Identification method for backbone curve of cantilever beam using van der Pol-type self-excited oscillation

2020 ◽  
Author(s):  
Shinpachiro Urasaki ◽  
Hiroshi Yabuno
Keyword(s):  
Cantilever Beam ◽  
Backbone Curve ◽  
Van Der Pol ◽  
Identification Method ◽  
Excited Oscillation

Stiffness Sensor for Cubic Nonlinear Elasticity Using Nonlinear Self-Excited Oscillation

2014 ◽  
Vol 136 (3) ◽  
Author(s):  
Yosuke Kokubun ◽  
Hiroshi Yabuno
Keyword(s):  
Nonlinear Elasticity ◽  
Response Amplitude ◽  
Feedback Gain ◽  
Nonlinear Stiffness ◽  
Nonlinear Feedback ◽  
Backbone Curve ◽  
Van Der Pol ◽  
Stiffness Sensor ◽  
Excited Oscillation ◽  
Measurement Object

The present paper develops a nonlinear stiffness sensor for measuring cubic nonlinear elasticity. The measurement system consists of a vibrator with a control circuit. We apply linear-plus-nonlinear feedback to actuate the vibrator attached to a measurement object for inducing van der Pol type self-excited oscillation so that the response amplitude of the oscillation can be set arbitrarily by changing the nonlinear feedback gain. We focus on the fact that the nonlinear elasticity of the measurement object causes a natural frequency shift related to the magnitude of vibration amplitude of the vibrator. We can set the response amplitude to various values by changing the nonlinear feedback gain and measuring the shift of the response frequency depending on the magnitude of the response amplitude. As a result, based on the bend of the experimentally obtained backbone curve, the nonlinear elasticity of the measurement object is identified.

Hardness Detection Sensor for Cubic Nonlinear Elasticity Using Nonlinear Self-Excited Oscillation

2013 ◽  
Author(s):  
Yosuke Kokubun ◽  
Hiroshi Yabuno ◽  
Masaharu Kuroda ◽  
Yasuyuki Yamamoto
Keyword(s):  
Nonlinear Elasticity ◽  
Vibration Amplitude ◽  
Measurement Method ◽  
Response Amplitude ◽  
Feedback Gain ◽  
Nonlinear Feedback ◽  
Backbone Curve ◽  
Van Der Pol ◽  
Response Frequency ◽  
Excited Oscillation

This paper proposes a measurement method of cubic non-linear elasticity. The measurement system consists of a vibrator and a control circuit. We apply a nonlinear feedback to actuate the vibrator for inducing van der Pol type self-excited oscillation, so that the response amplitude of the oscillation can be arbitrarily set by changing the nonlinear feedback gain. We focus on the fact that the nonlinear elasticity causes a natural frequency shift related to the vibration amplitude of the object. We can set the response amplitude various values by changing the nonlinear feedback gain and measure the shift of the response frequency depending on the magnitude of the response amplitude. As a result, the bend of the backbone curve reflecting the nonlinear elasticity of the object is obtained.

Nonlinear Analysis of a Self-Excited Cantilever Beam

2005 ◽  
Author(s):  
Hiroyuki Kaneko ◽  
Hiroshi Yabuno ◽  
Masaharu Kuroda
Keyword(s):  
Cantilever Beam ◽  
Positive Feedback ◽  
Response Amplitude ◽  
The Self ◽  
Steady State Response ◽  
Nonlinear Feedback ◽  
Van Der Pol ◽  
Restoring Force ◽  
State Response ◽  
Excited Oscillation

In this study, we investigate the dynamics of a self-excited cantilever beam by a positive feedback proportional to the velocity. In particular, we focus on the response amplitude in the self-excited oscillation and analyze the effect of the nonlinear component of the restoring force in the cantilever. It is theoretically and experimentally clarified that the response amplitude grows with time under the positive feedback proportional to the velocity (positive feedback). Furthermore, van der Pol type self-excited cantilever beam is designed by applying the nonlinear feedback proportional to the squared deflection and the velocity, and the steady state response is realized in the cantilever beam. The theoretically predicted effects of the nonlinear feedback are qualitatively confirmed by performing some experiments.

Parameter Identification of a Cantilever Beam Immersed in Viscous Fluids With Potential Applications to the Probe Calibration of Atomic Force Microscopes

2009 ◽  
Author(s):  
Wenlung Li ◽  
S. P. Tseng
Keyword(s):  
Parameter Identification ◽  
Natural Frequency ◽  
Cantilever Beam ◽  
Present Method ◽  
Present Report ◽  
Excitation Frequency ◽  
Spring Constant ◽  
Target System ◽  
Phase Lag ◽  
Identification Method

The main objective of the report is to present a new identification method has been derived for single-degree, base-excited systems. The system is actually to mimic a probe of cantilever type of AFMs. In fact, the idea of the present report was initiated by needs for in situ spring constant calibration for such probe systems. Calibration processes can be treated as parameter identification for the stiffness of the probe before it is used. However, sine a real probe is too small to be seen by bare eyes and too costly to verify, a cantilever beam was adopted to replace it during the study. The present method starts with giving a chirp excitation to the target system, and to lock the damped natural frequency. Once the damped natural frequency is obtained, it is possible to locate the frequency at which the phase lag is equal to π/2. From which, the excitation frequency is then purposely changed to that frequency and the corresponding steady-state responses are measured. In the meantime, the system dissipative energy or power may also need to be stored. In fact, the present identification formulation is to express the spring constant of the target systems in terms of two measurable parameters: the phase angle and the system damping. The former can be computed from the damped natural frequency while the latter can be identified along with measuring the input power. The novel formulation is then numerically simulated using the Simulink toolbox of MATLAB. The simulation results clearly showed the current identification method can work with good accuracy. Following the numerical simulation, experimental measurements were also carried out by a cantilever beam that its free end was immersed to viscid fluids. The fluids of different viscosity were used to mimic the environments of a probe in use. The experimental results again substantiated the correctness of the present method. Thus it is accordingly concluded that the new recognition algorithm can be applied with confidence.

656 Self-excited oscillation cantilever beam

2004 ◽  
Vol 2004 (0) ◽  
pp. _656-1_-_656-4_
Author(s):  
Hiroyuki KANEKO ◽  
Hiroshi YABUNO ◽  
Masaharu KURODA ◽  
Nobuharu AOSHIMA
Keyword(s):  
Cantilever Beam ◽  
Excited Oscillation

scholarly journals Self- excited oscillation under the influence of non - linear frictions

1982 ◽  
Vol 4 (3) ◽  
pp. 7-10
Author(s):  
Nguyen Van Dao
Keyword(s):  
Equilibrium Position ◽  
The Self ◽  
Van Der Pol Oscillator ◽  
Van Der Pol ◽  
Excited System ◽  
Non Linear ◽  
Excited Oscillation

In this article the influence of friction R1, R2 on Van der Pol oscillator is considered. It turned out that the mentioned frictions decrease the amplitude of self – excited oscillations and they stabilize the equilibrium position of the self – excited system.

scholarly journals Piezoelectric Power Generation from the Vortex-Induced Vibrations of a Semi-Cylinder Exposed to Water Flow

Energies ◽  
2021 ◽  
Vol 14 (21) ◽  
pp. 6964
Author(s):  
Christina Hamdan ◽  
John Allport ◽  
Azadeh Sajedin
Keyword(s):  
Power Generation ◽  
Cantilever Beam ◽  
Bluff Body ◽  
Design Parameters ◽  
Van Der Pol ◽  
Element Analysis ◽  
Water Stream ◽  
Optimization Study ◽  
Vortex Induced Vibrations ◽  
Van Der Pol Model

The aim of this work is to design a piezoelectric power generation system that extracts power from the vibration of a cantilever beam. A semi-cylinder placed in a water stream and attached to the beam is excited into vortex-induced vibrations (VIV), which triggers the piezoelectric deformation. The mechanical system is modelled using parametric equations based on Hamilton’s extended principle for the cantilever beam and the modified Van der Pol model for the bluff body (the semi-cylinder). These equations are simulated using the MATLAB software. The dimensions of the model, the flow velocity and the resistance are treated as design parameters and an optimization study is conducted using MATLAB to determine the combination of optimal values at which maximum power is extracted. The key findings of this research lie in the identification of the effect of changing the design parameters on output power. In addition to the numerical simulation, a finite element analysis is carried out on the bluff body and the hydrodynamic forces and velocity profiles are observed. It is determined that the vibration amplitudes increase with increasing diameter of the bluff body, length of the bluff body and water velocity.

scholarly journals An identification method of the weak link of stiffness for cantilever beam structure

2020 ◽  
Vol 103 (3) ◽  
pp. 003685042095267
Author(s):  
Tieneng Guo ◽  
Lingjun Meng ◽  
Jinxuan Cao ◽  
Chunsheng Bai
Keyword(s):  
Machine Tool ◽  
Cantilever Beam ◽  
Weak Link ◽  
Difficult Problem ◽  
Beam Structure ◽  
Identification Method ◽  
Acceleration Data ◽  
Cantilever Structure ◽  
Practical Engineering ◽  
Value Decomposition

To find the weak link of the structural stiffness is important to improve machine tool stiffness. However, how to overcome the static deformation with difficulty acquisition is a difficult problem in machine tool structure. The article takes the cantilever beam structure as a numerical example, the weak link is modeled as EA reduction in stiffness. Thorough finite element simulations are performed to assess the robustness and limitations of the method in several scenarios with single and multiple weaknesses. The sensors are used to acquire the acceleration data, the structural modal parameters are obtained by the singular value decomposition technique, and the dynamic characteristics are systematically reconstructed by using the modal state-space method to obtain static stiffness. Then, an identification method proposed by measured data and reconstructed data to identify the weak link of stiffness of the cantilever structure. Furthermore, the comparison of numerical and experimental results validate the correctness and effectiveness of this method. The research has certain practical engineering value and provides an accurate guidance for the optimization of machine tool stiffness.

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