Size-dependent vibrations of a micro beam conveying fluid and resting on an elastic foundation

2016 ◽  
Vol 23 (7) ◽  
pp. 1106-1114 ◽  
Author(s):  
Saim Kural ◽  
Erdoğan Özkaya
Keyword(s):  
Elastic Foundation ◽  
Couple Stress Theory ◽  
Fluid Velocity ◽  
Equations Of Motion ◽  
Beam Theory ◽  
Approximate Solutions ◽  
Modified Couple Stress Theory ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Classical Beam Theory

In this study, fluid conveying continuous media was considered as micro beam. Unlike the classical beam theory, the effects of shear stress on micro-structure's dynamic behavior not negligible. Therefore, modified couple stress theory (MCST) were used to see the effects of being micro-sized. By using Hamilton's principle, the nonlinear equations of motion for the fluid conveying micro beam were obtained. Micro beam was considered as resting on an elastic foundation. The obtained equations of motion were became independence from material and geometric structure by nondimensionalization. Approximate solutions of the system were achieved with using the multiple time scales method (a perturbation method). The effects of micro-structure, spring constant, the occupancy rate of micro beam, the fluid velocity on natural frequency and solutions were researched. MCST compared with classical beam theory and showed that beam models that based on classical beam theory are not capable of describing the size effects. Comparisons of classical beam theory and MCST were showed in graphics and these graphics also proved that obtained mathematical model suitable for describe the behavior of normal sized beams.

scholarly journals Investigation of 3:1 and 2:1 internal resonances in fluid conveying microbeam

2018 ◽  
Vol 12 (1) ◽  
pp. 18-26
Author(s):  
Saim Kural
Keyword(s):  
Couple Stress Theory ◽  
Fluid Velocity ◽  
Equations Of Motion ◽  
High Sensitivity ◽  
Approximate Solutions ◽  
Modified Couple Stress Theory ◽  
Multiple Time ◽  
Internal Resonances ◽  
Electrical Field ◽  
Stress Theory

Microbeams are widely used in micro-electro-mechanical systems (MEMS). These systems are alternatives to piezo-resistive sensors because of their high sensitivity and low power consumption. Unlike with the classical theory of continuous media, in order to see the effects of the system being micro-sized, the effect of micro-structure was added to the system based on the modified couple stress theory (MCST) for fluid conveying microbeam. By using Hamilton’s principle, the nonlinear equations of motion for the fluid conveying micro beam were obtained. Microbeam was investigated under electrical field and resting on an elastic foundation. It is assumed that the fluid velocity changes harmonically around a constant velocity and that the electrical field force changes harmonically with time. Approximate solutions of the system were achieved by using the multiple time scale method. 3:1 and 2:1 internal resonance cases were investigated. Detuning parameter-amplitude variation graphs were obtained, and stability areas were shown.

Vibration behavior of a micro cylindrical sandwich panel reinforced by graphene platelet

2020 ◽  
Vol 26 (13-14) ◽  
pp. 1311-1343 ◽  
Author(s):  
Mohammadreza Anvari ◽  
Mehdi Mohammadimehr ◽  
Ali Amiri
Keyword(s):  
Elastic Foundation ◽  
Sandwich Panel ◽  
Natural Frequencies ◽  
Volume Fraction ◽  
Couple Stress Theory ◽  
Equations Of Motion ◽  
Modified Couple Stress Theory ◽  
Theoretical Background ◽  
Graphene Platelet ◽  
Vibration Behavior

In this article, vibration behavior of a micro cylindrical sandwich panel with foam core and reinforced graphene platelet composite layers on the top and bottom resting on elastic foundation based on modified couple stress theory is investigated. Hamilton’s principle is used to determine the governing equations of motion. These equations are solved by Navier’s method to obtain the natural frequencies. The results are compared with the extracted results by the other literatures. The effects of different parameters such as temperature change, volume fraction of graphene platelet, length to radius ratio, and the elastic foundation on the natural frequencies have been carried out. Also, the effects of reinforced materials for layers is discussed and compared with unreinforced composites layers. Sandwich structures are wildly used in different applications such as spacecraft, aeronautical, pressurized gas tanks, boilers, aircraft fuselage, marines, and civil structures, and these cases need high strength and low weight. The present work is a theoretical background for more explorations and further experimental researchers in the field of cylindrical reinforced panels.

Nonlocal elastic medium modeling for vibration analysis of asymmetric conveyed-fluid Y-shaped single-walled carbon nanotube considering viscothermal effects

2016 ◽  
Vol 231 (3) ◽  
pp. 574-595 ◽  
Author(s):  
AH Ghorbanpour-Arani ◽  
A Rastgoo ◽  
M.Sh Zarei ◽  
A Ghorbanpour Arani ◽  
E Haghparast
Keyword(s):  
Carbon Nanotube ◽  
Couple Stress Theory ◽  
Equations Of Motion ◽  
Surrounding Medium ◽  
Beam Theory ◽  
Modified Couple Stress Theory ◽  
Basic Element ◽  
Single Walled Carbon Nanotube ◽  
Single Walled Carbon ◽  
Conveying Fluid

In the present research, vibration and instability analysis of a viscoelastic Y-shaped single-walled carbon nanotube conveying fluid is carried out. The surrounding viscoelastic medium is simulated by various models such as Kelvin–Voigt, Maxwell, standard linear solid Reissner, and nonlocal models. The size effects are considered based on modified couple stress theory. In order to achieve more accurate results, fourth-order beam theory is utilized. Surface stress effects are considered based on Gurtin–Murdoch theory. In addition, effects of the asymmetry of Y-shaped single-walled carbon nanotube are also taken into account. Regarding fluid–structure interaction, the equations of motion as well as boundary conditions are derived using Hamilton’s principle and solved by means of hybrid analytical–numerical method. Regarding the temperature changes on visco-Pasternak foundation, the effects of different surrounding medium models are discussed in detail. The overall results indicated that the stability and vibration characteristics of Y-shaped single-walled carbon nanotube conveying fluid are strongly dependent on damping coefficient. The results of this work are hoped to be useful in design and manufacturing of nanodevices where Y-shaped nanotubes act as a basic element.

Size-dependent free vibration analysis of a three-layered exponentially graded nano-/micro-plate with piezomagnetic face sheets resting on Pasternak’s foundation via MCST

2017 ◽  
Vol 22 (1) ◽  
pp. 55-86 ◽  
Author(s):  
Mohammad Arefi ◽  
Masoud Kiani ◽  
Ashraf M Zenkour
Keyword(s):  
Couple Stress ◽  
Couple Stress Theory ◽  
Equations Of Motion ◽  
Free Vibration Analysis ◽  
Modified Couple Stress Theory ◽  
Stress Theory ◽  
Modified Couple Stress ◽  
Material Length Scale ◽  
Material Length ◽  
Exponentially Graded

The present work is devoted to the free vibration analysis of elastic three-layered nano-/micro-plate with exponentially graded core and piezomagnetic face-sheets using the modified couple stress theory. To capture size-dependency for a nano-/micro-sized rectangular plate, the couple stress theory is used as a non-classical continuum theory. The rectangular elastic three-layered nano-/micro-plate is resting on Pasternak’s foundation. The present model contains one material length scale parameter and can capture the size effect. Material properties of the core are supposed to vary along the thickness direction based on the exponential function. The governing equations of motion are derived from Hamilton’s principle based on the modified couple stress theory and first-order shear deformation theory. The analytical solution is presented to solve seven governing equations of motion using Navier’s solution. Eventually the natural frequency is scrutinized for different side length ratio, thickness ratio, inhomogeneity parameter, material length scale, and parameters of foundation numerically.

scholarly journals Vibration Characteristics of Piezoelectric Microbeams Based on the Modified Couple Stress Theory

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
R. Ansari ◽  
M. A. Ashrafi ◽  
S. Hosseinzadeh
Keyword(s):  
Boundary Conditions ◽  
Couple Stress ◽  
Natural Frequencies ◽  
Couple Stress Theory ◽  
Equations Of Motion ◽  
Modified Couple Stress Theory ◽  
Beam Model ◽  
Governing Equations ◽  
Stress Theory ◽  
Modified Couple Stress

The vibration behavior of piezoelectric microbeams is studied on the basis of the modified couple stress theory. The governing equations of motion and boundary conditions for the Euler-Bernoulli and Timoshenko beam models are derived using Hamilton’s principle. By the exact solution of the governing equations, an expression for natural frequencies of microbeams with simply supported boundary conditions is obtained. Numerical results for both beam models are presented and the effects of piezoelectricity and length scale parameter are illustrated. It is found that the influences of piezoelectricity and size effects are more prominent when the length of microbeams decreases. A comparison between two beam models also reveals that the Euler-Bernoulli beam model tends to overestimate the natural frequencies of microbeams as compared to its Timoshenko counterpart.

scholarly journals Active Vibration Control of a Nonlinear Beam with Self- and External Excitations

2013 ◽  
Vol 20 (6) ◽  
pp. 1033-1047 ◽  
Author(s):  
J. Warminski ◽  
M. P. Cartmell ◽  
A. Mitura ◽  
M. Bochenski
Keyword(s):  
Analytical Solutions ◽  
Order Approximation ◽  
Equations Of Motion ◽  
Active Vibration Control ◽  
Harmonic Excitation ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Nonlinear Beam ◽  
Approximate Analytical Solutions ◽  
Full Structure

An application of the nonlinear saturation control (NSC) algorithm for a self-excited strongly nonlinear beam structure driven by an external force is presented in the paper. The mathematical model accounts for an Euler-Bernoulli beam with nonlinear curvature, reduced to first mode oscillations. It is assumed that the beam vibrates in the presence of a harmonic excitation close to the first natural frequency of the beam, and additionally the beam is self-excited by fluid flow, which is modelled by a nonlinear Rayleigh term for self-excitation. The self- and externally excited vibrations have been reduced by the application of an active, saturation-based controller. The approximate analytical solutions for a full structure have been found by the multiple time scales method, up to the first-order approximation. The analytical solutions have been compared with numerical results obtained from direct integration of the ordinary differential equations of motion. Finally, the influence of a negative damping term and the controller's parameters for effective vibrations suppression are presented.

Nonlinear Forced Vibration Analysis of Smart Curved CNTs Conveying Fluid

2021 ◽  
Author(s):  
Vahid Mohamadhashemi ◽  
Amir Jalali ◽  
Habib Ahmadi
Keyword(s):  
Carbon Nanotube ◽  
Velocity Vector ◽  
Multiple Scales ◽  
Fluid Velocity ◽  
Equations Of Motion ◽  
Primary Resonance ◽  
Maximum Amplitude ◽  
Beam Theory ◽  
Physical Parameters ◽  
Conveying Fluid

In this study, the nonlinear vibration of a curved carbon nanotube conveying fluid is analyzed. The nanotube is assumed to be covered by a piezoelectric layer and the Euler–Bernoulli beam theory is employed to establish the governing equations of motion. The influence of carbon nanotube curvature on structural modeling and fluid velocity vector is considered and the slip boundary conditions of CNT conveying fluid are included. The mathematical modeling of the structure is developed using Hamilton’s principle and then, the Galerkin procedure is employed to discretize the equation of motion. Furthermore, the frequency response of the system is extracted by applying the multiple scales method of perturbation. Finally, a comprehensive study is carried out on the primary resonance and piezoelectric-based parametric resonance of the system. It is shown that consideration of nanotube curvature may lead to an increase in nonlinearity. Implementing the fluid velocity vector in which nanotube curvature is included highly affects the maximum amplitude of the response and should not be ignored. Furthermore, different system parameters have evident impacts on the behavior of the system and therefore, selecting the reasonable geometrical and physical parameters of the system can be very useful to achieve a favorable response.

Nonlinear Dynamic Response of a Thin Plate in a Fractional Viscoelastic Medium under Internal Resonance 1:1:2

2014 ◽  
Vol 518 ◽  
pp. 60-65 ◽  
Author(s):  
Yury Rossikhin ◽  
Marina Shitikova
Keyword(s):  
Nonlinear Equations ◽  
Time Scales ◽  
Viscoelastic Medium ◽  
Equations Of Motion ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Internal Resonances ◽  
Nonlinear Dynamic Response ◽  
New Approach ◽  
New Type

Dynamic behaviour of a nonlinear plate embedded in a fractional derivative viscoelastic medium and subjected to the conditions of the internal resonances two-to-one has been studied by Rossikhin and Shitikova in [1]. Nonlinear equations, the linear parts of which occur to be coupled, were solved by the method of multiple time scales. A new approach proposed in this paper allows one to uncouple the linear parts of equations of motion of the plate, while the same method, the method of multiple time scales, has been utilized for solving nonlinear equations. The new approach enables one to find a new type of the internal resonanse, i.e., one-to-one-to-two, as well as to solve the problems of vibrations of thin bodies more efficiently.

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