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

Warmiński, Jerzy; Cartmell, M.P.; Mitura, Andrzej; Bocheński, M.

doi:10.1155/2013/792795

Cited by 33 publications

(25 citation statements)

References 14 publications

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“…MATLAB ® ode45 solver is implemented to solve the Eqs. (13), (16), and (17) numerically, to obtain the frequency response in the neighborhood frequencies of the fundamental mode. The results of the perturbation solution and the numerical results are shown in Fig.…”

Section: Numerical and Perturbation Results Comparisonmentioning

confidence: 99%

“…This control method focuses on the problem of intrinsic time delay between the control input and the real-time system actuation. Nonlinear saturation controller (NSC) is one of the frequently applied approaches [11], as it has been used with some other selected algorithms on a geometrically nonlinear beam-like composite structure [12,13]. Neural Network [14] and Receptance [15] are two other methods implemented for nonlinear vibration suppression.…”

Section: Introductionmentioning

confidence: 99%

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Nonlinear vibration suppression of flexible structures using nonlinear modified positive position feedback approach

Omidi

Mahmoodi

2014

Nonlinear Dyn

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This paper introduces Nonlinear ModifiedPositive Position Feedback (NMPPF) control approach for nonlinear vibration suppression at primary resonance. Nonlinearity in the system is due to large deformations caused by high-amplitude disturbances, while this control approach is applicable to all types of nonlinearities in resonant structures. NMPPF controller consists of a resonant second-order nonlinear compensator, which is enhanced by a lossy integrating compensator. The two compensators create a combination of exponential and periodic control inputs, which needs innovative time scaling for using the Method of Multiple Scales to obtain the analytical solution of the closedloop system. The results of the analytical solution for the closed-loop NMPPF controller are presented and compared with the result of the conventional PPF controller. Effects of the control parameters on the system response are comprehensively studied by parameter variations. The approximate solution is then verified using numerical simulations. According to the results, the NMPPF controller provides a higher level of suppression in the overall frequency domain, as the peak amplitude at the neighborhood frequencies of the primary mode is reduced by 44 %, compared to the PPF method. The tunable control parameters also give more flexibility to create the expected type of system response.

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Section: Numerical and Perturbation Results Comparisonmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Nonlinear vibration suppression of flexible structures using nonlinear modified positive position feedback approach

Omidi

Mahmoodi

2014

Nonlinear Dyn

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“…The investigation of a nonlinear control method based on the saturation phenomenon in systems coupled with quadratic nonlinearities, was treated in more details by [22][23][24][25][26]. The implementation of an active saturation control was proposed in [27][28][29][30] and studied by [31][32][33][34][35][36]. In addition, saturation phenomenon was used to suppress steady-state vibrations of a system by connecting it to a second-order controller using quadratic position coupling terms [34].…”

Section: Introductionmentioning

confidence: 99%

“…The equations of motion were developed by the method of energy of Lagrange. After that, the analysis of the vibration energy transferred was performed in order to see the saturation phenomenon as studied by [19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36], Section 3 discussed about the frequency of the external force, because it is an important factor of the saturation.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear piezoelectric vibration energy harvesting from a portal frame with two-to-one internal resonance

et al. 2017

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In the few decades, the study of electromechanical systems which are capable to extract energy from an operating system in the environment has been of most importance. In this work, we present the extraction of energy from a simple portal frame structure excited by a harmonic force, where the energy harvesting is computed by using of a nonlinear piezoelectric material. The dynamical response of the system is examined, when there is 2:1 internal resonance between the symmetric and the sway mode, resulting the saturation phenomenon and vibration energy transfer between the symmetric (vertical) mode and the horizontal (sway) mode. An evaluation of the energy available for harvesting, in each of the considered modes, is computed.

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“…This may yield a nonlinear anti-vibration system that is less complex. Various types of active controllers have been investigated for vibration attenuation of nonlinear systems [16][17][18][19][20][21][22][23][24][25]. Among them, linear positive position feedback (LPPF) and nonlinear positive position feedback (NPPF) controllers are found to be particularly effective if they are aimed to damp one particular structural vibration mode.…”

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confidence: 99%

Nonlinear positive position feedback control for mitigation of nonlinear vibrations

Zhao

Paknejad

Raze

et al. 2019

Mechanical Systems and Signal Processing

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a b s t r a c tThis paper investigates the potential of using a nonlinear positive position feedback controller for vibration mitigation of a Duffing oscillator. The proposed controller is designed based on the principle of similarity which states that anti-vibration devices should be governed by the same equations as those of the host structure. Closed-form expressions for the H 1 optimal control parameters that minimise the maximal response of the structure are firstly derived for the linear positive position feedback controller and then extended to the nonlinear counterpart. The harmonic balance method is employed to approximate the analytical solutions. Both numerical simulations and experimental validations are performed to demonstrate the proposed control strategy.vibration absorbers can be designed as a mirror of the primary structures i.e. nonlinear vibration absorbers should possess the same nonlinearities as those in the primary systems. This design principle is also referred to as the principle of similarity. It was reported that nonlinear primary systems attached with nonlinear vibration absorbers designed based on the principle of similarity behave in a similar fashion as their linear counterpart. Although this concept is promising, it may become cumbersome and expensive to realise them in practice using passive means for complex nonlinear primary systems.On the other hand, in an active approach it is attempted to introduce the desired nonlinear control forces using sensors and actuators. This may yield a nonlinear anti-vibration system that is less complex. Various types of active controllers have been investigated for vibration attenuation of nonlinear systems [16][17][18][19][20][21][22][23][24][25]. Among them, linear positive position feedback (LPPF) and nonlinear positive position feedback (NPPF) controllers are found to be particularly effective if they are aimed to damp one particular structural vibration mode. This type of controller is implemented by feeding the structural position directly to a linear or nonlinear compensator, whose output is then fed through a fixed gain positively back to drive the actuator. In this context, they would be well suited for the applications where piezoelectric sensors and actuators are employed for vibration damping. This is because the voltage from the sensor is proportional to the strain of the attached structure, which can be directly measured to drive the strain-based piezoelectric actuators. Warminski et al. [21] compared the control performance of a LPPF controller with three other controllers, namely proportional position feedback, cubic position feedback and nonlinear saturation feedback, for suppression of nonlinear composite beam vibrations. It was found that the LPPF controller is only effective for weakly nonlinear systems and the nonlinear saturation controller was concluded to be superior for the nonlinear primary structure under consideration. The performance of the LPPF controller was also investigated in [22], but on a four-degree-of-freedo...

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

Cited by 33 publications

References 14 publications

Nonlinear vibration suppression of flexible structures using nonlinear modified positive position feedback approach

Nonlinear vibration suppression of flexible structures using nonlinear modified positive position feedback approach

Nonlinear piezoelectric vibration energy harvesting from a portal frame with two-to-one internal resonance

Nonlinear positive position feedback control for mitigation of nonlinear vibrations

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