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Nano-resonator frequency response based on strain gradient theory
, Article Journal of Physics D: Applied Physics ; Vol. 47, Issue. 36 , 2014 ; ISSN: 00223727 ; Yousefi Koma, A ; Pishkenari, H. N ; Fathi, M ; Sharif University of Technology
Abstract
This paper aims to explore the dynamic behaviour of a nano-resonator under ac and dc excitation using strain gradient theory. To achieve this goal, the partial differential equation of nano-beam vibration is first converted to an ordinary differential equation by the Galerkin projection method and the lumped model is derived. Lumped parameters of the nano-resonator, such as linear and nonlinear springs and damper coefficients, are compared with those of classical theory and it is demonstrated that beams with smaller thickness display greater deviation from classical parameters. Stable and unstable equilibrium points based on classic and non-classical theories are also compared. The results...
Chaos prediction in MEMS-NEMS resonators
, Article International Journal of Engineering Science ; Vol. 82 , 2014 , pp. 74-83 ; ISSN: 00207225 ; Pishkenari, H. N ; Yousefi-Koma, A ; Tajaddodianfar, F ; Sharif University of Technology
Abstract
Different nonlinearities in micro-electro-mechanical resonators lead to various nonlinear behaviors such as chaotic motion which can affect the resonator performance. As a result, it is important to properly identify and analyze the chaotic regions in resonators. In this paper, a novel method is proposed for prediction of the chaos in the micro- and nano-electro-mechanical resonators. Based on the proposed method, first an accurate analytical solution for the dynamics behavior of the nano-resonators is derived using the multiple scales method up to the second order. The results obtained by this analytical solution are validated by comparing them with the numerical ones. Using the analytical...
Vibration control through the robust nonlinear absorber with negative stiffness and internal resonance creation
, Article JVC/Journal of Vibration and Control ; 2022 ; 10775463 (ISSN) ; Khajeh Ahmad Attari, N ; Rahimzadeh Rofooei, F ; Sharif University of Technology
SAGE Publications Inc
2022
Abstract
In this study, a nonlinear absorber that works with a negative stiffness mechanism is suggested to mitigate vibration, and its effect on the reduction of vibration is investigated. The negative stiffness, which is inherently nonlinear, creates internal resonance; therefore, the vibration energy can be transmitted from low-frequency to high-frequency vibrating modes, causing vibration suppression. The nonlinear absorber is added to the primary nonlinear system, and when the main system is subjected to external resonance due to harmonic excitation, the negative stiffness parameter of absorber is so adjusted that autoparametric resonance occurs and vibration is reduced. First, the mathematical...
Investigation of Nonlinear Vibration and Stability Analysis of Rotor with Journal and Axial Bearings
, M.Sc. Thesis Sharif University of Technology ; Haddadpour, Hassan (Supervisor)
Abstract
Vibrational analysis of a rotor with journal and axial bearings requires modelling of forces acted on the journal of the rotor by the bearings. The aim of the present research firstly is to extract the linear dynamic coefficients of the tilting-pad thrust bearing and then to analyze nonlinear vibrations and stability of the rotor. By use of the partial derivative method along with Perturbation method the linear dynamic coefficients are calculated. Full dynamic coefficients are extracted by solving Reynolds equation and its perturbed forms using finite difference method. Dynamic equilibrium equations of pad are used to obtain reduced-order dynamic coefficients. In the following the equations...
Nonlinear dynamics of an inclined beam subjected to a moving load
, Article Nonlinear Dynamics ; Volume 60, Issue 3 , 2010 , Pages 277-293 ; 0924090X (ISSN) ; Kargarnovin, M. H ; Younesian, D ; Sharif University of Technology
Abstract
In this paper, the nonlinear dynamic response of an inclined pinned-pinned beam with a constant cross section, finite length subjected to a concentrated vertical force traveling with a constant velocity is investigated. The study is focused on the mode summation method and also on frequency analysis of the governing PDEs equations of motion. Furthermore, the steady-state response is studied by applying the multiple scales method. The nonlinear response of the beam is obtained by solving two coupled nonlinear PDEs governing equations of planar motion for both longitudinal and transverse oscillations of the beam. The dynamic magnification factor and normalized time histories of mid-pint of the...
Prediction of chaos in electrostatically actuated arch micro-nano resonators: Analytical approach
, Article Communications in Nonlinear Science and Numerical Simulation ; Volume 30, Issue 1-3 , 2016 , Pages 182-195 ; 10075704 (ISSN) ; Nejat Pishkenari, H ; Hairi Yazdi, M. R ; Sharif University of Technology
Elsevier
2016
Abstract
Chaotic vibrations of a bistable resonator comprised of doubly clamped shallow arch under simultaneous harmonic AC and static DC distributed electrostatic actuation are investigated. A single degree of freedom model obtained by application of the Galerkin decomposition method to the Euler-Bernoulli shallow arch equation is used for the studies. The bistable arch possessing an asymmetric double-well potential is vulnerable to homoclinic chaos at certain values of parameters. We have implemented the Melnikov's method to derive a necessary condition for the initiation of chaos in this type of resonators. Moreover, we have used a heuristic chaos prediction criterion, together with an analytical...
On nonlinear perturbation analysis of a structure carrying a circular cylindrical liquid tank under horizontal excitation
, Article JVC/Journal of Vibration and Control ; Volume 25, Issue 5 , 2019 , Pages 1058-1079 ; 10775463 (ISSN) ; Rahimzadeh Rofooei, F ; Waezi, Z ; Sharif University of Technology
SAGE Publications Inc
2019
Abstract
The lateral response of a single degree of freedom structural system containing a rigid circular cylindrical liquid tank under harmonic and earthquake excitations at a 1:2 autoparametric resonance case is considered. The governing nonlinear differential equations of motion for the combined system are solved by means of a multiple scales method considering the first three liquid sloshing modes (1,1), (0,1), and (2,1), under horizontal excitation. The fixed points of the gyroscopic type of governing differential equations are determined and their stability is investigated employing the perturbation method. The obtained results reveal an increase in the stability region for a single-mode...
Vibration Analysis of viscoelastic Sandwich Plates Under the Effects of Nonlinearities and Random Excitations
, Ph.D. Dissertation Sharif University of Technology ; Haddadpour, Hassan (Supervisor)
Abstract
Different aspects of oscillatory behaviors of sandwich structures with viscoelastic cores are investigated in the present study in four parts. In the first part, an analytical study is conducted to determine the variation of linear frequencies and damping ratio of different families of modes with system parameters. The participation of different families of modes such as the so-called pumping or thickness-shear modes along with the overall bending modes in the transverse response of the structure to transverse wide-band excitation is also investigated in this part. The formulation of the problem is established by assuming quadratic variation of displacement components of the core through the...
Nonlinear Vibration Analysis of a Rotor with Nonlinear Pedestal by use of Jeffcott Model
, M.Sc. Thesis Sharif University of Technology ; Haddadpour, Hassan (Supervisor) ; Dehghani Firouzabadi, Rouhollah (Supervisor)
Abstract
The present research aims to achieve two major objectives in the Rotordynamic phenomenon. The first one is to study the linear and nonlinear dynamic characteristics of tilting pad journal bearings and calculating their dynamic coefficients like damping and stiffness, and the second one, studies the linear and nonlinear behavior of rotors standing on nonlinear pedestal, say nonlinear tilting pad journal bearing. By use of Partial Derivative method along with Perturbation method the linear dynamic coefficients are calculated for three different model of tilting pad journal bearing and these results are validated with the results presented by previous researches. The presented procedure is...
Stability of Fractional Viscoelastic Pipes Conveying Fluid in the External Cross Flow
, M.Sc. Thesis Sharif University of Technology ; Hosseini Kordkhaili, Ali (Supervisor) ; Haddadpour, Hassan (Co-Advisor)
Abstract
In this thesis, the dynamic behavior of a pinned-pinned fractional viscoelastic pipe conveying fluid is examined in the external cross flow. The Galerkin method is employed to discretize the nonlinear coupled equations of motion for viscoelastic pipe conveying fluid in the external cross flow. Consequently, four modes of system are obtained. In addition, direct perturbation method of multiple scale is used to solve the governing nonlinear coupled equations of motion for the fractional viscoelastic pipe conveying pulsating fluid in the external cross flow. Moreover, time response diagrams are drawn in order to investigate under effects of the internal fluid velocity, external fluid reduced...
Nonlinear Vibrations of a Circular Plate Using Perturbation and Experimental Methods
, M.Sc. Thesis Sharif University of Technology ; Navazi, Hossein Mohammad (Supervisor)
Abstract
In this thesis, the nonlinear vibrations of the circular plate is examined using multiple scale methods and experimental tests. At first step, the nonlinear equations governing the problem are written using von Karman's assumption. In the next step, to solve nonlinear equations and calculate natural frequency, the problem is solved using multiple scale method and frequency charts are extracted as a function of the amplitude of vibration. . The design of the setup has been done in such a way that it is possible to simulate the boundary conditions. In the first phase, experimental tests was performed on a 0.3 mm thick aluminum sheet, which did not produce the desired results due to the...
Non-Linear Vibration and Stability Analysis of a Rotor with Rubbing and NonLinear Support
, M.Sc. Thesis Sharif University of Technology ; Mohammad Navazi, Hossein (Supervisor)
Abstract
The present study aims to achieve two major objectives in the field of Rotordynamics. The first one is to investigate the frequency response function by considering rubbing between fixed and rotating components of the system and also the presence of nonlinear support such as tiling-pad bearings using analytical approach and the second one is to study the stability of the system using both analytical and numerical methods. In first step, by using assumptions and laws of physics, a model for dealing with the rubbing phenomenon and the friction force between fixed and rotating components of the system is presented. In the next step, the rubbing force is modeled. Then using the Jeffcott rotor...
Vibration and Stability Analysis of a Rotor with Nonlinear Bearings
, Ph.D. Dissertation Sharif University of Technology ; Haddadpour, Hassan (Supervisor) ; Mohammad Navazi, Hossein (Supervisor)
Abstract
In the present study, the nonlinear vibrations of the rotor on the nonlinear bearing have been studied by the multiple scale method. To achieve this goal, Jeffcott models, two degrees of freedom and rotating Euler-Bernoulli beam have been used as rotors and insulators and nonlinear tilting-bearing bearings have been used as supports.To better understand the importance of the supports in the analysis of rotating systems, the rotor joints with isolates with high static stiffness and low dynamic stiffness have been considered and the dynamic behavior of the system has been studied using the multiple scale method. The results of this study showed that this type of nonlinear isolator has a good...
Non-linear Vibration Analysis of Timoshenko Curved Beam with Non-linear End Supports
, M.Sc. Thesis Sharif University of Technology ; Mohammad Navazi, Hossein (Supervisor)
Abstract
Three dimensional analyses have been carried out for predicting the behavior of the jointed rock slope of the abutments of the bridge which is proposed to be constructed across the river Karun4 in Iran using 3DEC. The rock overall slope angle is approximately 60 to 70 degrees, composed of highly jointed rock mass and the joint spacing and orientation are varying at different locations. Since 3DEC is a three-dimensional numerical code, utilizes a Lagrangian calculation scheme to model large movements and deformations of a blocky system, allows for modeling of large movements and rotations, and including complete detachment of rigid or deformable discrete blocks has been utilized for the...
Nonlinear oscillation analysis of a pendulum wrapping on a cylinder
, Article Scientia Iranica ; Volume 19, Issue 2 , 2012 , Pages 335-340 ; 10263098 (ISSN) ; Hosseinzadeh, A ; Ahmadian, M. T ; Sharif University of Technology
2012
Abstract
In this paper, the nonlinear oscillation of a pendulum wrapping and unwrapping on two cylindrical bases is studied, and an analytical solution is obtained using the multiple scales method. The equation of motion is derived based on an energy conservation technique. By applying the perturbation method to the differential equation, the nonlinear natural frequency of the system is calculated, along with its time response. Analytical results are compared with numerical findings and good agreement is found. The effect of large amplitude and radius of cylinders on system frequency is evaluated. The results indicate that as the radius of the cylinder increases, the system frequency is increased....
Analytical approach to vibration analysis of a pendulum wrapping on a cylinder
, Article ASME 2011 International Mechanical Engineering Congress and Exposition, IMECE 2011, 11 November 2011 through 17 November 2011 ; Volume 7, Issue PARTS A AND B , November , 2011 , Pages 761-765 ; 9780791854938 (ISBN) ; Hosseinzadeh, A ; Ahmadian, M. T ; Barari, A ; Sharif University of Technology
Abstract
In this paper, nonlinear oscillation of a pendulum wrapping and unwrapping around two cylindrical bases is studied and an analytical solution is obtained using multiple scales method. Equations of motion are derived based on energy conservation technique. Applying perturbation method on the equations, nonlinear natural frequency of the system is calculated along with its time response. Analytical results are compared with numerical findings and good agreement is found. Effect of nonlinearity due to large amplitude and radius of cylinders on the system frequency is evaluated. Results indicate that as the radius of cylinder is increased, nonlinear frequency is enhanced. Initial amplitude plays...
Nonlinear vibrations and stability analysis of a rotor on high-static-low-dynamic-stiffness supports using method of multiple scales
, Article Aerospace Science and Technology ; Volume 63 , 2017 , Pages 259-265 ; 12709638 (ISSN) ; Hojjati, M ; Sharif University of Technology
Elsevier Masson SAS
2017
Abstract
This paper presents the vibration and stability analyses of an unbalanced rotor mounted on high-static-low-dynamic-stiffness supports. The stiffness of the supports is modeled as symmetric of cubic order. Then a second-order multiple scales method is used for studying the primary resonance of the system. The types of singular points are investigated and phase-plane of the system is plotted using analytical and numerical methods. The difference between analytical and numerical solutions is less than 2 percent. © 2017 Elsevier Masson SAS
Size-dependent dynamic behavior of microcantilevers under suddenly applied DC voltage
, Article Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science ; Vol. 228, Issue. 5 , May , 2014 , pp. 896-906 ; ISSN: 09544062 ; Ahmadian, M. T ; Firoozbakhsh, K ; Sharif University of Technology
Abstract
This paper investigates the dynamic behavior of microcantilevers under suddenly applied DC voltage based on the modified couple stress theory. The cantilever is modeled based on the Euler-Bernoulli beam theory and equation of motion is derived using Hamilton's principle. Both analytical and numerical methods are utilized to predict the dynamic behavior of the microbeam. Multiple scales method is used for analytical analysis and the numerical approach is based on a hybrid finite element/finite difference method. The results of the modified couple stress theory are compared with those from the literature as well as the results predicted by the classical theory. It is shown that the modified...
Analysis of nonlinear oscillations in spur gear pairs with approximated modelling of backlash nonlinearity
, Article Mechanism and Machine Theory ; Volume 51 , 2012 , Pages 14-31 ; 0094114X (ISSN) ; Salarieh, H ; Sharif University of Technology
2012
Abstract
Due to international competition and strict limitations of standards regarding the noise level, investigation of gear vibration is of great importance. In this paper, nonlinear oscillations of spur gear pairs including the backlash nonlinearity is studied. Dynamic system is described through the classical single degree of freedom (SDOF) model in terms of dynamic transmission error (DTE). Using multiple scale method, forced vibration responses of the gear system including primary, super-harmonic and sub-harmonic resonances are investigated. In each case, the jump phenomenon and stability analysis are studied. In addition, the effect of dynamic and manufacturing parameters of the gear system...
Nonlinear dynamics of nano-resonators: an analytical approach
, Article Microsystem Technologies ; 2015 ; 09467076 (ISSN) ; Nejat Pishkenari,, H ; Yousefi Koma, A ; Sharif University of Technology
Abstract
Prior to the design and fabrication of MEMS/NEMS devices, analysis of static and dynamic behaviors of these systems is necessary. In the present study, the nonlinear dynamic behavior of micro- and nano-mechanical resonators is investigated and classified based on the resonator’s physical parameters for first time. The Galerkin method is used to convert the distributed-parameter model to a nonlinear ordinary differential equation where mid-plane stretching, axial stress, DC electrostatic and AC harmonic voltages are taken into account. To obtain the analytical frequency response of the micro resonator near its primary resonance, the second order multiple scales method is applied to the...