discussed. It is revealed that the natural frequency and rotation angle of the sandwich shell are directly related. Moreover, mid-radius to thickness ratio enhancement results in the natural frequency reduction. The results of this study can be helpful for the future investigations in such a broad context. Furthermore, for the pipe factories current study can be effective at their designing procedure.

Synthesis of biquad filters using two VD-DIBAs with independent control of quality factor and natural frequency

2021 ◽  
Vol 132 ◽  
pp. 153601
Author(s):  
Winai Jaikla ◽  
Surapong Siripongdee ◽  
Fabian Khateb ◽  
Roman Sotner ◽  
Phamorn Silapan ◽  
...  
Keyword(s):  
Quality Factor ◽  
Natural Frequency ◽  
Independent Control

Free volume based nonlinear viscoelastic model for polyurea over a wide range of strain rates and temperatures

2021 ◽  
Vol 152 ◽  
pp. 103650
Author(s):  
Chencheng Gong ◽  
Yan Chen ◽  
Ting Li ◽  
Zhanli Liu ◽  
Zhuo Zhuang ◽  
...  
Keyword(s):  
Free Volume ◽  
Viscoelastic Model ◽  
Strain Rates ◽  
Nonlinear Viscoelastic ◽  
Wide Range ◽  
Nonlinear Viscoelastic Model

Identification of Nonlinear Viscoelastic Models of Flexible Polyurethane Foam From Uniaxial Compression Data

2016 ◽  
Vol 138 (2) ◽  
Author(s):  
Yousof Azizi ◽  
Patricia Davies ◽  
Anil K. Bajaj
Keyword(s):  
Uniaxial Compression ◽  
Viscoelastic Model ◽  
Viscoelastic Behavior ◽  
Model Parameters ◽  
Viscoelastic Models ◽  
Nonlinear Viscoelastic ◽  
Compression Data ◽  
Computationally Intensive ◽  
Nonlinear Viscoelastic Model ◽  
Flexible Polyurethane

Flexible polyethylene foam is used in many engineering applications. It exhibits nonlinear and viscoelastic behavior which makes it difficult to model. To date, several models have been developed to characterize the complex behavior of foams. These attempts include the computationally intensive microstructural models to continuum models that capture the macroscale behavior of the foam materials. In this research, a nonlinear viscoelastic model, which is an extension to previously developed models, is proposed and its ability to capture foam response in uniaxial compression is investigated. It is hypothesized that total stress can be decomposed into the sum of a nonlinear elastic component, modeled by a higher-order polynomial, and a nonlinear hereditary type viscoelastic component. System identification procedures were developed to estimate the model parameters using uniaxial cyclic compression data from experiments conducted at six different rates. The estimated model parameters for individual tests were used to develop a model with parameters that are a function of strain rates. The parameter estimation technique was modified to also develop a comprehensive model which captures the uniaxial behavior of all six tests. The performance of this model was compared to that of other nonlinear viscoelastic models.

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