Coupled effects of surface interaction and damping on electromechanical stability of functionally graded nanotubes reinforced torsional micromirror actuator

2021 ◽  
pp. 030932472110368
Author(s):  
Weidong Yang ◽  
Menglong Liu ◽  
Linwei Ying ◽  
Xi Wang
Keyword(s):  
Casimir Force ◽  
Volume Fraction ◽  
Nonlocal Parameter ◽  
Saddle Points ◽  
Functionally Graded ◽  
Heteroclinic Orbits ◽  
Phase Portraits ◽  
Squeeze Film ◽  
Squeeze Film Damping ◽  
Tilting Angle

This paper demonstrated the coupled surface effects of thermal Casimir force and squeeze film damping (SFD) on size-dependent electromechanical stability and bifurcation of torsion micromirror actuator. The governing equations of micromirror system are derived, and the pull-in voltage and critical tilting angle are obtained. Also, the twisting deformation of torsion nanobeam can be tuned by functionally graded carbon nanotubes reinforced composites (FG-CNTRC). A finite element analysis (FEA) model is established on the COMSOL Multiphysics platform, and the simulation of the effect of thermal Casimir force on pull-in instability is utilized to verify the present analytical model. The results indicate that the numerical results well agree with the theoretical results in this work and experimental data in the literature. Further, the influences of volume fraction and geometrical distribution of CNTs, thermal Casimir force, nonlocal parameter, and squeeze film damping on electrically actuated instability and free-standing behavior are detailedly discussed. Besides, the evolution of equilibrium states of micromirror system is investigated, and bifurcation diagrams and phase portraits including the periodic, homoclinic, and heteroclinic orbits are described as well. The results demonstrated that the amplitude of the tilting angle for FGX-CNTRC type micromirror attenuates slower than for FGO-CNTRC type, and the increment of CNTs volume ratio slows down the attenuation due to the stiffening effect. When considering squeeze film damping, the stable center point evolves into one focus point with homoclinic orbits, and the dynamic system maintains two unstable saddle points with the heteroclinic orbits due to the effect of thermal Casimir force.

Free vibration problem of embedded magneto-electro-thermo-elastic nanoplate made of functionally graded materials via nonlocal third-order shear deformation theory

2017 ◽  
Vol 29 (5) ◽  
pp. 741-763 ◽  
Author(s):  
Ali Kiani ◽  
Moslem Sheikhkhoshkar ◽  
Ali Jamalpoor ◽  
Mostafa Khanzadi
Keyword(s):  
Boundary Conditions ◽  
Functionally Graded Materials ◽  
Volume Fraction ◽  
Nonlocal Parameter ◽  
Plate Thickness ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Third Order ◽  
Graded Materials ◽  
Simply Supported

In the present article, according to the nonlocal elasticity theory within the framework of the third-order shear deformable plate assumption, the theoretical analysis of thermomechanical vibration response of magneto-electro-thermo-elastic nanoplate made of functionally graded materials resting on the visco-Pasternak medium is carried out. The simply supported magneto-electro-thermo-elastic nanoplate is supposed to subject to initial external electric, magnetic potentials, and temperature environment. The material characteristics of magneto-electro-thermo-elastic nanoplate are assumed to be variable continuously across the thickness direction based upon power law distribution. Hamilton’s principle is utilized to achieve the partial differential equations and corresponding boundary conditions. The equilibrium equations are solved analytically to determine the complex eigenfrequency using Navier’s approach which satisfies the simply supported boundary conditions. Numerical studies are performed to illustrate the dependency of the natural frequency of the system on the damping coefficient of the visco-Pasternak medium, nonlocal parameter, aspect ratio, temperature change, volume fraction index of functionally graded material, initial external electric voltage, initial external magnetic potential, and plate thickness. It is clearly indicated that these factors have highly significant impacts on the dynamic behavior of the proposed system.

Analytical Modeling of Squeeze Film Damping in Micromirrors

2011 ◽  
Author(s):  
Hamid Moeenfard ◽  
Mohammad Taghi Ahmadian ◽  
Anoushiravan Farshidianfar
Keyword(s):  
Galerkin Approximation ◽  
Initial Guess ◽  
Squeeze Film ◽  
Kantorovich Method ◽  
Closed Form Solutions ◽  
Extended Kantorovich Method ◽  
Dynamical Simulation ◽  
Squeeze Film Damping ◽  
Tilting Angle ◽  
Damping Torque

In the current paper, Extended Kantorovich Method (EKM) has been utilized to analytically solve the problem of squeezed film damping in micromirrors. A one term Galerkin approximation is used and following the extended Kantorovich procedure, the solution of the Reynolds equation which governs the squeezed film damping in micromirrors is reduced to solution of two uncoupled ordinary differential equation which can be solved iteratively with a rapid convergence for finding the pressure distribution underneath the micromirror. It is shown that the EKM results are independent of the initial guess function. It is also shown that since EKM is highly convergent, practically one iterate is sufficient for obtaining a precise response. Furthermore using the presented closed form solutions for the squeezed film damping torque, it is proved that when the tilting angle of the mirror is small, the damping is linear viscous one. Results of this paper can be used for accurate dynamical simulation of micromirrors under the effect of squeezed film damping.

Size-dependent free vibration and buckling analysis of sigmoid and power law functionally graded sandwich nanobeams with microstructural defects

2020 ◽  
Vol 234 (18) ◽  
pp. 3667-3688
Author(s):  
Ismail Bensaid ◽  
Ahmed Amine Daikh ◽  
Ahmed Drai
Keyword(s):  
Free Vibration ◽  
Power Law ◽  
Functionally Graded Material ◽  
Volume Fraction ◽  
Nonlocal Parameter ◽  
Shear Deformation Theory ◽  
Nonlocal Elasticity Theory ◽  
Functionally Graded ◽  
Size Dependent ◽  
Graded Material

The investigation conducted in this paper aims to study free vibration and buckling behaviors of size-dependent functionally graded sandwich nanobeams. In order to take into account the small size effects, nonlocal elasticity theory of Eringen's is incorporated. Material properties of the functionally graded sandwich beams are supposed to change continuously through the thickness direction according to two forms of the volume fraction of constituents by power law functionally graded material and sigmoid law functionally graded material. These rules are modified to consider the effect of porosity, which covers four kinds of porosity distributions. Two types of sandwich nanobeams were provided: (a) homogeneous core and functionally graded skins and (b) functionally graded core and homogeneous skins. Third-order shear deformation theory without any shear correction factor in conjunction with Hamilton's principle is used to extract the governing equations of motions of porous functionally graded sandwich nanobeams and then solved analytically for two hinged ends. The effects of nonlocal parameter, length to thickness ratios, material graduation index, amount of porosity, porosity distribution shape, on the nondimensional frequency and critical buckling load of the functionally graded sandwich nanobeams made of porous materials are exhibited by a parametric study.

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.

scholarly journals Nonlocal Buckling Analysis of Composite Curved Beams Reinforced with Functionally Graded Carbon Nanotubes

Molecules ◽  
2019 ◽  
Vol 24 (15) ◽  
pp. 2750 ◽  
Author(s):  
Behrouz Karami ◽  
Maziar Janghorban ◽  
Davood Shahsavari ◽  
Rossana Dimitri ◽  
Francesco Tornabene
Keyword(s):  
Boundary Conditions ◽  
Volume Fraction ◽  
Slenderness Ratio ◽  
Nonlocal Parameter ◽  
Beam Theory ◽  
Functionally Graded ◽  
Opening Angle ◽  
Curved Beams ◽  
Differential Model ◽  
Mechanical Buckling

This work deals with the size-dependent buckling response of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) (FG-CNTRC) curved beams based on a higher-order shear deformation beam theory in conjunction with the Eringen Nonlocal Differential Model (ENDM). The material properties were estimated using the rule of mixtures. The Hamiltonian principle was employed to derive the governing equations of the problem which were, in turn, solved via the Galerkin method to obtain the critical buckling load of FG-CNTRC curved beams with different boundary conditions. A detailed parametric study was carried out to investigate the influence of the nonlocal parameter, CNTs volume fraction, opening angle, slenderness ratio, and boundary conditions on the mechanical buckling characteristics of FG-CNTRC curved beams. A large parametric investigation was performed on the mechanical buckling behavior of FG-CNTRC curved beams, which included different CNT distribution schemes, as useful for design purposes in many practical engineering applications.

scholarly journals Dynamic Response of Multilayered Polymer Functionally Graded Carbon Nanotube Reinforced Composite (FG-CNTRC) Nano-Beams in Hygro-Thermal Environment

Polymers ◽  
2021 ◽  
Vol 13 (14) ◽  
pp. 2340
Author(s):  
Rosa Penna ◽  
Giuseppe Lovisi ◽  
Luciano Feo
Keyword(s):  
Dynamic Response ◽  
Volume Fraction ◽  
Thermal Environment ◽  
Nonlocal Parameter ◽  
Stress Gradient ◽  
Theory Of Elasticity ◽  
Functionally Graded ◽  
Gradient Theory ◽  
Thermal Environments ◽  
Reinforced Composite

This work studies the dynamic response of Bernoulli–Euler multilayered polymer functionally graded carbon nanotubes-reinforced composite nano-beams subjected to hygro-thermal environments. The governing equations were derived by employing Hamilton’s principle on the basis of the local/nonlocal stress gradient theory of elasticity (L/NStressG). A Wolfram language code in Mathematica was written to carry out a parametric investigation on the influence of different parameters on their dynamic response, such as the nonlocal parameter, the gradient length parameter, the mixture parameter and the hygro-thermal loadings and the total volume fraction of CNTs for different functionally graded distribution schemes. It is shown how the proposed approach is able to capture the dynamic behavior of multilayered polymer FG-CNTRC nano-beams under hygro-thermal environments.

scholarly journals Global Portraits of Nonminimal Teleparallel Inflation

Universe ◽  
2021 ◽  
Vol 7 (6) ◽  
pp. 179
Author(s):  
Laur Järv ◽  
Joosep Lember
Keyword(s):  
Saddle Point ◽  
Fixed Points ◽  
Saddle Points ◽  
Heuristic Method ◽  
Gravity Models ◽  
Heteroclinic Orbits ◽  
Phase Portraits ◽  
Late Time ◽  
Nonminimal Coupling ◽  
De Sitter

We construct global phase portraits of inflationary dynamics in teleparallel gravity models with a scalar field nonminimally coupled to torsion scalar. The adopted set of variables can clearly distinguish between different asymptotic states as fixed points, including the kinetic and inflationary regimes. The key role in the description of inflation is played by the heteroclinic orbits that run from the asymptotic saddle points to the late time attractor point and are approximated by nonminimal slow roll conditions. To seek the asymptotic fixed points, we outline a heuristic method in terms of the “effective potential” and “effective mass”, which can be applied for any nonminimally coupled theories. As particular examples, we study positive quadratic nonminimal couplings with quadratic and quartic potentials and note how the portraits differ qualitatively from the known scalar-curvature counterparts. For quadratic models, inflation can only occur at small nonminimal coupling to torsion, as for larger coupling, the asymptotic de Sitter saddle point disappears from the physical phase space. Teleparallel models with quartic potentials are not viable for inflation at all, since for small nonminimal coupling, the asymptotic saddle point exhibits weaker than exponential expansion, and for larger coupling, it also disappears.

Dynamic Stability Analysis of Size-Dependent Viscoelastic/Piezoelectric Nano-beam

2022 ◽  
Author(s):  
Zahra Tadi Beni ◽  
Yaghoub Tadi Beni
Keyword(s):  
Stability Analysis ◽  
Dynamic Stability ◽  
Piezoelectric Materials ◽  
Equilibrium Points ◽  
Geometrical Nonlinearity ◽  
Saddle Points ◽  
Heteroclinic Orbits ◽  
Phase Portraits ◽  
Bifurcation Points ◽  
Size Dependent

This paper analyzes the dynamic stability of an isotropic viscoelastic Euler–Bernoulli nano-beam using piezoelectric materials. For this purpose, the size-dependent theory was used in the framework of the modified couple stress theory (MCST) for piezoelectric materials. In order to capture the geometrical nonlinearity, the von Karman strain displacement relation was applied. Hamilton’s principle was also employed to obtain the governing equations. Furthermore, the Galerkin method was used in order to convert the governing partial differential equations (PDEs) to a nonlinear second-order ordinary differential one. Dynamic stability analysis was performed and the effects of such parameters as viscoelastic coefficients, size effect, and piezoelectric coefficient were investigated. The results showed that in this system, saddle points, central points, Hopf bifurcation points, and fork bifurcation points could be created, and the phase portraits connecting these equilibrium points exhibit periodic orbits, heteroclinic orbits, and homoclinic orbits.

scholarly journals Dynamic Behavior Analysis of a Rotating Smooth and Discontinuous Oscillator with Irrational Nonlinearity

2018 ◽  
Vol 12 (7) ◽  
pp. 37
Author(s):  
Ning Han ◽  
Mingjuan Liu
Keyword(s):  
Periodic Solution ◽  
Saddle Points ◽  
Hamiltonian Function ◽  
Original System ◽  
Heteroclinic Orbits ◽  
Phase Portraits ◽  
Restoring Force ◽  
Remarkable Feature ◽  
Approximate System ◽  
Irrational Nonlinearity

This paper focuses on a novel rotating mechanical model which provides a cylindrical example of transition from smooth to discontinuous dynamics. The remarkable feature of the proposed system is a cylindrical dynamical system with strongly irrational nonlinearity exhibiting both smooth and discontinuous characteristics due to the geometry configuration. By using nonlinear dynamical technique, the unperturbed dynamics of the proposed system are studied including the irrational restoring force, stability of equilibria, Hamiltonian function and phase portraits. Note that a pair of double heteroclinic-like orbits connecting two non-standard saddle points are proposed in discontinuous case. For the perturbed system, we introduce a cylindrical approximate system for which the analytical solutions can be obtained successfully to reflect the nature of the original system without barrier of the irrationalities. Melnikov method is employed to detect the chaotic thresholds for the double heteroclinic orbits under the perturbation of viscous damping and external harmonic forcing in smooth regime. Finally, numerical simulations show the efficiency of the proposed method and demonstrate the predicated periodic solution and chaotic attractors. It is found that a good degree of correlation is demonstrated in the bifurcation diagram, the phase portraits of periodic solution, the chaotic attractor’ structures and the Lyapunov characteristics between the original system and approximate system.

scholarly journals Hygro-Thermal Vibration of Porous FG Nano-Beams Based on Local/Nonlocal Stress Gradient Theory of Elasticity

Nanomaterials ◽  
2021 ◽  
Vol 11 (4) ◽  
pp. 910
Author(s):  
Rosa Penna ◽  
Luciano Feo ◽  
Giuseppe Lovisi ◽  
Francesco Fabbrocino
Keyword(s):  
Volume Fraction ◽  
Nonlocal Parameter ◽  
Stress Gradient ◽  
Structural Response ◽  
Theory Of Elasticity ◽  
Functionally Graded ◽  
Gradient Theory ◽  
Thermal Environments ◽  
Structural Problems ◽  
Nonlocal Stress

In this manuscript the dynamic response of porous functionally-graded (FG) Bernoulli–Euler nano-beams subjected to hygro-thermal environments is investigated by the local/nonlocal stress gradient theory of elasticity. In particular, the influence of several parameters on both the thermo-elastic material properties and the structural response of the FG nano-beams, such as material gradient index, porosity volume fraction, nonlocal parameter, gradient length parameter, mixture parameter is examined. It is shown how the proposed approach is able to capture the dynamic behavior of porous functionally graded Bernoulli–Euler nano-beams under hygro-thermal loads and leads to well-posed structural problems of nano-mechanics.

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