Nonlinear vibrations Research Papers - Academia.edu (original) (raw)

Purpose-The purpose of this paper is to investigate nonlinear vibrations of triple-walled carbon nanotubes buried within Pasternak foundation carrying viscous fluids. Design/methodology/approach-Considering the geometry of nanotubes, the governing equations were initially derived using Timoshenko and modified couple stress theories and by taking into account Von-Karman expressions. Then, by determining boundary conditions, type of fluid motion, Knudsen number and, ultimately, fluid viscosity, the principal equation was solved using differential quadrature method, and linear and nonlinear nanotube frequencies were calculated. Findings-The results indicated that natural frequency is decreased as the fluid velocity and aspect ratio increase. Moreover, as the aspect ratio is increased, the results converge for simple and fixed support boundary conditions, and the ratio of nonlinear to linear frequencies approaches. Natural frequency of vibrations and critical velocity increase as Pasternak coefficient and characteristic length increase. As indicated by the results, by assuming a non-uniform velocity for the fluid and a slip boundary condition at Kn = 0.05, reductions of 10.714 and 28.714% were observed in the critical velocity, respectively. Moreover, the ratio of nonlinear to linear base frequencies decreases as the Winkler and Pasternak coefficients, maximum deflection of the first wall and characteristic length are increased in couple stress theory. Originality/value-This paper is a numerical investigation of nonlinear vibration analysis for triple-walled carbon nanotubes conveying viscous fluid.

- by Mahdi Moghimi Zand
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- MEMS, Vibrations, Nonlinear vibrations, NEMS

The influence of a rough road surface on vehicle vertical vibrations and on the driver and passengers is an important research among automotive manufacturers. ISO international standard defines the terminology of vehicle dynamics and roadholding ability. In addition, ISO international standard proposes the test procedures for steady-state circular driving behavior and lateral transient response characteristics against step steering input, sinusoidal steering input, random steering input, and
braking in a turn. The standardized test procedure of a double-lane-change test
as a severe lane-change maneuver is proposed. In order to estimate the influence of vertical vibration on seated human body, the apparent mass of the human body is evaluated by mechanical lumped models. In this research, a mechanical equivalent model has been developed to characterize the response of the vehicle excited by road profiles. The mechanical equivalent model offers a quantitative evaluation
of accelerations of vehicle along vertical axis in terms of natural frequencies and dissipative properties of vehicle. In order to calibrate the mathematical model, an experimental design has been developed by the ride test.

This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal non-commercial research and education use, including for instruction at the authors institution and sharing with colleagues. Other uses, including reproduction and distribution, or selling or licensing copies, or posting to personal, institutional or third party websites are prohibited. In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier's archiving and manuscript policies are encouraged to visit: http://www.elsevier.com/authorsrights a b s t r a c t In this article, large amplitude vibration and thermal post-buckling of shape memory alloy (SMA) fiber reinforced hybrid composite beams with symmetric and asymmetric lay-up are analytically investigated. To predict the behavior of the smart laminated beam, the EulereBernoulli beam theory and the nonlinear von-Karman strain field are employed. Also, one-dimensional Brinson SMA model is utilized to calculate the recovery stress of SMA fibers in the case of restrained strain. Nonlinear governing equations of motion are derived via the Hamilton principle. Using an analytical approach based on the Galerkin procedure together with the simple harmonic motion assumption, a closed-form solution is obtained for the thermal post-buckling and nonlinear free vibration analysis of SMA fiber reinforced hybrid composite beams. Due to lack of any results on the free vibration and thermal stability of SMA fiber reinforced composite beams, the results obtained from the present solution for laminated composite beams without SMA fiber are compared with counterpart data in the open literature, which validate the present solution. Then, a set of parametric study is carried out to show the influence of SMA volume fraction, amount of prestrain in the SMA fiber, orientation of composite fiber, SMA-reinforced layer thickness to total thickness ratio, location of SMA layer, vibration amplitude, boundary conditions and temperature on the vibration characteristic of the laminated beam reinforced with SMA in the pre-and post-buckled domains.

- by DR Aghdam and +2
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- Nonlinear vibrations, Post buckling, Buckling, Smart Materials and Structures

The development of nonlinear vibration formulations for beams in the literature can be seen to have gone through distinct phases — earlier continuum solutions, development of appropriate forms, extra-variational simplifications, debate and discussions, variationally correct formulations and finally applications. A review of work in each of these phases is very necessary in order to have a complete understanding of the

- by Sudhakar Marur
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- Nonlinear dynamics, Nonlinear vibrations, Beams
- by Mohamed Eid
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- Structural Health Monitoring, Nonlinear vibrations, Nonlinear Vibration

The angular and radial backlashes due to intensive wear are the most distinctive feature of the cold and hot rolling mills drive trains. It causes nonlinear torsional vibration and significant torque amplification. It leads to equipment failures but it could be used for wear diagnostics in the range of natural frequencies of the drive trains during the transient processes. The static load and dynamic response interrelation, non isochronisms and other nonlinear system features are used for wear diagnostics under the non stationary loads and speeds.

Introduction : L'analyse vibratoire est aujourd'hui un outil incontestable pour la maintenance conditionnelle des machines tournantes. Son but final est de tendre à la suppression des maintenances curatives et décaler les maintenances préventives. L'analyse vibratoire permet d'avoir une image de l'état de santé mécanique des machines tournantes et ainsi détecter d'éventuels dysfonctionnements afin de prévoir des actions correctives. Contexte : Le contrôle et le diagnostic sont aujourd'hui d'importance dans la plupart des secteurs industriels. Ils consistent à mesurer des signaux physiques sur des machines, installations industrielles, …puis grâce à leur analyse, il s'agit de délivrer un diagnostic sur leur état mécanique. Cette démarche permet de garantir et d'assurer la sécurité des biens et des personnes, de respecter les contraintes d'environnement (normes…), d'optimiser les opérations de maintenance en pratiquant la maintenance conditionnelle ou prédictive et ainsi, d'assurer la disponibilité des machines. Objectifs : Présenter une méthode d'analyse du signal temporel que nous avons considérée très importante pour le diagnostic des réducteurs planétaires. L'analyse est effectuée sur le logiciel DDS et le résultat de diagnostic sera validé par l'image endoscopique. Méthodes : Analyse du signal temporel et diagnostic par reconnaissance des formes sur un réducteur planétaire. Résultats : Analyse du signal temporel et le diagnostic par reconnaissance des formes ont montré qu'il y a la présence d'un défaut au niveau du flanc de la denture de la couronne et le signal temporel filtré à la fréquence de rotation porte satellite nous a permis de voir clairement la géométrie des impacts générés entre les dents. La mise en forme circulaire d'onde temporelle nous a aidés à préciser que la source de la vibration du réducteur est la défaillance au niveau de la denture de couronne. Conclusions : Cette étude prouve l'importance d'analyse approfondie des signaux vibratoire pour le diagnostic d'état de santé d'un réducteur planétaire. La méthode proposée est d'intérêt et suffisante pour appréhender la plupart des problèmes de diagnostic d'engrenages ; elle est très importante lorsqu'on fait le diagnostic des machines complexes telles que les réducteurs planétaire et les multiplicateurs d'éolienne. La méthode d'analyse de signal temporel permet donc dans ce cas de détecter la présence d'un défaut et de déterminer quelle est la partie abîmée.

In recent years, much research has been done on nonlinear vibrations, and analytical and numerical methods have been used to solve complex nonlinear equations. The behavior of nonlinear oscillating equations is discussed until the second order is approximated. Harmonic balance method, which itself has limitations in application. This method continues to be able to study a wider range of nonlinear differential equations. In general, nonlinear vibration problems are of great importance in physics, mechanical structures, and other engineering research. First, the equation of nonlinear vibrations governing the mass of the particle mass connect to the drawn cable is calculated and then the Newton Harmonic Balance Method is used to study the nonlinear vibrations of the set and obtain the answer and its frequency. The method (NHBM) is done with Maple software and a comparison between the results of this method with the solution methods used by other researchers is shown to be a good match.

- by Amin Moslemi Petrudi
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- Nonlinear vibrations
- by Mohamed Eid
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- Structural Health Monitoring, Nonlinear vibrations, Nonlinear Vibration

This article proposes a control strategy to stabilize the axial-torsional dynamics of a distributed drill-string system. An infinite-dimensional model for the vibrational dynamics of the drill string is used as a basis for controller design. In this article, both the cutting process and frictional contact effects are considered in the bit-rock interaction model. Moreover, models for the top-side boundary conditions regarding axial and torsional actuation are considered. The resulting model is formulated in terms of neutral-type delay differential equations that involve constant state delays, state-dependent state delays, and constant input delays arising from the distributed nature of the drill-string dynamics and the cutting process at the bit. Using a spectral approach, the stability and stabilizability of the associated linearized dynamics are analyzed to support controller design. An optimization-based continuous pole-placement technique has been employed to design a stabilizing controller. Since the designed state-feedback control law needs state prediction, a predictor with observer structure is proposed. Both the controller and the predictor only employ top-side measurements. The effectiveness of the control strategy, in the presence of measurement noise, is shown in a representative case study. It is also shown that the controller is robust to parametric uncertainty in the bit-rock interaction.

- by Shabnam Tashakori
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- Control Engineering, Prediction, Drilling Engineering, Distributed System

The proposed method for diagnosing the bearings of the drive mechanism shaft of a rolling mill consists in repeatedly measuring vibrations of the bearings within the period of the increase of the load at the working rolls of the mill, with a specified time interval between the measurements, determining the natural vibrations and harmonic components of the vibrations, determining the degree of wear and tear of the bearings and clearances in the bearings by the amplitude and phase of the vibrations. The proposed method is distinctive by its enhanced accuracy.

- by Pavlo Krot
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- Nonlinear vibrations, Bearing Fault Detection

The rolling mills drivelines are under investigation. Their dynamics is characterized by the extremely high torque amplification factors. The main problem is to identify non-smooth piece-wise linear stiffness characteristics in the multi-body system produced by the angular and radial backlashes. Different smoothening functions are analyzed. Frequency domain is used to determine amplitudes and phases of natural frequencies and harmonics due to angular and radial backlashes appearance. It was shown that interrelations between the static torsional loads and dynamic responses can be utilized for diagnostics.

- by JAMES KURIA
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- Nonlinear vibrations, Design optimization, Gear optimization

Closed cell foams are commonly used in protective packaging. In order to characterize foam’s impact performance and design protective packaging systems with foam; cushion curves are used. These curves are two-dimensional representations of the de-acceleration of an impacting mass versus the static stress of the mass loaded foam. The curves are currently generated from exhaustive experimental test data. One prior study uses a simple nonlinear, discontinuous model of the mass-foam impact to predict cushion curves. This study represents the first time the physics of the impact have been analyzed using an analytical solution of a nonlinear, continuous model of a drop test. The result is a closed form expression of the shock pulse's shape that in turn provides a closed form expression for the cushion curve of the foam. Bifurcation studies show that the model is able to provide predictions of the shock pulse's shape, duration, and amplitude at various static stresses, foam thickness, and drop heights. Furthermore, the analytical solution agrees with numerical results and is within the expected lab-to-lab variability of 18% documented in ASTM D1596 - Standard Test Method for Dynamic Shock Cushioning Characteristics of Packaging Material.

- by Amin Joodaky
- •
- Nonlinear vibrations

Nonlinear vibration of a fluid-filled single walled carbon nanotube (SWCNT) with simply supported ends is investigated in this paper based on Von-Karman’s geometric nonlinearity and the simplified Donnell’s shell theory. The effects of the small scales are considered by using the nonlocal theory and the Galerkin's procedure is used to discretize partial differential equations of the governing into the ordinary differential equations of motion. To achieve an analytical solution, the method of averaging is successfully applied to the nonlinear governing equation of motion. The SWCNT is assumed to be filled by the fluid (water) and the fluid is presumed to be an ideal non compression, non rotation and in viscid type. The fluid-structure interaction is described by the linear potential flow theory. An analytical formula was obtained for the nonlinear model and the effects of an internal fluid on the coupling vibration of the SWCNT-fluid system with the different aspect ratios and th...

- by Payam Soltani
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- Fluid Mechanics, Nanotechnology, Nonlinear vibrations, Nonlinear Vibration

In this paper, nonlinear dynamic behaviour of the carbon nanotube conveying fluid in slip boundary conditions is studied using the variation iteration method. The developed solutions are used to investigate the effects of various parameters on the nonlinear vibration of the nanotube. The results indicate that an increase in the slip parameter leads to a decrease in the frequency of vibration and the critical velocity, while the natural frequency and the critical fluid velocity increase as the stretching effect increases. Also, as the nonlocal parameter increases, the natural frequency and the critical velocity decreases. The analytical solutions help to have better insights and understand the relationship between the physical quantities of the problem.

- by Gbeminiyi Sobamowo
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- Nanotechnology, Nonlinear vibrations, Nonlocal Elasticity

An approach to analyze structural vibration considering structure-soil-structure interaction and nonlinearities is presented. The structures are described by finite elements and the subsoil by boundary elements in the Laplace domain. Nonlinearities, e.g., pounding between buildings during earthquakes, will be taken into account by alternatively performing the calculations in the Laplace domain and time domain. Investigations show that a realistic vibration response of buildings cannot be obtained from analysis without consideration of the structure-soil-structure interaction.

Polymer foams are commonly used in the protective packaging of fragile products. Cushion curves are commonly used within the packaging industry to characterize a foam's impact performance. These curves are two‐dimensional representations of the deceleration of an impacting mass versus static stress. Cushion curves are currently generated from exhaustive experimental test data. This study represents the first time that the physics of the mass‐cushion impact have been analysed by modelling the foam as nonlinear, continuous rod. Using a single mode of vibration and excluding the effects of damping, the maximum displacement during the impact can be obtained from a polynomial describing the maximum elastic energy in the foam. The displacements can be used to recover the amplitude of the deceleration shock pulse. Numerical and analytical analysis of the model with damping is considered in its ability to predict the shock pulse shape, duration, and amplitude at various static stresses, foam thickness, and drop heights as compared with experimental data. Furthermore, both the analytical and numerical results agree and are primarily within the expected lab‐to‐lab variability of 18% documented in ASTM D1596 ‐ Standard Test Method for Dynamic Shock Cushioning Characteristics of Packaging Material. Cushion curves are used within the packaging industry to characterize foam's impact performance; they are generated from experimental test data. This study represents the physics of the mass‐cushion impact as a nonlinear, continuous rod. Using a single mode of vibration, the maximum displacement and acceleration during the impact can be obtained from a polynomial, describing the maximum elastic energy in the foam. Numerical and analytical analysis of the model with damping is considered to predict the shock pulse shape.

- by Amin Joodaky
- •
- Nonlinear dynamics, Nonlinear vibrations, Shock, Polymeric foams

The dispute about the well-known 1D vibrating string model and its solutions, known as ”The Vibrating
String Controversy”, spanned the whole of 1700s and involved a group of the most eminent scientists of
the time. After that, the model stood undisputed for over two centuries. In this study, it is shown that
not only this 300-year-old model cannot correspond to reality, but it is theoretically not quite plausible,
either. A new 2D model is developed removing all the assumptions of the classical model. The result is a
pair of non-linear partial differential equations modeling 2D motions of a finite 1D string. A theorem that
can be used to determine the initial displacement functions from the initial shape of the string is proven.
The new model is capable of representing initial conditions that cannot be handled in the classical model.
It also allows initially non-taut/non-slack strings and self-intersecting shapes. The classical model and the
non-taut strings emerge as special limit cases. It is proven that pure transverse motions of a 1D string
are possible only in very rare cases. A theorem that sets the conditions for pure transverse motions is also
presented. Numerical studies of interesting cases are presented in support of the new model. High-speed
camera experiments are also conducted, the results of which also support the new theory.

- by Namik Ciblak
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- Nonlinear vibrations, Wave Equations, Vibrating String

In this study, we analyzed the kind of psychological effects that were caused by nonlinear, possibly chaotic vibrations as compared to regular vibrations. For this analysis, we produced a chaotic low-frequency electrical therapy device to generate chaotic vibrations. Using the device, we analyzed the direct effects of chaotic vibrations on the human body. In the experiments, we generated fully chaotic vibrations, intermittent chaotic vibrations, and periodic vibrations. To evaluate the effects of the vibrations on the human body, we used one of the subjective methods; a paired comparison method. We identified a rank-order scale by comparing pairs of two vibrations. The results indicate that complicated vibrations are more effective than periodic vibrations.

Previous nonlinear spinning disk models neglected the in-plane inertia of the disk since this permits the use of a stress function. This paper aims to consider the effect of including the in-plane inertia of the disk on the resulting nonlinear dynamics and to construct approximate solutions that capture the new dynamics. The inclusion of the in-plane inertia results in a nonlinear coupling between the in-plane and transverse vibrations of the spinning disk. The full nonlinear partial differential equations are simplified to a simpler nonlinear two degrees of freedom model via the method of Galerkin. A canonical perturbation approach is used to derive an approximate solution to this simpler nonlinear problem. Numerical simulations are used to evaluate the effectiveness of the approximate solution. Through the use of these analytical and numerical tools, it becomes apparent that the inclusion of in-plane inertia gives rise to new phenomena such as internal resonance and the possibility of instability in the system that are not predicted if the in-plane inertia is ignored. It is also demonstrated that the canonical perturbation approach can be used to produce an effective approximate solution. © 2005 Elsevier Inc. All rights reserved.

- by Natalie Baddour
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- Vibrations, Nonlinear vibrations, Spinning Disks