Optimizing parametric oscillators with tunable boundary conditions

Plat, Harel; Bucher, Izhak

doi:10.1016/j.jsv.2012.09.017

Cited by 11 publications

(10 citation statements)

References 11 publications

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“…3. Note that, in accordance with (13), the energy exchange period increases to infinity as the energy decreases to zero. Indeed, for given dynamic parameters of the system the frequency weakly depends on the energy, that is, on the oscillation amplitude; hence the derivative, dw 2 (t)/ dt is of the same order as w 2 and the energy E w , (11).…”

Section: Free Oscillationssupporting

confidence: 63%

Coupled mode parametric resonance in a vibrating screen model

Slepyan

Slepyan²

2014

Mechanical Systems and Signal Processing

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We consider a simple dynamic model of the vibrating screen operating in the parametric resonance (PR) mode. This model was used in the course of designing and setting of such a screen in LPMC. The PR-based screen compares favorably with conventional types of such machines, where the transverse oscillations are excited directly. It is characterized by larger values of the amplitude and by insensitivity to damping in a rather wide range. The model represents an initially strained system of two equal masses connected by a linearly elastic string. Self-equilibrated, longitudinal, harmonic forces act on the masses. Under certain conditions this results in transverse, finite-amplitude oscillations of the string. The problem is reduced to a system of two ordinary differential equations coupled by the geometric nonlinearity. Damping in both the transverse and longitudinal oscillations is taken into account. Free and forced oscillations of this mass-string system are examined analytically and numerically. The energy exchange between the longitudinal and transverse modes of free oscillations is demonstrated. An exact analytical solution is found for the forced oscillations, where the coupling plays the role of a stabilizer. In a more general case, the harmonic analysis is used with neglect of the higher harmonics. Explicit expressions for all parameters of the steady nonlinear oscillations are determined. The domains are found where the analytically obtained steady oscillation regimes are stable. Over the frequency ranges, where the steady oscillations exist, a perfect correspondence is found between the amplitudes obtained analytically and numerically. Illustrations based on the analytical and numerical simulations are presented.Comment: Pages 16, figures 1

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Section: Free Oscillationssupporting

confidence: 63%

Coupled mode parametric resonance in a vibrating screen model

Slepyan

Slepyan²

2014

Mechanical Systems and Signal Processing

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“…Taking into account that only the first mode can be excited, the nondecaying first-order solution obtained from Eqs. (11) and (12) can be expressed as follows:…”

Section: Change In the Nonlinear Characteristics Of The Frequency Resmentioning

confidence: 99%

“…This method uses an actuator to change the cubic nonlinearity but is not a passive method. Plat and Bucher [11] proposed a method by which to change the cubic nonlinear characteristics of a string without an actuator and tuned the boundary conditions based on a spring-mass connected in the axial direction in order to increase the response amplitude in a parametrically excited string. However, their method does not deal with changing the cubic nonlinearity of the beam.…”

Section: Introductionmentioning

confidence: 99%

“…The response amplitude is governed primarily by cubic nonlinear effects in the lateral direction, which are produced by the geometric nonlinear elastic force and the nonlinear inertia force due to the large curvature of the beam, as well as the inertia force of the tip mass in the axial direction. The inertia force in the axial direction increases the effect of the softening characteristics [12], whereas the linear stiffness in the axial direction increases the effect of the hardening characteristics [11]. Therefore, tuning the inertia force and the linear stiffness may change the nonlinear characteristics of the backbone curve and the frequency response curve.…”

Section: Introductionmentioning

confidence: 99%

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Passive method for controlling the nonlinear characteristics in a parametrically excited hinged-hinged beam by the addition of a linear spring

Shibata

Ohishi

Yabuno

2015

Journal of Sound and Vibration

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“…Usually, the principal parametric resonance is employed where the first linear instability tongue in the Ince-Strutt diagram [22][23][24][25][26] resides. Parametric excitation can amplify some forces through a combination of their frequencies in a manner the structural dynamics favours [27][28][29].…”

Section: Introductionmentioning

confidence: 99%

Dynamic balancing of super-critical rotating structures using slow-speed data via parametric excitation

Tresser

Dolev

Bucher

2018

Journal of Sound and Vibration

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High-speed machinery is often designed to pass several "critical speeds", where vibration levels can be very high. To reduce vibrations, rotors usually undergo a mass balancing process, where the machine is rotated at its full speed range, during which the dynamic response near critical speeds can be measured. High sensitivity, which is required for a successful balancing process, is achieved near the critical speeds, where a single deflection mode shape becomes dominant, and is excited by the projection of the imbalance on it. The requirement to rotate the machine at high speeds is an obstacle in many cases, where it is impossible to perform measurements at high speeds, due to harsh conditions such as high temperatures and inaccessibility (e.g., jet engines). This paper proposes a novel balancing method of flexible rotors, which does not require the machine to be rotated at high speeds. With this method, the rotor is spun at low speeds, while subjecting it to a set of externally controlled forces. The external forces comprise a set of tuned, response dependent, parametric excitations, and nonlinear stiffness terms. The parametric excitation can isolate any desired mode, while keeping the response directly linked to the imbalance. A software controlled nonlinear stiffness term limits the response, hence preventing the rotor to become unstable. These forces warrant sufficient sensitivity required to detect the projection of the imbalance on any desired mode without rotating the machine at high speeds. Analytical, numerical and experimental results are shown to validate and demonstrate the method.

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Optimizing parametric oscillators with tunable boundary conditions

Cited by 11 publications

References 11 publications

Coupled mode parametric resonance in a vibrating screen model

Coupled mode parametric resonance in a vibrating screen model

Passive method for controlling the nonlinear characteristics in a parametrically excited hinged-hinged beam by the addition of a linear spring

Dynamic balancing of super-critical rotating structures using slow-speed data via parametric excitation

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