scholarly journals On the Dynamics of a Visco–Piezo–Flexoelectric Nanobeam

Symmetry ◽  
2020 ◽  
Vol 12 (4) ◽  
pp. 643 ◽  
Author(s):  
Mohammad Malikan ◽  
Victor A. Eremeyev
Keyword(s):  
Natural Frequencies ◽  
Viscoelastic Model ◽  
Gradient Elasticity ◽  
Frequency Equation ◽  
Solution Technique ◽  
Internal Damping ◽  
Internal Property ◽  
First Time ◽  
Piezoelectric Nanobeam ◽  
Nonlocal Strain Gradient

The fundamental motivation of this research is to investigate the effect of flexoelectricity on a piezoelectric nanobeam for the first time involving internal viscoelasticity. To date, the effect of flexoelectricity on the mechanical behavior of nanobeams has been investigated extensively under various physical and environmental conditions. However, this effect as an internal property of materials has not been studied when the nanobeams include an internal damping feature. To this end, a closed-circuit condition is considered taking converse piezo–flexoelectric behavior. The kinematic displacement of the classical beam using Lagrangian strains, also applying Hamilton’s principle, creates the needed frequency equation. The natural frequencies are measured in nanoscale by the available nonlocal strain gradient elasticity model. The linear Kelvin–Voigt viscoelastic model here defines the inner viscoelastic coupling. An analytical solution technique determines the values of the numerical frequencies. The best findings show that the viscoelastic coupling can directly affect the flexoelectricity property of the material.

scholarly journals Vibration Modes and Parameter Analysis of V-Shaped Electrothermal Microactuators

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Zhuo Zhang ◽  
Yueqing Yu ◽  
Xuping Zhang
Keyword(s):  
Modal Analysis ◽  
Natural Frequencies ◽  
Frequency Equation ◽  
Parameter Analysis ◽  
Mode Shapes ◽  
Element Analysis ◽  
Shaped Beam ◽  
The Finite Element Analysis ◽  
Parametric Studies ◽  
First Time

Comprehensive analysis on the modal characteristics of V-shaped electrothermal microactuators is presented in this paper for the first time. Considering the unique geometric characteristics of the V-shaped beam, that is, two inclined beams supporting a movable shuttle, both the lateral and longitudinal deflections are taken into account in the modal analysis. Boundary and continuity conditions are employed to obtain the frequency equation. Natural frequencies are then obtained by solving the frequency equation. Mode shapes corresponding to their natural frequencies are also calculated analytically. The theoretical modal analysis is verified with the finite element analysis using ANSYS software. Based on the model analysis, this paper further investigates the relationship between natural frequencies and the volume scaling of the V-shaped beam. Finally, comprehensive parametric studies in terms of material properties and structural dimensions are conducted to provide insights and guidance in designing the V-shaped beam electrothermal microactuators.

Vibrations of Spinning Rings With Radial and Circumferential Displacement Constraints

1991 ◽  
Author(s):  
Shyh-Chin Huang ◽  
Chen-Kai Su
Keyword(s):  
Natural Frequencies ◽  
Point Contact ◽  
Frequency Equation ◽  
Mode Shapes ◽  
Complex Conjugate ◽  
Constrained System ◽  
Form Complex ◽  
Circumferential Displacement ◽  
On The Road ◽  
Displacement Constraints

Abstract The frequencies and mode shapes of rolling rings with radial and circumferential displacement constraints are investigated. The displacement constraints practically come from the point contact, e.g., rolling tire on the road, or other applications. The proposed approach to analysis is calculating the natural frequencies and modes of a non-contacted spinning ring, then employing the receptance method for displacement constraints. The frequency equation for the constrained system is hence obtained, and it can be solved numerically or graphically. The receptance matrix developed for the spinning ring is surprisingly found not symmetric as usual. Moreover, the cross receptances are discovered to form complex conjugate pairs. That is a feature that has never been described in literature. The results show that the natural frequencies for the spinning ring in contact, as expected, higher than those for the non-contacted ring. The variance of frequencies to rotational speeds are then illustrated. The analytic forms of mode shapes are also derived and sketched. The traveling modes are then shown for cases.

Torsional vibration of nano-cone based on nonlocal strain gradient elasticity theory

2017 ◽  
Vol 132 (9) ◽  
Author(s):  
Mohsen Mahdavi Adeli ◽  
Amin Hadi ◽  
Mohammad Hosseini ◽  
Hamid Haghshenas Gorgani
Keyword(s):  
Elasticity Theory ◽  
Strain Gradient ◽  
Torsional Vibration ◽  
Gradient Elasticity ◽  
Strain Gradient Elasticity ◽  
Strain Gradient Elasticity Theory ◽  
Gradient Elasticity Theory ◽  
Nonlocal Strain Gradient

Nonlinear semi-analytical nonlocal strain-gradient dynamic response investigation of phase-transition-induced transversely graded hierarchical viscoelastic nano/microplates

2019 ◽  
Vol 233 (15) ◽  
pp. 5388-5409 ◽  
Author(s):  
M Shariyat ◽  
F Farrokhi
Keyword(s):  
Strain Gradient ◽  
Viscoelastic Model ◽  
Functionally Graded ◽  
Special Technique ◽  
Stress And Strain ◽  
Transient Vibration ◽  
Size Dependent ◽  
Integration Schemes ◽  
Series Type ◽  
Nonlocal Strain Gradient

A functionally graded Boltzmann hierarchical viscoelastic model with both stress- and strain-gradient nonlocalities is developed and implemented to extract results that are more precise than results of Eringen's nonlocal elasticity model. The available size-dependent vibration analyses of the nano/microplates have focused on the frequency analysis and even not the time-dependent transient vibration analyses. In the present research, the forced and transient responses of the microplates are studied comprehensively, for the first time, using a three-element standard solid viscoelastic model. The studied transversely symmetric graded viscoelastic microplate and the relevant function of the material properties variations contain notable hints as well. Furthermore, the resulting new sixth-order nonlocal strain gradient integrodifferential equations are solved by a special technique that includes an analytical spatial Navier series-type solution and a trapezoidal and Runge–Kutta integration schemes, in time domain. Finally, the influences of the stress- and strain-gradient nonlocality parameters and the viscoelasticity parameters on the dynamic behaviors of the viscoelastic FGM microplates are investigated in details. Results show that the effects of the strain gradient nonlocality on the viscodynamic results may be much remarkable than those of the length scale nonlocality, in microscales.

Free Flexural Vibrations Response of Composite Mindlin Plates or Panels With a Centrally Bonded Symmetric Double Lap Joint (or Symmetric Double Doubler Joint)

2005 ◽  
Author(s):  
U. Yuceoglu ◽  
O. Gu¨vendik ◽  
V. O¨zerciyes
Keyword(s):  
Natural Frequencies ◽  
Mode Shapes ◽  
Solution Technique ◽  
Shear Stresses ◽  
Lap Joint ◽  
Adhesive Layers ◽  
Present Solution ◽  
Flexural Vibrations ◽  
Support Conditions ◽  
Interpolation Polynomials

The present study is concerned with the “Free Flexural Vibrations Response of Composite Mindlin Plates or Panels with a Centrally Bonded Symmetric Double Lap Joint (or Symmetric Double Doubler Joint). The plate “adherends” and the plate “doublers” are considered as dissimilar, orthotropic “Mindlin Plates” with the transverse and the rotary moments of inertia. The relatively, very thin adhesive layers are taken into account in terms of their transverse normal and shear stresses. The mid-center of the bonded region of the joint is at the mid-center of the entire system. In order to facilitate the present solution technique, the dynamic equations of the plate “adherends” and the plate “doublers” with those of the adhesive layers are reduced to a set of the “Governing System of First Order ordinary Differential Equations” in terms of the “state vectors” of the problem. This reduced set establishes a “Two-Point Boundary Value Problem” which can be numerically integrated by making use of the “Modified Transfer Matrix Method (MTMM) (with Interpolation Polynomials)”. In the adhesive layers, the “hard” and the “soft” adhesive cases are accounted for. It was found that the adhesive elastic constants drastically influence the mode shapes and their natural frequencies. Also, the numerical results of some parametric studies regarding the effects of the “Position Ratio” and the “Joint Length Ratio” on the natural frequencies for various sets of support conditions are presented.

Natural Frequencies and Normal Modes of a Spinning Timoshenko Beam With General Boundary Conditions

1992 ◽  
Vol 59 (2S) ◽  
pp. S197-S204 ◽  
Author(s):  
Jean Wu-Zheng Zu ◽  
Ray P. S. Han
Keyword(s):  
Boundary Conditions ◽  
Mode Shape ◽  
Timoshenko Beam ◽  
Natural Frequencies ◽  
Normal Modes ◽  
Single Mode ◽  
Mode Shapes ◽  
Simulation Studies ◽  
Classical Boundary ◽  
First Time

A free flexural vibrations of a spinning, finite Timoshenko beam for the six classical boundary conditions are analytically solved and presented for the first time. Expressions for computing natural frequencies and mode shapes are given. Numerical simulation studies show that the simply-supported beam possesses very peculiar free vibration characteristics: There exist two sets of natural frequencies corresponding to each mode shape, and the forward and backward precession mode shapes of each set coincide identically. These phenomena are not observed in beams with the other five types of boundary conditions. In these cases, the forward and backward precessions are different, implying that each natural frequency corresponds to a single mode shape.

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