High-frequency vibrational control of principal parametric resonance of a nonlinear cantilever beam: Theory and experiment

Sahoo, Pradyumna Kumar; Chatterjee, Satyajit

doi:10.1016/j.jsv.2021.116138

Cited by 17 publications

(5 citation statements)

References 70 publications

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“…The theoretical predictions are backed up by experimental evidence for various physical systems, see e.g. [5,[15][16][17][18] and references cited there.…”

Section: Introductionmentioning

confidence: 88%

Strong nonlinearity and external high-frequency forcing for controlling effective mechanical stiffness: theory and experiment

Thomsen

Ebbehøj

2023

Nonlinear Dyn

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High-frequency excitation (HFE) can be used to change the effective stiffness of an elastic structure, and related quantities such as resonance frequencies, wave speeds, buckling loads, and equilibrium states. There are two ways to do this: By using parametric HFE (with or without nonlinearity), or by using external HFE along with strong nonlinearity. The first way, parametric stiffening, has been examined for many different systems, and analytical predictions exist that have been repeatedly confirmed against numerical simulation and laboratory experiments. The current work contributes results on the other way, external stiffening: Combining the method of direct separation of motions with results of a modified multiple scales approach, valid also for strong or even essential nonlinearity, quantitative measures of the stiffening effect is predicted for a generic 1-DOF system, and tested with generally good agreement against numerical simulation and laboratory experiments.

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“…The theoretical predictions are backed up by experimental evidence for various physical systems, see e.g. [5,[15][16][17][18] and references cited there.…”

Section: Introductionmentioning

confidence: 88%

Strong nonlinearity and external high-frequency forcing for controlling effective mechanical stiffness: theory and experiment

Thomsen

Ebbehøj

2023

Nonlinear Dyn

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“…Based on aerodynamics [45,46], the air drag forces acting on the mass particle in the x and y directions (in the global coordinate) can be simulated by [31,45,46]…”

Section: Calculation Of Quadratic Damping Force (Air Drag) For Large ...mentioning

confidence: 99%

“…Similarly, through theoretical and experimental approaches, Sahoo and Chatterjee [31] studied the high-frequency vibrational control method of principal parametric resonance of a nonlinear cantilever beam.…”

Section: Introductionmentioning

confidence: 99%

A Nonlinear Parametric Resonance Analysis of Planar Beam Structures Using Vector Form Intrinsic Finite Element Method

Shen

Que

2023

Preprint

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The parametric resonance of a frame structure may lead to a disastrous consequence. Structural engineers need a straightforward and practical method to calculate the large nonlinear parametric resonance responses of the frame structure for assessing structural safety. This paper reports on a new Vector Form Intrinsic Finite Element (VFIFE) method to analyse the nonlinear parametric resonance of planar beam structures. By taking into account the geometric stiffness effect of the internal axial force for the frame element, a relationship between internal nodal forces and deformation components is firstly established based on the VFIFE principle and the parametric resonance mechanism of frame structures. The VFIFE scheme is then developed to analyse the nonlinear parametric resonance of frame structures. To demonstrate the efficacy of this approach, a simply-supported beam is used as a numerical example, and the resulting VFIFE calculations are compared to the solutions obtained by current analytical methods. A parametric resonance test of the cantilever beam is conducted to verify the applicability of the VFIFE method. The numerical results show that this approach can overcome the limitations of existing analytical methods, well simulate the nonlinear phenomena of parametric resonances, and produce predictions that are consistent with experimental observations. The numerical stability boundary of parametric resonance agrees well with the experimental boundary. Possible causes of deviations between the numerical and experimental results are discussed. The proposed VFIFE method is a simple and effective means of analyzing the stability and nonlinear responses of parametric resonance of planar beam structures.

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“…First, input nonlinearity is often encountered in vibration control systems, which may severely limit the performance of the controller and cause damage itself [15]. In order to solve this problem, many scholars have proposed their methods [16][17][18][19][20][21][22][23]. In [20], Liu et al presented a boundary control method based on the original PDEs to regulate the hose's vibration and handle the effect of the input constraint.…”

Section: Introductionmentioning

confidence: 99%

Adaptive neural network control of multiple‐sectioned flexible riser with time‐varying output constraint and input nonlinearity

Liu,

Yao,

Liu

2023

Asian Journal of Control

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In this paper, an adaptive neural network controller is proposed for vibration suppression of a multisectional riser system with unknown boundary disturbance, time‐varying asymmetric output constraint, and input nonlinearity. The considered riser system is composed of a continuous connection of several different pipes, and its dynamic models are represented by a set of multiple continuously connected partial differential equations (PDEs) and an ordinary differential equation (ODE) at the top boundary. Considering input nonlinearity, external disturbance, and system uncertainty, radial basis function (RBF) neural networks are adopted to eliminate the effect of these uncertain terms. Besides, a barrier Lyapunov function is employed to guarantee the restrictions. With the proposed boundary control, the stability of the closed‐loop system is proved and simulations are given to illustrate the well performance of the proposed control strategy.

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High-frequency vibrational control of principal parametric resonance of a nonlinear cantilever beam: Theory and experiment

Cited by 17 publications

References 70 publications

Strong nonlinearity and external high-frequency forcing for controlling effective mechanical stiffness: theory and experiment

Strong nonlinearity and external high-frequency forcing for controlling effective mechanical stiffness: theory and experiment

A Nonlinear Parametric Resonance Analysis of Planar Beam Structures Using Vector Form Intrinsic Finite Element Method

Adaptive neural network control of multiple‐sectioned flexible riser with time‐varying output constraint and input nonlinearity

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