scholarly journals On the Vibrations and Stability of Moving Viscoelastic Axially Functionally Graded Nanobeams

Materials ◽  
2020 ◽  
Vol 13 (7) ◽  
pp. 1707 ◽  
Author(s):  
Ali Shariati ◽  
Dong won Jung ◽  
Hamid Mohammad-Sedighi ◽  
Krzysztof Kamil Żur ◽  
Mostafa Habibi ◽  
...  
Keyword(s):  
Critical Velocity ◽  
Natural Frequencies ◽  
Nonlocal Parameter ◽  
Dynamical Behavior ◽  
Functionally Graded ◽  
Fine Tuning ◽  
Dynamical Response ◽  
Power Law Distribution ◽  
Axially Moving ◽  
The Stability

In this article, size-dependent vibrations and the stability of moving viscoelastic axially functionally graded (AFG) nanobeams were investigated numerically and analytically, aiming at the stability enhancement of translating nanosystems. Additionally, a parametric investigation is presented to elucidate the influence of various key factors such as axial gradation of the material, viscosity coefficient, and nonlocal parameter on the stability boundaries of the system. Material characteristics of the system vary smoothly along the axial direction based on a power-law distribution function. Laplace transformation in conjunction with the Galerkin discretization scheme was implemented to obtain the natural frequencies, dynamical configuration, divergence, and flutter instability thresholds of the system. Furthermore, the critical velocity of the system was evaluated analytically. Stability maps of the system were examined, and it can be concluded that the nonlocal effect in the system can be significantly dampened by fine-tuning of axial material distribution. It was demonstrated that AFG materials can profoundly enhance the stability and dynamical response of axially moving nanosystems in comparison to homogeneous materials. The results indicate that for low and high values of the nonlocal parameter, the power index plays an opposite role in the dynamical behavior of the system. Meanwhile, it was shown that the qualitative stability of axially moving nanobeams depends on the effect of viscoelastic properties in the system, while axial grading of material has a significant role in determining the critical velocity and natural frequencies of the system.

scholarly journals Stability and Dynamics of Viscoelastic Moving Rayleigh Beams with an Asymmetrical Distribution of Material Parameters

Symmetry ◽  
2020 ◽  
Vol 12 (4) ◽  
pp. 586 ◽  
Author(s):  
Ali Shariati ◽  
Dong won Jung ◽  
Hamid Mohammad-Sedighi ◽  
Krzysztof Kamil Żur ◽  
Mostafa Habibi ◽  
...  
Keyword(s):  
Elastic Modulus ◽  
Critical Velocity ◽  
Natural Frequencies ◽  
Longitudinal Direction ◽  
Variable Density ◽  
Functionally Graded ◽  
Dynamic Configuration ◽  
Stability Maps ◽  
Gradient Parameter ◽  
The Stability

In this article, vibration of viscoelastic axially functionally graded (AFG) moving Rayleigh and Euler–Bernoulli (EB) beams are investigated and compared, aiming at a performance improvement of translating systems. Additionally, a detailed study is performed to elucidate the influence of various factors, such as the rotary inertia factor and axial gradation of material on the stability borders of the system. The material properties of the beam are distributed linearly or exponentially in the longitudinal direction. The Galerkin procedure and eigenvalue analysis are adopted to acquire the natural frequencies, dynamic configuration, and instability thresholds of the system. Furthermore, an exact analytical expression for the critical velocity of the AFG moving Rayleigh beams is presented. The stability maps and critical velocity contours for various material distributions are examined. In the case of variable density and elastic modulus, it is demonstrated that linear and exponential distributions provide a more stable system, respectively. Furthermore, the results revealed that the decrease of density gradient parameter and the increase of the elastic modulus gradient parameter enhance the natural frequencies and enlarge the instability threshold of the system. Hence, the density and elastic modulus gradients play opposite roles in the dynamic behavior of the system.

scholarly journals UNCOUPLED VIBRATIONS IN FUNCTIONALLY GRADED TIMOSHENKO BEAM

2016 ◽  
Vol 54 (6) ◽  
pp. 785 ◽  
Author(s):  
Nguyen Tien Khiem ◽  
Nguyen Ngoc Huyen
Keyword(s):  
Free Vibration ◽  
Timoshenko Beam ◽  
Natural Frequencies ◽  
Flexural Vibration ◽  
Functionally Graded ◽  
Mode Shapes ◽  
Power Law Distribution ◽  
Material Parameters ◽  
Flexural Vibrations ◽  
Fgm Beam

Free vibration of FGM Timoshenko beam is investigated on the base of the power law distribution of FGM. Taking into account the actual position of neutral plane enables to obtain general condition for uncoupling of axial and flexural vibrations in FGM beam. This condition defines a class of functionally graded beams for which axial and flexural vibrations are completely uncoupled likely to the homogeneous beams. Natural frequencies and mode shapes of uncoupled flexural vibration of beams from the class are examined in dependence on material parameters and slendernes

Resonance Responses of Geometrically Imperfect Functionally Graded Extensible Microbeams

2017 ◽  
Vol 12 (5) ◽  
Author(s):  
Mergen H. Ghayesh ◽  
Hamed Farokhi ◽  
Alireza Gholipour ◽  
Shahid Hussain ◽  
Maziar Arjomandi
Keyword(s):  
Couple Stress Theory ◽  
Continuation Method ◽  
Dynamical Behavior ◽  
Beam Theory ◽  
Modified Couple Stress Theory ◽  
Functionally Graded ◽  
Dynamical Response ◽  
Weighted Residual Method ◽  
Size Dependent ◽  
Rotational Motions

This paper aims at analyzing the size-dependent nonlinear dynamical behavior of a geometrically imperfect microbeam made of a functionally graded (FG) material, taking into account the longitudinal, transverse, and rotational motions. The size-dependent property is modeled by means of the modified couple stress theory, the shear deformation and rotary inertia are modeled using the Timoshenko beam theory, and the graded material property in the beam thickness direction is modeled via the Mori–Tanaka homogenization technique. The kinetic and size-dependent potential energies of the system are developed as functions of the longitudinal, transverse, and rotational motions. On the basis of an energy method, the continuous models of the system motion are obtained. Upon application of a weighted-residual method, the reduced-order model is obtained. A continuation method along with an eigenvalue extraction technique is utilized for the nonlinear and linear analyses, respectively. A special attention is paid on the effects of the material gradient index, the imperfection amplitude, and the length-scale parameter on the system dynamical response.

scholarly journals A Nonlocal Strain Gradient Approach for Out-of-Plane Vibration of Axially Moving Functionally Graded Nanoplates in a Hygrothermal Environment

2021 ◽  
Vol 2021 ◽  
pp. 1-19
Author(s):  
Chengxiu Zhu ◽  
Jianwei Yan ◽  
Pingyuan Wang ◽  
Cheng Li
Keyword(s):  
Scale Parameter ◽  
Nonlocal Parameter ◽  
Functionally Graded ◽  
Characteristic Scale ◽  
Vibration Frequencies ◽  
Material Characteristic ◽  
Moisture Concentration ◽  
Axially Moving ◽  
Nonlocal Strain Gradient ◽  
Axial Speed

Vibration analyses on axially moving functionally graded nanoplates exposed to hygrothermal environments are presented. The theoretical model of the nanoplate is described via the Kirchhoff plate theory in conjunction with the concept of the physical neutral layer. By employing the nonlocal strain gradient theory, the governing equation of motion is derived based on Hamilton’s principle. The composite beam function method, as well as the complex modal approach, is utilized to obtain the vibration frequencies of axially moving functionally graded nanoplates. Some benchmark results related to the effects of temperature changing, moisture concentration, axial speed, aspect ratio, nonlocal parameter, and the material characteristic scale parameter on the stiffness of axially moving functionally graded nanoplates are obtained. The results reveal that with increasing the nonlocal parameter, gradient index, temperature changing, moisture concentration, and axial speed, the vibration frequencies decrease. The frequencies increase while increasing the material characteristic scale parameter and aspect ratio. Moreover, there is an interaction between the nonlocal parameter and material characteristic scale parameter, influencing and restricting each other.

scholarly journals Modeling the Size Effect on the Mechanical Behavior of Functionally Graded Curved Micro/Nanobeam

2018 ◽  
Vol 1 (2) ◽  
Author(s):  
Seyyed Amirhosein Hosseini1 ◽  
O. Rahmani2
Keyword(s):  
Size Effect ◽  
Boundary Conditions ◽  
Natural Frequencies ◽  
Power Index ◽  
Nonlocal Parameter ◽  
Functionally Graded ◽  
Opening Angle ◽  
Simply Supported ◽  
Fg Nanobeam ◽  
Good Agreement

The size effect on the free vibration and bending of a curved FG micro/nanobeam is studied in this paper. Using the Hamilton principle the differential equations and boundary conditions is derived for a nonlocal Euler-Bernoulli curved micro/nanobeam.  The material properties vary through radius direction. Using the Navier approach an analytical solution for simply supported boundary conditions is obtained where the power index law of FGM, the curved micro/nanobeam opening angle, the effect of aspect ratio and nonlocal parameter on natural frequencies and the radial and tangential displacements were analyzed. It is concluded that increasing the curved micro/nanobeam opening angle results in decreasing and increasing the frequencies and displacements, respectively. To validate the natural frequencies of curved nanobeam, when the radius of it approaches to infinity, is compared with a straight FG nanobeam and showed a good agreement.

scholarly journals Buckling Analysis of Smart Size-Dependent Higher Order Magneto-Electro-Thermo-Elastic Functionally Graded Nanosize Beams

2016 ◽  
Vol 33 (1) ◽  
pp. 23-33 ◽  
Author(s):  
F. Ebrahimi ◽  
M. R. Barati
Keyword(s):  
Power Law ◽  
Thermal Loading ◽  
Slenderness Ratio ◽  
Nonlocal Parameter ◽  
Higher Order ◽  
Thermal Buckling ◽  
Functionally Graded ◽  
Beam Model ◽  
Thickness Direction ◽  
Power Law Distribution

AbstractThe present paper examines the thermal buckling of nonlocal magneto-electro-thermo-elastic functionally graded (METE-FG) beams under various types of thermal loading namely uniform, linear and sinusoidal temperature rise and also heat conduction. The material properties of nanobeam are graded in the thickness direction according to the power-law distribution. Based on a higher order beam theory as well as Hamilton's principle, nonlocal governing equations for METE-FG nanobeam are derived and are solved using Navier type method. The small size effect is captured using Eringen's nonlocal elasticity theory. The most beneficial feature of the present beam model is to provide a parabolic variation of the transverse shear strains across the thickness direction and satisfies the zero traction boundary conditions on the top and bottom surfaces of the beam without using shear correction factors. Various numerical examples are presented investigating the influences of thermo-mechanical loadings, magnetic potential, external electric voltage, power-law index, nonlocal parameter and slenderness ratio on thermal buckling behavior of nanobeams made of METE-FG materials.

scholarly journals Nonlinear postbuckling of eccentrically stiffened functionally graded plates and shallow shells

2011 ◽  
Vol 33 (3) ◽  
pp. 131-147 ◽  
Author(s):  
Dao Huy Bich ◽  
Vu Hoai Nam ◽  
Nguyen Thi Phuong
Keyword(s):  
Volume Fraction ◽  
Geometrical Nonlinearity ◽  
Functionally Graded ◽  
Functionally Graded Plates ◽  
Power Law Distribution ◽  
Governing Equations ◽  
Shallow Shells ◽  
The Stability ◽  
The Galerkin Method ◽  
Rich Side

The paper deals with the formulation of governing equations of eccentrically stiffened functionally graded plates and shallow shells based upon the classical shell theory and the smeared stiffeners technique taking into account geometrical nonlinearity in Von Karman-Donnell sense. Material properties are assumed to be temperature-independent and graded in the thickness direction according to a simple power law distribution in terms of the volume fraction of constituents. The shells are reinforced by eccentrically longitudinal and transversal stiffeners made of full metal or full ceramic depending on situation of stiffeners at metal-rich side or ceramic-rich side of the shell respectively. Obtained governing equations can be used in research on nonlinear postbuckling of mentioned above structures. By use of the Galerkin method an approximated analytical solution to the nonlinear stability problem of reinforced FGM plates and shallow shells is performed. The postbuckling load-deflection curves of the shells are investigated and analytical expressions of the upper and lower buckling loads are presented. A comparison of the effectiveness of stiffeners in enhancing the stability of FGM plates and shallow shells is given.

Vibration characteristics and stable region of a parabolic FGM thin-walled beam with axial and spinning motion

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Baichuan Lin ◽  
Bo Chen ◽  
Yinghui Li ◽  
Jie Yang
Keyword(s):  
Natural Frequencies ◽  
Angular Speed ◽  
Vibration Characteristics ◽  
Functionally Graded ◽  
Stable Region ◽  
Graded Material ◽  
Axially Moving ◽  
Fgm Beam ◽  
Spinning Speed ◽  
Axial Speed

Abstract This paper focuses on the vibration characteristics of the parabolic functionally graded material (FGM) beam considering the axially moving and spinning motion. Based on the Hamilton’s principle, the governing equation of the beam is derived. Then, the Galerkin’s method is employed to solve the equation. The combined influence of axial speed, spinning speed, and geometric parameters on natural frequencies of the beam are investigated. What’s more, the axially moving and spinning motion can lead to a critical axial speed and critical spinning angular speed, respectively. These two critical speeds and stable region affected by different parameters are also discussed.

The Dynamics of MEMS Arches of Non-Ideal Boundary Conditions

2011 ◽  
Author(s):  
Sami A. Alkharabsheh ◽  
Mohammad I. Younis
Keyword(s):  
Boundary Conditions ◽  
Natural Frequencies ◽  
Electrostatic Force ◽  
Dynamical Behavior ◽  
Experimental Investigations ◽  
Harmonic Load ◽  
Ideal Boundary ◽  
Shooting Technique ◽  
Softening Behavior ◽  
The Stability

We present an investigation into the dynamics of MEMS arches when actuated electrically including the effect of their flexible (non-ideal) supports. First, the eigenvalue problem of a nonlinear Euler-Bernoulli shallow arch with torsional and transversal springs at the boundaries is solved analytically. Several results are shown to demonstrate the possibility of tuning the theoretically obtained natural frequencies of an arch to match the experimentally measured. Then, simulation results are shown for the forced vibration response of an arch when excited by a DC electrostatic force superimposed to an AC harmonic load. Shooting technique is utilized to find periodic motions. The stability of the captured periodic motion is examined using the Floquet theory. The results show several jumps in the response during snap-through motion and pull-in. Theoretical and experimental investigations are conducted on a microfabricated curved beam actuated electrically. Results show softening behavior and superharmonic resonances. It is demonstrated that non-ideal boundary conditions can have significant effect on the qualitative dynamical behavior of the MEMS arch, including its natural frequencies, snap-through behavior, and dynamic pull-in.

scholarly journals Mechanical Property Variation of a Rotating Cantilever FGSW Beam under Parametric Excitation

2019 ◽  
Vol 8 (11) ◽  
pp. 495-499
Keyword(s):  
Shear Modulus ◽  
Power Law ◽  
Parametric Excitation ◽  
Excitation Power ◽  
Functionally Graded ◽  
Timoshenko Beams ◽  
Power Law Distribution ◽  
Property Variation ◽  
Graded Material ◽  
The Stability

We report here the dynamic stability of functionally graded sandwich (FGSW) rotating cantilever Timoshenko beams under parametric excitation. Power law with various indices as well as exponential law were used to find out the properties along the thickness of the FGSW beam. The stability boundaries were established using Floquet’s theory. The equation of motion was governed by Hamilton’s principle and solved by Finite element method. The power index was optimized for uniform variation of shear modulus along the thickness of FGSW beam.The shear modulus variation along the thickness of the FGSW beam was compared both by power law and exponential law.It has been confirmed that the Exponential distribution of constituent phases renders better stability compared to power law distribution of the phases in the functionally graded material(FGM).

Sign in / Sign up

Export Citation Format

Share Document