Frequency response of variants of a cantilever beam

2012 ◽  
Author(s):  
Almudena Rivadeneyra ◽  
Juan A. Lopez-Villanueva ◽  
Rosemary O'Keeffe ◽  
Nathan Jackson ◽  
Mike O'Neill ◽  
...  
Keyword(s):  
Frequency Response ◽  
Cantilever Beam

scholarly journals Experimental Identification of Backbone Curves of Strongly Nonlinear Systems by Using Response-Controlled Stepped-Sine Testing (RCT)

Vibration ◽  
2020 ◽  
Vol 3 (3) ◽  
pp. 266-280
Author(s):  
Taylan Karaağaçlı ◽  
H. Nevzat Özgüven
Keyword(s):  
Frequency Response ◽  
Case Studies ◽  
Cantilever Beam ◽  
Force Control ◽  
Turning Points ◽  
Nonlinear Structures ◽  
Response Curves ◽  
Strongly Nonlinear ◽  
Actuation Mechanism ◽  
Backbone Curves

In stepped-sine testing of strongly nonlinear structures with the classical force-control strategy, corrective force perturbations of a standard controller used to capture the reference signal in the proximity of turning points of frequency response curves may often lead to a premature jump before reaching the actual resonance peak. Accordingly, a classical force-control approach is not suitable to identify backbone curves of strongly nonlinear structures. This paper shows that currently available commercial modal test equipment can accurately identify backbone curves of strongly nonlinear structures by using Response-Controlled stepped-sine Testing (RCT) and the Harmonic Force Surface (HFS) concept, both recently proposed by the authors. These methods can be applied to systems where there are many nonlinearities at several different (and even unknown) locations. However, these techniques are not applicable to systems where internal resonances occur. In RCT, the displacement amplitude of the driving point, rather than the amplitude of the applied force, is kept constant during the stepped-sine testing. Spectra of the harmonic excitation force measured at several different displacement amplitude levels are used to build up a smooth HFS. Isocurves of constant amplitude forcing on the HFS lead to constant-force frequency response curves with accurately measured turning points and unstable branches (if there are any), which makes it possible to identify backbone curves of strongly nonlinear structures experimentally. The validation of the proposed approach is demonstrated with numerical and experimental case studies. A five degree-of-freedom (DOF) lumped system with five cubic stiffness elements, which create strong conservative nonlinearity, is used in the numerical example. Experimental case studies consist of a cantilever beam and a control fin actuation mechanism of a real missile structure. The cantilever beam is supported at its free-end by two metal strips constrained at both ends to create strong stiffening nonlinearity. The control fin actuation mechanism exhibits very complex and strong nonlinearity due to backlash and friction.

Amplitude-Frequency Response of Superharmonic Resonance of Third Order of Electrostatically Actuated MEMS Cantilever Resonators

2019 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Christopher Reyes
Keyword(s):  
Frequency Response ◽  
Cantilever Beam ◽  
Multiple Scales ◽  
Electrostatic Force ◽  
Beam Theory ◽  
Driving Frequency ◽  
Third Order ◽  
Reduced Order ◽  
Superharmonic Resonance ◽  
Amplitude Frequency Response

Abstract This work deals with amplitude frequency response of MEMS cantilever resonators undergoing superharmonic resonance of third order. The cantilever resonator is parallel to a ground plate and under alternating current (AC) voltage that excites the cantilever into vibrations. The driving frequency of the AC voltage is near one sixth of the first natural frequency of the cantilever beam resulting into superharmonic resonance of third order. The cantilever beam is modeled using Euler-Bernoulli beam theory. The electrostatic force is modeled using Palmer’s formula to include the fringe effect. In order to investigate the amplitude frequency behavior of the system reduced order models (ROMs) are developed. Three methods are used to solve these ROMs they are 1) the method of multiple scales (MMS) for ROM with one mode of vibration, 2) homotopy analysis method (HAM) for ROM with one mode of vibration, and 3) direct numerical integration for 2 modes of vibration Reduced Order Model (2T ROM) producing time responses of the tip of the cantilever resonator. In this work the limitations of MMS and HAM are highlighted when considering large voltage values i.e hard excitations. For large voltage values MMS and HAM cannot accurately predict the amplitude frequency response; the results from 2T ROM time responses disagree significantly with the MMS and HAM solutions. The effect of voltage on the frequency response is investigated. As the voltage values in the system increase the responses shift to lower frequencies and larger amplitudes.

Nonlinear Vibration of a Magneto-Elastic Cantilever Beam With Tip Mass

2009 ◽  
Vol 131 (2) ◽  
Author(s):  
Barun Pratiher ◽  
Santosha K. Dwivedy
Keyword(s):  
Magnetic Field ◽  
Frequency Response ◽  
Cantilever Beam ◽  
Multiple Scales ◽  
Flexible Structures ◽  
Nonlinear Damping ◽  
Equation Of Motion ◽  
Response Curves ◽  
Temporal Form ◽  
Tip Mass

In this work the effect of the application of an alternating magnetic field on the large transverse vibration of a cantilever beam with tip mass is investigated. The governing equation of motion is derived using D’Alembert’s principle, which is reduced to its nondimensional temporal form by using the generalized Galerkin method. The temporal equation of motion of the system contains nonlinearities of geometric and inertial types along with parametric excitation and nonlinear damping terms. Method of multiple scales is used to determine the instability region and frequency response curves of the system. The influences of the damping, tip mass, amplitude of magnetic field strength, permeability, and conductivity of the beam material on the frequency response curves are investigated. These perturbation results are found to be in good agreement with those obtained by numerically solving the temporal equation of motion and experimental results. This work will find extensive applications for controlling vibration in flexible structures using a magnetic field.

scholarly journals Mixed controller (IRC+NSC) involved in the harmonic vibration response cantilever beam model

2020 ◽  
pp. 002029402096424
Author(s):  
Hany Samih Bauomy ◽  
Ashraf Taha EL-Sayed
Keyword(s):  
Frequency Response ◽  
Cantilever Beam ◽  
Perturbation Technique ◽  
Control Technique ◽  
Beam Model ◽  
Lumped Mass ◽  
Response Curves ◽  
Before And After ◽  
Time Histories ◽  
Measured System

This manuscript aims for improving the vibrational behaviors of a cantilever beam model through an intermediate lumped mass via offering a new control methodology to suppress for such high oscillations of the system. The equation of the considered cantilever beam structure is gained applying Euler–Lagrange technique. Accordingly, the considered model is modified by mixing Integral Resonant Control (IRC) along with the Nonlinear Saturation Controller (NSC) as anew controller to the considered system. Due to the recommended control technique, the modified system model is studied and analyzed by the perturbation technique. Time histories figures of the measured system plus the new controller are involved to display the response before and after control. The frequency response figures of the modified model before and after new controller near simultaneous condition [Formula: see text] are gained. Each frequency-response curves have stable and unstable regions are determined numerically. Numerical results show the vibrations of the system are eliminated when adding combined IRC and NSC controllers. Finally, numerical outcomes are performed that illustrated an excellent agreement with the analytical ones. Comparison between this paper and recent papers of the cantilever beam are done.

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