Relevant bibliographies by topics / Parametric vibrations

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Parametric vibrations'

Author: Grafiati
Published: 30 May 2022
Last updated: 31 May 2022

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Journal articles on the topic "Parametric vibrations"

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Dohnal, F. "Experimental studies on damping by parametric excitation using electromagnets." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 226, no. 8 (March 1, 2012): 2015–27. http://dx.doi.org/10.1177/0954406212439515.

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Transient vibrations in mechanical systems are a common problem in engineering. Several theoretical studies have shown analytically and numerically that a vibrating system can be stabilised or its vibrations can be reduced when excited close to a specific parametric combination resonance frequency. At this operation, the transient vibrations are effectively damped by parametric excitation. The basic step in exploiting this method is its experimental implementation in mechanical systems. In this review, recent experiments are discussed for a simple chain mass system, a continuous cantilever and a flexible rotor system. The parametric excitation is realised by electromagnetic variable-stiffness actuators driven by a periodic open-loop control. It is demonstrated experimentally that a parametrically excited structure can exhibit enhanced damping properties. A certain level of the excitation amplitude has to be exceeded to achieve the damping effect in which the existing damping in the system is artificially amplified. Upon exceeding this value, the additional artificial damping provided to the system is significant and most effective for vibration suppression of the lower vibration modes.
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Frumen, A. "Imitative simulation of parametric beam vibrations." Transactions of the Krylov State Research Centre S-I, no. 2 (December 28, 2020): 110–12. http://dx.doi.org/10.24937/2542-2324-2020-2-s-i-110-112.

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This paper discusses two approaches to the investigation of parametric vibrations for beam structures: the approximate approach also known as VKB method (phase integrals) and the iterative algorithm basically simulating the process of vibration. The study compares the results yielded by these two approaches for a compressed freely supported beam and a ring under external compression load. The problem was solved through graphic programming in PVISSIM environment.
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Gao, Nan, Chanannipat Meesap, Shiyu Wang, and Dongsheng Zhang. "Parametric vibrations and instabilities of an elliptical gear pair." Journal of Vibration and Control 26, no. 19-20 (February 14, 2020): 1721–34. http://dx.doi.org/10.1177/1077546320902543.

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Parametric vibrations and instabilities can be induced in an elliptical gear pair. This study examined the effects of basic parameters on vibration instability. Geometric parameters and time-variant mesh stiffness are calculated. A torsional dynamic model is established by introducing the lumped parameter assumption. Based on the model, the parametric vibrations caused by the excitations of eccentricity and time-variant mesh stiffness are investigated, and the additive and difference combination resonances are identified. Comparison between the elliptical and circular gears implies that the vibration amplitude at mesh frequency of the elliptical gears is lower than that of the regular circular gears. The vibrations caused by load torque are also examined. The results show that the vibrations with different frequencies are coupled with each other. The inherent reason behind the coupling is the interaction between the eccentricity, time-variant stiffness, and load.
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Strelnikova, E., D. Kriutchenko, V. Gnitko, and A. Tonkonozhenko. "Liquid Vibrations in Cylindrical Tanks with and Without Baffles Under Lateral and Longitudinal Excitations." International Journal of Applied Mechanics and Engineering 25, no. 3 (September 1, 2020): 117–32. http://dx.doi.org/10.2478/ijame-2020-0038.

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AbstractThe paper is devoted to issues of estimating free surface elevations in rigid cylindrical fluid-filled tanks under external loadings. The possibility of baffles installation is provided. The liquid vibrations caused by lateral and longitudinal harmonic loadings are under consideration. Free, forced and parametrical vibrations are examined. Modes of the free liquid vibrations are considered as basic functions for the analysis of forced and parametric vibrations. The modes of the free liquid vibrations in baffled and un-baffled cylindrical tanks are received by using single-domain and multi-domain boundary element methods. Effects of baffle installation are studied. The problems of forced vibrations are reduced to solving the systems of second order ordinary differential equations. For parametric vibrations the system of Mathieu equations is obtained. The numerical simulation of free surface elevations at different loadings and baffle configurations is accomplished. Beat phenomena effects are considered under lateral harmonic excitations. The phenomenon of parametric resonance is examined under longitudinal harmonic excitations.
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Pešek, Ludek, Petr Šulc, and Ladislav Půst. "Numerical Study of Forced Vibration Suppression by Parametric Anti-Resonance." Archives of Acoustics 41, no. 3 (September 1, 2016): 527–33. http://dx.doi.org/10.1515/aoa-2016-0051.

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Abstract The parametric anti-resonance phenomenon as an active damping tool for suppression of externally excited resonant vibration is numerically studied herein. It is well known fact that the anti-resonance phenomenon, i.e. the stiffness periodic variation by subtractive, combination resonance frequency, brings stabilization and cancelling into self-excited vibrations. But this paper aims at a new possibility of its application, namely a damping of externally excited resonant vibration. For estimation of its effect we come both from a characteristic exponent of the analytical solution and numerical solution of forced vibration of 2DOF linear system with additional parametric excitation. The amplitude suppression owing to the parametric anti-resonance is studied on several parameters of the system: a depth of parametric excitation, mass ratio, damping coefficient and small frequency deviations from the parametric anti-resonance.
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Beltran-Carbajal, Francisco, Hugo Francisco Abundis-Fong, Luis Gerardo Trujillo-Franco, Hugo Yañez-Badillo, Antonio Favela-Contreras, and Eduardo Campos-Mercado. "Online Frequency Estimation on a Building-like Structure Using a Nonlinear Flexible Dynamic Vibration Absorber." Mathematics 10, no. 5 (February 24, 2022): 708. http://dx.doi.org/10.3390/math10050708.

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The online frequency estimation of forced harmonic vibrations on a building-like structure, using a nonlinear flexible vibration absorber in a cantilever beam configuration, is addressed in this article. Algebraic formulae to compute online the harmonic excitation frequency on the nonlinear vibrating mechanical system using solely available measurement signals of position, velocity, or acceleration are presented. Fast algebraic frequency estimation can, thus, be implemented to tune online a semi-active dynamic vibration absorber to obtain a high attenuation level of undesirable vibrations affecting the main mechanical system. A semi-active vibration absorber can be tuned for application where variations of the excitation frequency can be expected. Adaptive vibration absorption for forced harmonic vibration suppression for operational scenarios with variable excitation frequency can be then performed. Analytical, numerical, and experimental results to demonstrate the effectiveness and efficiency of the operating frequency estimation, as well as the acceptable attenuation level achieved by the tunable flexible vibration absorber, are presented. The algebraic parametric estimation approach can be extended to add capabilities of variable frequency vibration suppression for several configurations of dynamic vibration absorbers.
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Landolsi, Fakhreddine, Slim Choura, and Ali H. Nayfeh. "Control of 2D Flexible Structures by Confinement of Vibrations and Regulation of Their Energy Flow." Shock and Vibration 16, no. 2 (2009): 213–28. http://dx.doi.org/10.1155/2009/727236.

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In this paper, we investigate the control of 2D flexible structures by vibration confinement and the regulation of their energy flow along prespecified spatial paths. A discretized-model-based feedback strategy, aiming at confining and suppressing simultaneously the vibration, is proposed. It is assumed that the structure consists of parts that are sensitive to vibrations. The control design introduces a new pseudo-modal matrix derived from the computed eigenvectors of the discretized model. Simulations are presented to show the efficacy of the proposed control law. A parametric study is carried out to examine the effects of the different control parameters on the simultaneous confinement and suppression of vibrations. In addition, we conducted a set of simulations to investigate the flow control of vibrational energy during the confinement-suppression process. We found that the energy flow can be regulated via a set of control parameters for different confinement configurations.
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Dimentberg, M. F., and A. S. Bratus'. "Bounded parametric control of random vibrations." Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences 456, no. 2002 (October 8, 2000): 2351–63. http://dx.doi.org/10.1098/rspa.2000.0615.

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Rowland, David R. "Parametric resonance and nonlinear string vibrations." American Journal of Physics 72, no. 6 (June 2004): 758–66. http://dx.doi.org/10.1119/1.1645281.

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Guthy, C., C. W. Van Neste, S. Mitra, S. Bhattacharjee, and T. Thundat. "Parametric energy conversion of thermoacoustic vibrations." Applied Physics Letters 100, no. 20 (May 14, 2012): 203902. http://dx.doi.org/10.1063/1.4714693.

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Dissertations / Theses on the topic "Parametric vibrations"

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Manzione, Piergiuseppe. "Nonlinear transverse vibrations of centrally clamped rotating circular disks." Thesis, Virginia Tech, 1999. http://hdl.handle.net/10919/31524.

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A study is presented of the instability mechanisms of a damped axisymmetric circular disk of uniform thickness rotating about its axis with constant angular velocity and subjected to various transverse space-fixed loading systems. The natural frequencies of spinning floppy disks are obtained for various nodal diameters and nodal circles with a numerical and an approximate method. Exploiting the fact that in most physical applications the thickness of the disk is small compared with its outer radius, we use their ratio to define a small parameter. Because the nonlinearities appearing in the governing partial-differential equations are cubic, we use the Galerkin procedure to reduce the problem into a finite number of coupled weakly nonlinear second-order equations. The coefficients of the nonlinear terms in the reduced equations are calculated for a wide range of the lowest modes and for different rotational speeds. We have studied the primary resonance of a pair of orthogonal modes under a space-fixed constant loading, the principal parametric resonance of a pair of orthogonal modes when the disk is subject to a massive loading system, and the combination parametric resonance of two pairs of orthogonal modes when the excitation is a linear spring. Considering the case of a spring moving periodically along the radius of the disk, we show how its frequency can be coupled to the rotational speed of the disk and lead to a principal parametric resonance. In each of these cases, we have used the method of multiple scales to determine the equations governing the modulation of the amplitudes and phases of the interacting modes. The equilibrium solutions of the modulation equations are determined and their stability is studied.
Master of Science
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Sternchuss, Arnaud Balmès Etienne. "Multi-level parametric reduced models of rotating bladed disk assemblies." S. l. : Ecole centrale de Paris, 2009. http://theses.abes.fr/2009ECAP0001.

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Megnounif, Abdellatif. "Parametric study on human response to vibrations of box girder bridges." Thesis, University of Ottawa (Canada), 1988. http://hdl.handle.net/10393/5339.

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Oueini, Shafic Sami. "Techniques for Controlling Structural Vibrations." Diss., Virginia Tech, 1999. http://hdl.handle.net/10919/27176.

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We tackle the problem of suppressing high-amplitude vibrations of cantilever beams when subjected to either primary external or principal parametric resonances. Guided by results of previous investigations into the nonlinear dynamics of single- and multi-degree-of-freedom structures, we design mechatronic systems of sensors, actuators, and electronic devices and implement nonlinear active feedback control. In the case of external excitation, we devise two vibration absorbers based on either quadratic or cubic feedback. We conduct theoretical analyses and demonstrate that when a two-to-one (one-to-one) internal resonance condition is imposed between the plant and the quadratic (cubic) absorber, there exists a saturation phenomenon. When the plant is forced near its resonant frequency and the forcing amplitude exceeds a certain small threshold, the nonlinear coupling creates an energy-transfer mechanism that limits (saturates) the response of the plant. Our theoretical studies reveal that the cubic absorber creates regimes of high-amplitude quasiperiodic and chaotic responses, thereby limiting its utility. However, we show that superior results can be achieved when the natural frequency of the quadratic absorber is set equal to one-half the excitation frequency. Consequently, we apply the quadratic technique through a variety of linear and nonlinear actuators, sensors, and electronic devices. We design and build second-order analog circuits that emulate the quadratic absorber. Using a DC motor, piezoelectric ceramics, and Terfenol-D struts as actuators and potentiometers, strain gages, and accelerometers as sensors, we demonstrate successful single- and multi-mode vibration control. In order to realize a more versatile implementation of the control strategy, we resort to a digital signal processing (DSP) board. We compose a code in C and design a digital absorber by developing algorithms that, in addition to replacing the analog circuit, automatically detect the amplitude and frequency of oscillation of the plant and fine-tune the absorber parameters. We take advantage of the digital realization, implement a linear absorber, and compare the performance of the quadratic absorber with that of its linear counterpart. In the case of parametric excitation, we investigate two techniques. First, we explore application of the quadratic absorber. We prove theoretically and demonstrate experimentally that this control scheme is not reliable. Then, we propose an alternate approach. We devise a control law based on cubic velocity feedback. We conduct theoretical and experimental investigations and show that the latter strategy leads to effective vibration suppression and bifurcation control.
Ph. D.
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Winnard, Thomas Johan. "Theoretical Parametric Study of Through-Wall Acoustic Energy Transfer Systems." Thesis, Virginia Tech, 2021. http://hdl.handle.net/10919/103387.

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Technological advances require novel solutions for contactless energy transfer. Many engineering applications require unique approaches to power electrical components without using physical wires. In the past decade, awareness of the need to wirelessly power electrical components spawned many forays into the field of wireless power transfer (WPT). WPT techniques include capacitive energy transfer, electromagnetic inductive power transfer, electromagnetic radiative power transfer, electrostatic induction, and acoustic energy transfer. Acoustic energy transfer (AET) has many advantages over other methods. These advantages include lower operating frequency, shorter wavelengths enabling the use of smaller sized receiver and transmitter, extended transmitter-to-receiver distance therefore more manageable design constraints, achieving lower attenuation, higher penetration depth, and no electromagnetic losses. Most AET systems operate in the ultrasonic frequency range and are more commonly referred to as ultrasonic acoustic energy transfer (UAET) systems. Through-wall UAET systems are constructed of a transmitter bonded to a transmission elastic layer, which in turn is bonded to a receiver. The transmitter and receiver layers are constructed of a piezoelectric material. Piezoelectric materials behave according to the piezoelectric effect, which is when a material generates an electric charge in response to mechanical strain. The transmitter utilizes the reverse of the piezoelectric effect. A sinusoidal input voltage is applied to the transmitter, inducing vibrations in the transmitter. The vibration-induced acoustic waves emanating from the transmitter travel through the initial bonding layer, the transmission layer, and the final bonding layer to the receiver. In turn, the acoustic waves cause the receiver to deform and undergo strain. This induces a flow of charge in the receiver, which is an electric current. The receiver feeds current to a resistive load. In this manner, energy is acoustically transferred between two transducers without wires. The performance of UAET systems can be evaluated based on power transfer efficiency, voltage magnification, and input admittance. UAET systems require extensive modeling before experimental assembly can be attempted. The analytical models of UAET are either based on the mechanics of the constitutive relations of piezoelectricity and solid mechanics or using equivalent circuit methods. The equivalent circuit method approximates the physics of the UAET system with electrical assumptions. The mechanics-based method is the most comprehensive description of the physics of all the intermediate layers in a UAET system. The mechanics-based method has been based on the assumption that the UAET system is operated in the thickness mode of vibration, i.e., piston-like vibration mode where the transmitter and receiver disks vibrate only in the thickness direction. This poses an issue for disks with aspect ratios between 0.1 and 20 because the piezoelectric transducers vibrate in both the radial and thickness modes. In addition to this assumption, most of the works on UAET models only have accounted for the piezoelectric and transmission layers. The effects of the bonding layers were not considered. Bonding the piezoelectric layers to the transmission layer introduces epoxy material with mechanical properties that are not accounted for. The epoxy layers are extra barriers to the transmission that introduce attenuation and alter the vibrational and acoustical behaviors of the UAET system. Investigations into UAET commonly focus on metal through-wall applications. Alternate transmission layer materials are not investigated and the impact of varying mechanical properties on the performance of a through-wall UAET system has not been comprehensively studied. Even with the metal transmission layers, the impact of the metal thickness has not been extensively investigated thoroughly. This work addresses the issues of the thickness-mode assumption in UAET modeling, the effects of epoxy layers, the impacts of the metal layer geometry, and the performance of UAET systems with alternate transmission layer materials. Particularly, (1) we showed that the thickness-mode assumption, that has been used in the UAET modeling leads to inaccurate results. (2) We modified the available acoustic electro- elastic theoretical modeling to include the effects of radial modes as well as the epoxy bonding layers. (3) We showed that the geometry of the elastic/metal layer requires optimization for peak system efficiency. (4) The results show that using alternate transmission layer materials impacts the performance of UAET systems. The results of this work were investigated using an improved 5-layer analytical model and finite element modeling in COMSOL Multiphysics.
Master of Science
Wireless power transfer (WPT) is an innovative solution to the problem of powering sophisticated technological applications. Such instances include the powering of implanted medical devices, recharging inaccessible sensor networks, and wireless powering of components in sealed containers. Acoustic energy transfer (AET) is a feasible WPT method that addresses these needs. AET is based on the propagation of acoustic waves to a piezoelectric receiver which converts the vibrations caused by incident acoustic waves into electrical energy. Most AET systems operate in the ultrasonic frequency range, and so AET can also be referred to as ultrasonic acoustic energy transfer (UAET). Through-wall UAET systems are constructed from a transmitter that is bonded to a transmission elastic layer. The transmission layer is bonded to a receiver. The transmitter and receiver are made of a piezoelectric material. This thesis addresses the modeling process of through-wall UAET systems. In previous works, the fundamental assumption has been that such systems vibrate purely in the thickness mode. Additionally, other investigations did not comprehensively analyze the effects of the bonding layers, ascertain the performance of non-metal transmission layers, or provide practical insight on the effect of the resistive loading on such systems. This work addresses all these issues with a mathematical framework and finite element modeling results.
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Kurpa, Lidiya, Olga Mazur, and Igor Tsukanov. "Application of R-Functions Theory to Study Parametric Vibrations and Dynamical Stability of Laminated Plates." Thesis, Точка, 2013. http://repository.kpi.kharkov.ua/handle/KhPI-Press/37087.

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The problem of nonlinear parametric vibrations and stability analysis of the symmetric laminated plates is considered. The proposed method is based on multimode approximation of displacements and solving series auxiliary linear tasks. The main feature of the work is the application of the R-functions theory, which allows investigating parametric vibrations of plates with complex shape and different boundary conditions.
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Grenat, Clément. "Nonlinear Normal Modes and multi-parametric continuation of bifurcations : Application to vibration absorbers and architectured MEMS sensors for mass detection." Thesis, Lyon, 2018. http://www.theses.fr/2018LYSEI078/document.

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Un des buts de cette thèse est d’approfondir la compréhension de la dynamique non-linéaire, notamment celle des MEMS, en proposant de nouvelles méthodes d’analyse paramétrique et de calcul de modes normaux non-linéaires. Dans une première partie, les méthodes de détection, de localisation et de suivi de points de bifurcation selon un unique paramètre sont rappelées. Ensuite, une nouvelle méthode d’analyse multiparamétrique basée sur la continuation récursive d’extremums est présentée. Cette méthode est ensuite appliquée à un absorbeur de vibration non-linéaire afin de repousser l’apparition de solutions isolées. Deuxièmement, une méthode de calcul de modes normaux non-linéaires est présentée. Une condition de phase optimale et une régularisation de l’équation de mouvement sont proposées afin d’obtenir une méthode de continuation plus robuste au niveau des interactions modales. Ensuite, un problème quadratique aux valeurs propres modifié pour le calcul de stabilité et de points de bifurcation est présenté. Finalement, le calcul de modes normaux non-linéaires a été étendu aux systèmes non-conservatifs permettant la continuation des résonances d’énergie en déplacement et des résonances de phase. Troisièmement, la dynamique non-linéaire de réseaux de MEMS basé sur plusieurs micro-poutres résonantes est analysée à l’aide des méthodes proposées. Tout d'abord, un phénomène de synchronisation de points de bifurcations dû au couplage électrostatique dans les réseaux de MEMS est expliqué. Puis, la dynamique non-linéaire d'un réseau dissymétrisé par l'ajout d'une petite masse sur une micro-poutre est analysée. Enfin, des mécanismes de détection de masse exploitant ces phénomènes non-linéaires sont présentés
One of the goals of this thesis is to enhance the comprehension of nonlinear dynamics, especially MEMS nonlinear dynamics, by proposing new methods for parametric analysis and for nonlinear normal modes computation. In a first part, methods for the detection, the localization and the tracking of bifurcation points with respect to a single parameter are recalled. Then, a new method for parametric analysis, based on recursive continuation of extremum, is presented. This method is then applied to a Nonlinear Tuned Vibration Absorber in order to push isolated solutions at higher amplitude of forcing. Secondly, a method is presented for the computation of nonlinear normal modes. An optimal phase condition and a relaxation of the equation of motion are proposed to obtain a continuation method able to handle modal interactions. Then, a quadratic eigenvalue problem is shifted to compute the stability and bifurcation points. Finally, nonlinear normal modes are extended to non-conservatives systems permitting the continuation of phase and energy resonances. Thirdly, the nonlinear dynamics of MEMS array, based on multiple resonant micro-beams, is analyzed with the help of the proposed methods. A frequency synchronization of bifurcation points due to the electrostatic coupling is discovered. Then, the nonlinear dynamics of a MEMS array after symmetry breaking event induced by the addition of a small mass onto one of the beam of the array is analyzed. Finally, mass detection mechanisms exploiting the discovered phenomena are presented
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Schirén, Whokko, and Trixie Swahn. "Vibrations in residential timber floors : A comparison between the current and the revised Eurocode 5." Thesis, Linnéuniversitetet, Institutionen för byggteknik (BY), 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-89293.

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The European standard Eurocode 5, a design method for timber structures,is currently under revision. In this study the draft for a reviseddesign method for vibrations in timber floors was compared to the currentmethod. The hypothesis of the thesis was that the revised designmethod might force some changes to the present construction practiceand that these changes may carry with them increased costs for the industry.Six common floor structures used in Sweden today were identifiedand for these floors design calculations were made according to the currentand the revised design method. It was checked whether the floorspassed the criteria in the two design methods and a comparison was madefor the only criterion which could be compared between the methods, thepoint load deflection. Floor structures could pass or fail the current designmethod based on two criteria, the point load deflection and the unitimpulse velocity response. All floors passed the current design methodexcept one which had a fundamental frequency below 8 Hz, because ofthe low frequency the current design method was not applicable to thefloor structure. In the revised design method the final result is a responsefactor and based on the response factor floors are given floor performancelevels. The seven step scale for the floor performance level go from I toVII where I is excellent and VII is unacceptable. All floor structures excepttwo achieved an acceptable floor performance level according to therevised design method. The two floors which failed were floors commonlyused in single family houses, they failed for a span length commonly usedtoday. A limited parametric study was performed where it was found thatthe modal mass used had a larger impact on the floor performance levelthan the mass per square meter included. For floors with a fundamentalfrequency above 8 Hz, including a higher mass per square meter resultedin a lower, i.e. better, response factor in all cases except one. For floorswith a fundamental frequency between 4.5 and 8 Hz, a higher mass resultedin a higher, i.e. worse, response factor. The study found that notall floor structures used in Sweden today are acceptable according to therevised design method therefore changes may have to be implemented andthese changes could result in an increased cost.
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Airimitoaie, Tudor-Bogdan. "Commande robuste et calibrage des systèmes de contrôle actif de vibrations." Thesis, Grenoble, 2012. http://www.theses.fr/2012GRENT015/document.

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Dans cette thèse, nous présentons des solutions pour la conception des systèmes de contrôle actif de vibrations. Dans la première partie, des méthodes de contrôle par action anticipatrice (feedforward) sont développées. Celles-ci sont dédiées à la suppression des perturbations bande large en utilisant une image de la perturbation mesurée par un deuxième capteur, en amont de la variable de performance à minimiser. Les algorithmes présentés dans cette mémoire sont conçus pour réaliser de bonnes performances et maintenir la stabilité du système en présence du couplage positif interne qui apparaît entre le signal de commande et l'image de la perturbation. Les principales contributions de cette partie sont l'assouplissement de la condition de « Stricte Positivité Réelle » (SPR) par l'utilisation des algorithmes d'adaptation « Intégrale + Proportionnelle » et le développement de compensateurs à action anticipatrice (feedforward) sur la base de la paramétrisation Youla-Kučera. La deuxième partie de la thèse concerne le rejet des perturbations bande étroite par contre-réaction adaptative (feedback). Une méthode d'adaptation indirecte est proposée pour le rejet de plusieurs perturbations bande étroite en utilisant des filtres Stop-bande et la paramétrisation Youla-Kučera. Cette méthode utilise des Filtres Adaptatifs à Encoche en cascade pour estimer les fréquences de perturbations sinusoïdales puis des Filtres Stop-bande pour introduire des atténuations aux fréquences estimées. Les algorithmes sont vérifiés et validés sur un dispositif expérimental disponible au sein du département Automatique du laboratoire GIPSA-Lab de Grenoble
In this thesis, solutions for the design of robust Active Vibration Control (AVC) systems are presented. The thesis report is composed of two parts. In the first one, feedforward adaptive methods are developed. They are dedicated to the suppression of large band disturbances and use a measurement, correlated with the disturbance, obtained upstream from the performance variable by the use of a second transducer. The algorithms presented in this thesis are designed to achieve good performances and to maintain system stability in the presence of the internal feedback coupling which appears between the control signal and the image of the disturbance. The main contributions in this part are the relaxation of the Strictly Positive Real (SPR) condition appearing in the stability analysis of the algorithms by use of “Integral + Proportional” adaptation algorithms and the development of feedforward compensators for noise or vibration reduction based on the Youla-Kučera parameterization. The second part of this thesis is concerned with the negative feedback rejection of narrow band disturbances. An indirect adaptation method for the rejection of multiple narrow band disturbances using Band-Stop Filters (BSF) and the Youla-Kučera parameterization is presented. This method uses cascaded Adaptive Notch Filters (ANF) to estimate the frequencies of the disturbances' sinusoids and then, Band-stop Filters are used to shape the output sensitivity function independently, reducing the effect of each narrow band signal in the disturbance. The algorithms are verified and validated on an experimental setup available at the Control Systems Department of GIPSA-Lab, Grenoble, France
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Luboya, Silhady Tshitende. "Response of Footbridges equipped with TLD : A numerical and experimental assessment." Thesis, KTH, Bro- och stålbyggnad, 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-278563.

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In recent years, an increase to design slender and aesthetically-pleasing structures have resulted in some structures having a low natural frequency. This is because the design calculation did not meet the requirement of serviceability performance. Structures can experience excessive vibrations when they are subjected to different types of dynamic loading. A device can be installed to prevent these vibrations.In this thesis, we study the response of buildings and lateral vibrations of footbridges equipped with Tuned Liquid Damper. The aim is to mitigate the first mode of vibration. Tuned Liquid Damper consists of a container in rectangular, cylindrical or arbitrary shape partially filled with shallow liquid, most often water is used as a regulating device system. The design properties of Tuned Liquid Damper is introduced and it is based on the analogyof the most popular damper, Tuned Mass Damper.An experimental study of a building frame model with four floors is conducted to validate the numerical results obtained from the simulation of the model in ANSYS. The linear and non-linear analysis are performed through a system coupling between Ansys mechanical and Fluent solver. The simulation results obtained are in good agreement with the experimental results.A parametric study is conducted with a simply supported steel footbridge. It is a 45 m long span with 3 m width and the flexural rigidity is modified to get the lateral vibration mode. The first lateral natural frequency obtained is 0.713 Hz. The load case for the study considered is according to Sétra guide. The variable parameters studied is the Tuned Liquid Damper water mass ratios: 0.7%, 1.0%, 2.0%, 3.0% and 4.0%. The results show a satisfactory performance of the footbridge model equipped with Tuned Liquid Damper. The accelerations are below 0.1 m/s2 which satisfied the requirement of 0.15 m/s2.
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Books on the topic "Parametric vibrations"

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Cartmell, Matthew. Introduction to linear, parametric, and nonlinear vibrations. London: Chapman and Hall, 1990.

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de Sá Caetano, Elsa. Cable Vibrations in Cable-Stayed Bridges. Zurich, Switzerland: International Association for Bridge and Structural Engineering (IABSE), 2007. http://dx.doi.org/10.2749/sed009.

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<p>The fifty years of experience of construction of cable-stayed bridges since their establishment as a new category among the classical types have brought an immense progress, ranging from design and conception to materials, analysis, construction, observation and retrofitting. The growing construction of cable-stayed bridges has also triggered researchers’ and designers’ attention to the problem of cable vibrations. Intensive research has been developed all over the world during the last two decades as a consequence of the numerous cases of cable vibrations exhibited by all types of cable-stayed bridges.<p>Despite the increased knowledge of the various vibration phenomena, most of the outcomes and research results have been published in journals and conference proceedings and scarce information is currently provided by the existing recommendations and codes. <p>The present book provides a comprehensive survey on the governing phenomena of cable vibration, both associated with direct action of wind and rain: buffeting, vortex-shedding, wake effects, rain-wind vibration; and resulting from the indirect excitation through anchorage oscillation: external and parametric excitation. Methodologies for assessment of the effects of those phenomena are presented and illustrated by practical examples. Control of cable vibrations is then discussed and state-of-art results on the design of passive control devices are presented. <p>The book is complemented with a series of case reports reflecting the practical approach shared by experienced designers and consultants: Yves Bournand (VSL International), Chris Geurts (TNO), Carl Hansvold (Johs. Holt), Allan Larsen (Cowi) and Randall Poston (WDP & Associates).
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Parametric random vibration. Letchworth, Hertfordshire, England: Research Studies Press, 1985.

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Sneyd, A. D. Parametric resonance in systems of Mathieu equations. Hamilton, N.Z: University of Waikato, Mathematics and Statistics, 1991.

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Kanevskiĭ, I. N. Kolebatelʹnye sistemy s sosredotochennymi parametrami. Vladivostok: Dalʹnauka, 2004.

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Chun, R. C. Parametric study of pipe whip analysis. Washington, D.C: Division of Engineering, Office of Nuclear Regulatory Research, U.S. Nuclear Regulatory Commission, 1987.

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Redʹko, S. F. Identifikat͡s︡ii͡a︡ mekhanicheskikh sistem: Opredelenie dinamicheskikh kharakteristik i parametrov. Kiev: Nauk. dumka, 1985.

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Xie, Jueren. Numerical investigation of eccentrically loaded tied high strength concrete columns. Edmonton, Alta., Canada: Dept. of Civil Engineering, University of Alberta, 1994.

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Cartmell, M. C. Introduction to Linear, Parametric and Non-Linear Vibrations. Springer, 1990.

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Parametric Random Vibration. Dover Publications, 2007.

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Book chapters on the topic "Parametric vibrations"

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Karnovsky, Igor A., and Evgeniy Lebed. "Active and Parametric Vibration Protection of Transient Vibrations." In Theory of Vibration Protection, 485–517. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-28020-2_13.

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Vulfson, Iosif I. "Parametric Vibrations Excitation in Cyclic Mechanisms." In Advances in Mechanical Engineering, 133–43. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-53363-6_14.

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Mikhasev, Gennadi I., and Petr E. Tovstik. "Localized Parametric Vibrations of Thin Shells." In Localized Dynamics of Thin-Walled Shells, 139–87. First edition. | Boc Raton : CRC Press, 2020. | Series: Chapman & Hall/CRC monographs and research notes in mathematics: Chapman and Hall/CRC, 2020. http://dx.doi.org/10.1201/9781315115467-5.

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Wójcicki, Zbigniew. "Method of Stabilization of Resonant Parametric Vibrations." In Lecture Notes in Civil Engineering, 364–73. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-86001-1_43.

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Spelsberg-Korspeter, Gottfried. "Nonlinear Analysis of Systems Under Periodic Parametric Excitation." In Robust Structural Design against Self-Excited Vibrations, 81–93. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-36552-2_7.

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Sergaliyev, Almaz, Julius Kaplunov, and Lelya Khajiyeva. "About Multi-parametric Analysis of Drill String Vibrations." In Mechanisms and Machine Science, 373–77. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-09918-7_33.

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Liu, Airong, Hanwen Lu, Yong-Lin Pi, Youqing Huang, and Jing Li. "Out-of-Plane Parametric Resonance of Arches Under an In-Plane Central Harmonic Load." In Environmental Vibrations and Transportation Geodynamics, 45–51. Singapore: Springer Singapore, 2017. http://dx.doi.org/10.1007/978-981-10-4508-0_4.

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Spelsberg-Korspeter, Gottfried. "Perturbation of a Linear Conservative System by Periodic Parametric Excitation." In Robust Structural Design against Self-Excited Vibrations, 5–17. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-36552-2_2.

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Tylikowski, Andrzej. "Active Damping of Parametric Vibrations of Mechanical Distributed Systems." In Solid Mechanics and Its Applications, 409–18. Dordrecht: Springer Netherlands, 2003. http://dx.doi.org/10.1007/978-94-017-0371-0_40.

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Yurchenko, Daniil. "Tuned Mass and Parametric Pendulum Dampers Under Seismic Vibrations." In Encyclopedia of Earthquake Engineering, 1–22. Berlin, Heidelberg: Springer Berlin Heidelberg, 2015. http://dx.doi.org/10.1007/978-3-642-36197-5_338-1.

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Conference papers on the topic "Parametric vibrations"

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Ecker, Horst. "A Parametric Absorber for Friction-Induced Vibrations." In ASME 2003 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2003. http://dx.doi.org/10.1115/detc2003/vib-48474.

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This contribution deals with the suppression of friction-induced vibrations of a mechanical system. A two-mass system is considered, with the main mass excited by a friction-generated self-excitation force and a smaller second mass attached to the main mass. The parameter of the connecting stiffness between the main mass and the absorber mass is a harmonic function of time and represents a parametric excitation. The purpose of the second mass is to act as a “parametric absorber” and to cancel vibrations. Critical values for the damping parameters of the conventional system are calculated, where the system operates on the stability limit. Analytical and numerical methods are employed to determine the stability of the parameter-excited system. A study for selected parameters shows within which limits friction-induced vibrations can be suppressed effectively by a parametric absorber.
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Popov, A. A., J. M. T. Thompson, and F. A. McRobie. "Parametrically Excited Vibrations and Auto-Parametric Resonance in Cylindrical Shells." In ASME 2000 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2000. http://dx.doi.org/10.1115/imece2000-1011.

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Abstract Vibrations of cylindrical shells parametrically excited by external axial forcing or by internal auto-parametric resonances are considered. A Rayleigh-Ritz discretization of the von Kármán-Donnell equations through symbolic computations leads to low dimensional models of shell vibration. After applying methods and ideas of modern dynamical systems theory, complete bifurcation diagrams are constructed and analyzed with an emphasis on modal interactions and their relevance to structural behaviour. In the case of free shell vibrations, the Hamiltonian and a transformation into action-angle coordinates followed by averaging provides readily a geometric description of the interaction between concertina and chequerboard modes. It was established that the interaction should be most pronounced when there are slightly less than 2 N square chequerboard panels circumferentially, where N is the ratio of shell radius to thickness. The two mode interaction leads to preferred vibration patterns with larger deflection inwards than outwards, and at internal resonance, significant energy transfer occurs between the modes. The regular and chaotic features of this interaction are studied analytically and numerically.
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Dohnal, F. "Dissipative Energy Flow in Systems at Parametric Anti-Resonance." In ASME 2012 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/detc2012-70864.

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Recent investigations have shown theoretically and experimentally that the transient vibrations of a lightly damped system can be suppressed or even stabilized by a time-periodic open-loop control of one of its system parameters. Introducing time-periodicity in system parameters may lead, in general, to a dangerous and well-known parametric resonance. In contrast to such a resonance, a properly tuned time-periodicity is capable to extract vibration energy from the system and to increase the effective damping of transient vibrations. At this specific operation the system is tuned at parametric anti-resonance. The beneficial interaction of damping and time-periodicity was first formulated by A. Tondl in 1998. His pioneering work deals with stabilizing self-excited vibrations. It was proven by F. Dohnal in 2005 that the vibrations of a general lightly damped system (not necessarily unstable) can be reduced by parametric anti-resonance, too. A physical interpretation of the parametric anti-resonance is related to the coupling of vibration modes of the underlying system with constant coefficients. This interpretation leads intuitively to the calculation of the energy flow of each vibration mode and leads to clear physical insight of how parametric anti-resonances work. This interpretation of mode coupling is developed further resulting in an approximate analytical expression for the effective damping of a system driven at parametric anti-resonance. This expression allows the statement of the maximum effective damping achievable by this method. The discussion of the energy flow of a linear, lightly damped system possessing a time-periodic stiffness coefficient its physical and modal displacements highlights the coupling of vibration modes of the underlying system with constant coefficients.
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Tondl, Aleš, and Horst Ecker. "Cancelling of Self-Excited Vibrations by Means of Parametric Excitation." In ASME 1999 Design Engineering Technical Conferences. American Society of Mechanical Engineers, 1999. http://dx.doi.org/10.1115/detc99/vib-8071.

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Abstract The possibility of cancelling self-excited vibrations of a mechanical system using parametric excitation is discussed. A two-mass system is considered, with the top mass excited by a flow-generated self-exciting force. The parameter of the connecting stiffness between the base mass and the foundation is a harmonic function of time and represents a parametric excitation. For such a system general conditions for full vibration cancelling are derived and presented. By means of numerical simulation the system is investigated for several sets of parameters. The theoretical results are found to be in very good agreement with the results obtained by simulation. Parameter variations show the extent of the parameter space where significant vibration cancelling can be achieved and illustrate possible applications.
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Dosko, Sergey I., Sergey A. Sheptunov, Akelsey Yu Spasenov, and Kirill V. Kucherov. "Human Precardiac Zone Vibrations Analysis Using Parametric Spectral Methods." In 2020 International Conference on Quality Management, Transport and Information Security, Information Technologies (IT&QM&IS). IEEE, 2020. http://dx.doi.org/10.1109/itqmis51053.2020.9322983.

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Dohnal, Fadi, Wolfgang Paradeiser, and Horst Ecker. "Experimental Study on Cancelling Self-Excited Vibrations by Parametric Excitation." In ASME 2006 International Mechanical Engineering Congress and Exposition. ASMEDC, 2006. http://dx.doi.org/10.1115/imece2006-14552.

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This article reports on the experimental verification of an anti-resonance effect obtained by parametric stiffness excitation. From theoretical studies it is known that parametric excitation at non-resonant parametric resonances can improve the damping behavior of a mechanical system and even stabilize an otherwise unstable system. To demonstrate this effect, a test setup was designed, based on a two-mass vibration system, gliding on an air track. Parametric stiffness excitation (PSE) was realized by a mechanical device that creates a time-periodic stiffness by modulating the tension in an elastic rubber band. With this device it was possible to demonstrate the improved damping behavior of the system when the PSE device is operating at or near the first parametric combination resonance of difference type. Also, a simple electro-magnetic device was used to create self-exciting forces. It could be shown for the first time that it is indeed possible to stabilize the unstable system by introducing parametric stiffness excitation.
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HANAGUD, S. "Delaminations in smart composite structures - A parametric study on vibrations." In 31st Structures, Structural Dynamics and Materials Conference. Reston, Virigina: American Institute of Aeronautics and Astronautics, 1990. http://dx.doi.org/10.2514/6.1990-1173.

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Tuma, Jiri, Pavel Suranek, Miroslav Mahdal, and Marek Babiuch. "Simulation of the parametric excitation of the cantilever beam vibrations." In 2014 15th International Carpathian Control Conference (ICCC). IEEE, 2014. http://dx.doi.org/10.1109/carpathiancc.2014.6843679.

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Tanaka, Tomotsugu, Koetsu Takano, Hiroyuki Fujiwara, and Osami Matsushita. "Reduction of Flow-Induced Vibration Using Parametric Excitation." In ASME 2002 International Mechanical Engineering Congress and Exposition. ASMEDC, 2002. http://dx.doi.org/10.1115/imece2002-33576.

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Vibration of structures, such as suspension bridges, skyscrapers and high rises, sometimes cause people to feel anxious. These vibrations are usually induced by the fluid flow, especially vortex shedding and they grow into self-excited vibrations, which are normally accompanied by the extremely large vibration amplitude. In order to solve these vibration problems, many researchers have reported the effectiveness of vibration control methods and most of the methods are very practical for the actual structure. These control methods usually consist of feedback control systems for the active control and some kinds of damper for the passive control. This paper deals with one control method, which is using the parametric excitation. The efficiencies of this method for the self-excited vibration have already been analytically examined by Tondl. However, it is not confirmed experimentally, and it is necessary to discuss the possibility of realization and application for the actual system. In this study, our experiment confirms the effectiveness of this control method. For this purpose, an experimental apparatus, which expressed a two degrees of freedom system and consisted of an electromagnetic actuator, a steel beam and two masses, were prepared. A digital signal processor was used for the realization of the parametric excitation control. During the experiments, we confirmed the effectiveness of the control procedure and accuracy of the theoretical results. In addition, the relationships between the ratio of the two masses and the ratio of the natural and the parametric excitation frequency, which are required for the effective control, were cleared. According to this study, the quenching of self-excited vibration by using the parametric excitation is realized within the very narrow band of frequency and the mass ratio should be small.
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Ng, Leslie, and Richard Rand. "Nonlinear Effects on Coexistence Phenomenon in Parametric Excitation." In ASME 2002 International Mechanical Engineering Congress and Exposition. ASMEDC, 2002. http://dx.doi.org/10.1115/imece2002-32406.

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We investigate the effect of nonlinearites on a parametrically excited ordinary differential equation whose linearization exhibits the phenomena of coexistence. The differential equation studied governs the stability mode of vibration in an unforced conservative two degree of freedom system used to model the free vibrations of a thin elastica. Using perturbation methods, we show that at parameter values corresponding to coexistence, nonlinear terms can cause the origin to become nonlinearly unstable, even though linear stability analysis predicts the origin to be stable. We also investigate the bifurcations associated with this instability.
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