Nonlinear harmonic response characteristics and experimental investigation of cantilever hard-coating plate

Yang, Zhengxin; Han, Qunying; Chen, Y. G.; Jin, Zhihao

doi:10.1007/s11071-017-3433-1

Cited by 23 publications

(9 citation statements)

References 23 publications

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“…Cantilevered structural elements are present in a wide range of mechanical systems and civil structures [6,9,17,19,33,56]. They can be found in numerous engineering applications including, but not limited to, vibration energy harvesters, micro-gyroscopes, electromechanical systems, bio-inspired propulsion, and piezoelectric sensors and actuators [1,7,24,31,40,43,55,59].…”

Section: Introductionmentioning

confidence: 99%

Experimentally validated geometrically exact model for extreme nonlinear motions of cantilevers

2021

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A unique feature of flexible cantilevered beams, which is used in a range of applications from energy harvesting to bio-inspired actuation, is their capability to undergo motions of extremely large amplitudes. The well-known third-order nonlinear cantilever model is not capable of capturing such a behaviour, hence requiring the application of geometrically exact models. This study, for the first time, presents a thorough experimental investigation on nonlinear dynamics of a cantilever under base excitation in order to capture extremely large oscillations to validate a geometrically exact model based on the centreline rotation. To this end, a state-of-the-art in vacuo base excitation experimental set-up is utilised to excite the cantilever in the primary resonance region and drive it to extremely large amplitudes, and a high-speed camera is used to capture the motion. A robust image processing code is developed to extract the deformed state of the cantilever at each frame as well as the tip displacements and rotation. For the theoretical part, a geometrically exact model is developed based on the Euler–Bernoulli beam theory and inextensibility condition, while using Kelvin–Voigt material damping. To ensure accurate predictions, the equation of motion is derived for the centreline rotation and all terms are kept geometrically exact throughout the derivation and discretisation procedures. Thorough comparisons are conducted between experimental and theoretical results in the form of frequency response diagrams, time histories, motion snapshots, and motion videos. It is shown that the predictions of the geometrically exact model are in excellent agreement with the experimental results at both relatively large and extremely large oscillation amplitudes.

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Section: Introductionmentioning

confidence: 99%

Experimentally validated geometrically exact model for extreme nonlinear motions of cantilevers

2021

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“…Thus, as the basis of the nonlinear coupling vibrations for the blisk structures, the modal analysis is of great importance. Generally, three different methods were used to study the natural vibration characteristics of the blisk structures, namely, the reduced-order modeling (ROM) techniques [17][18][19], experiment methods [20,21] and numerical simulations [22,23]. The harmonic balance method [24], eigenmode method [25,26] and parameter identification method [27,28] were used to establish the reduced-order model of the blisk structures.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear and Dual-Parameter Chaotic Vibrations of Lumped Parameter Model in Blisk under Combined Aerodynamic Force and Varying Rotating Speed

Zhang

et al. 2021

Preprint

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In this paper, the nonlinear and dual-parameter chaotic vibrations are investigated for the blisk structure with the lumped parameter model under combined the aerodynamic force and varying rotating speed. The varying rotating speed and aerodynamic force are respectively simplified to the parametric and external excitations. The nonlinear governing equations of motion for the rotating blisk are established by using Hamilton’s principle. The free vibration and mode localization phenomena are studied for the tuning and mistuning blisks. Due to the mistuning, the periodic characteristics of the blisk structure are destroyed and uniform distribution of the energy is broken. It is found that there is a positive correlation between the mistuning variable and mode localization factor to exhibit the large vibration of the blisk in a certain region. The method of multiple scales is applied to derive four-dimensional averaged equations of the blisk under 1:1 internal and principal parametric resonances. The amplitude-frequency response curves of the blisk are studied, which illustrate the influence of different parameters on the bandwidth and vibration amplitudes of the blisk. Lyapunov exponent, bifurcation diagrams, phase portraits, waveforms and Poincare maps are depicted. The dual-parameter Lyapunov exponents and bifurcation diagrams of the blisk reveal the paths leading to the chaos. The influences of different parameters on the bifurcation and chaotic vibrations are analyzed. The numerical results demonstrate that the parametric and external excitations, rotating speed and damping determine the occurrence of the chaotic vibrations and paths leading to the chaotic vibrations in the blisk.

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“…Liew et al [19] discussed the nonlinear vibration behavior of cantilever plates with constant thickness based on the Mindlin plate theory. Yang et al [20] studied the nonlinear response characteristics and experiments of a cantilever hard-coating plate under transverse external excitation. The vibration response experiment agreed well with the numerical results.…”

Section: Introductionmentioning

confidence: 99%

Analysis of Nonlinear Vibrations and Dynamic Responses in a Trapezoidal Cantilever Plate Using the Rayleigh‐Ritz Approach Combined with the Affine Transformation

Tian

Yang

Zhao³

2019

Mathematical Problems in Engineering

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Nonlinear vibrations of a trapezoidal cantilever plate subjected to transverse external excitation are investigated. Based on von Karman large deformation theory, the Rayleigh-Ritz approach combined with the affine transformation is developed to obtain the nonlinear ordinary differential equation of a trapezoidal plate with irregular geometries. With the variation of geometrical parameters, there exists the 1:3 internal resonance for the trapezoidal plate. The amplitude-frequency formulations of the system in three different coupled conditions are derived by using multiple scales method for 1:3 internal resonance analysis. It is found that the strong coupling of two modes can change nonlinear stiffness behaviors of modes from hardening-spring to soft-spring characteristics. The detuning parameter and excitation amplitude have significant influence on nonlinear dynamic responses of the system. The bifurcation diagrams show that there exist the periodic, quasi-periodic, and chaotic motions for the trapezoidal cantilever plate in the 1:3 internal resonance cases and the nonlinear dynamic responses are dependent on the amplitude of excitation. The possible adverse dynamic behaviors and undesired resonance can be avoided by designing appropriate excitation and system parameters.

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Nonlinear harmonic response characteristics and experimental investigation of cantilever hard-coating plate

Cited by 23 publications

References 23 publications

Experimentally validated geometrically exact model for extreme nonlinear motions of cantilevers

Experimentally validated geometrically exact model for extreme nonlinear motions of cantilevers

Nonlinear and Dual-Parameter Chaotic Vibrations of Lumped Parameter Model in Blisk under Combined Aerodynamic Force and Varying Rotating Speed

Analysis of Nonlinear Vibrations and Dynamic Responses in a Trapezoidal Cantilever Plate Using the Rayleigh‐Ritz Approach Combined with the Affine Transformation

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