Nonlinear Dynamics of a Transversely Excited Flexible Cantilever Beam

1995 ◽  
Author(s):  
Mahmood Tabaddor ◽  
Ali H. Nayfeh
Keyword(s):  
Nonlinear Dynamics ◽  
Natural Frequency ◽  
Cantilever Beam ◽  
Experimental Results ◽  
Modal Interactions ◽  
Frequency Sweep ◽  
Second Mode ◽  
Fourth Mode

Abstract Some experimental results concerning the nonlinear dynamics of a transversely excited beam are presented. The excitation is harmonic. A frequency sweep around the fourth natural frequency of the beam reveals some interesting modal interactions. The first phenomenon is the transfer of energy from the fourth mode, approximately 33.10 Hz, to the first mode, approximately 0.70 Hz. This interaction involves modulation of the amplitude and phase of the fourth mode. The second interaction involves the participation of the fourth mode and the second mode, approximately 5.80 Hz. The mechanism by which the second mode is activated as yet remains unidentified.

Nonlinear Resonances in a Flexible Cantilever Beam

1994 ◽  
Vol 116 (4) ◽  
pp. 480-484 ◽  
Author(s):  
T. J. Anderson ◽  
B. Balachandran ◽  
A. H. Nayfeh
Keyword(s):  
Natural Frequency ◽  
Cantilever Beam ◽  
Natural Frequencies ◽  
Excitation Frequency ◽  
Continuous Systems ◽  
Modal Interactions ◽  
The Third ◽  
First Case ◽  
Second Mode ◽  
Band Limited

An experimental investigation into the response of a nonlinear continuous systems with many natural frequencies in the range of interest is presented. The system is a flexible cantilever beam whose first four natural frequencies are 0.65 Hz, 5.65 Hz, 16.19 Hz, and 31.91 Hz, respectively. The four natural frequencies correspond to the first four flexural modes. The fourth natural frequency is about fifty times the first natural frequency. Three cases were considered with this beam. For the first case, the beam was excited with a periodic base motion along its axis. The excitation frequency fe was near twice the third natural frequency f3, which for a uniform isotropic beam corresponds to approximately the fourth natural frequency f4. Thus the third mode was excited by a principal parametric resonance (i.e., fe ≈ 2f3) and the fourth mode was excited by an external resonance (i.e., fe ≈ f4) due to a slight curvature in the beam. Modal interactions were observed involving the first, third, and fourth modes. For the second case, the beam was excited with a band-limited random base motion transverse to the axis of the beam. The first and second modes were excited through nonlinear interactions. For the third case, the beam was excited with a base excitation along the axis of the beam at 138 Hz. The corresponding response was dominated by the second mode. The tools used to analyze the motions include Fourier spectra, Poincare´ sections, and dimension calculations.

Experimental Verification of the Importance of The Nonlinear Curvature in the Response of a Cantilever Beam

1996 ◽  
Vol 118 (1) ◽  
pp. 21-27 ◽  
Author(s):  
T. J. Anderson ◽  
A. H. Nayfeh ◽  
B. Balachandran
Keyword(s):  
Analytical Model ◽  
Cantilever Beam ◽  
Theoretical Investigation ◽  
Experimental Verification ◽  
Dominant Role ◽  
Experimental Results ◽  
Parametrically Excited ◽  
Second Mode ◽  
Quadratic Damping ◽  
Theoretical Results

An experimental and theoretical investigation into the first- and second-mode responses of a parametrically excited slender cantilever beam is presented. Inclusion of quadratic damping in the analytical model significantly improves the agreement between the experimental and theoretical results. In addition, the experimental results verify that the often ignored nonlinear curvature terms play a dominant role in the response of the first mode and that the nonlinear inertia terms play a dominant role in the response of the second mode.

Vibration Characteristics of Rotating Thin Disks—Part I: Experimental Results

2012 ◽  
Vol 79 (4) ◽  
Author(s):  
Ramin M. H. Khorasany ◽  
Stanley G. Hutton
Keyword(s):  
Frequency Response ◽  
Natural Frequency ◽  
Linear Theory ◽  
Lateral Force ◽  
Vibration Characteristics ◽  
Experimental Results ◽  
Rotating Disks ◽  
Critical Speeds ◽  
Applied Forces ◽  
Thin Disks

Analysis of the linear vibration characteristics of unconstrained rotating isotropic thin disks leads to the important concept of “critical speeds.” These critical rotational speeds are of interest because they correspond to the situation where a natural frequency of the rotating disk, as measured by a stationary observer, is zero. Such speeds correspond physically to the speeds at which a traveling circumferential wave, of shape corresponding to the mode shape of the natural frequency being considered, travel around the disk in the absence of applied forces. At such speeds, according to linear theory, the blade may respond as a space fixed stationary wave and an applied space fixed dc force may induce a resonant condition in the disk response. Thus, in general, linear theory predicts that for rotating disks, with low levels of damping, large responses may be encountered in the region of the critical speeds due to the application of constant space fixed forces. However, large response invalidates the predictions of linear theory which has neglected the nonlinear stiffness produced by the effect of in-plane forces induced by large displacements. In the present paper, experimental studies were conducted in order to measure the frequency response characteristics of rotating disks both in an idling mode as well as when subjected to a space fixed lateral force. The applied lateral force (produced by an air jet) was such as to produce displacements large enough that non linear geometric effects were important in determining the disk frequencies. Experiments were conducted on thin annular disks of different thickness with the inner radius clamped to the driving arbor and the outer radius free. The results of these experiments are presented with an emphasis on recording the effects of geometric nonlinearities on lateral frequency response. In a companion paper (Khorasany and Hutton, 2010, “Vibration Characteristics of Rotating Thin Disks—Part II: Analytical Predictions,” ASME J. Mech., 79(4), p. 041007), analytical predictions of such disk behavior are presented and compared with the experimental results obtained in this study. The experimental results show that in the case where significant disk displacements are induced by a lateral force, the frequency characteristics are significantly influenced by the magnitude of forced displacements.

Study on a Novel MEMS High G Acceleration Sensor

2012 ◽  
Vol 490-495 ◽  
pp. 499-503
Author(s):  
Ping Li ◽  
Yun Bo Shi ◽  
Jun Liu ◽  
Shi Qiao Gao
Keyword(s):  
Resonant Frequency ◽  
Natural Frequency ◽  
Impact Load ◽  
Hopkinson Bar ◽  
Experimental Results ◽  
Structure Parameters ◽  
Acceleration Sensor ◽  
Piezoresistive Effect ◽  
Sensor Structure ◽  
The Impact

This paper presents a novel MEMS high g acceleration sensor based on piezoresistive effect. For the designed sensor structure, the formula of stress, natural frequency and damping was derived in theory, and the resonant frequency can up to 500kHz. After the structure parameters were designed, the sensor was fabricated by the standard processing technology, and the sensitivity was tested by Hopkinson bar. According to the experimental results, the sensitivity of the high g acceleration sensor is 0.125μV/g at the impact load of 164,002g.

Stabilizing Effect of Yawning on Nasal Cycle

2020 ◽  
pp. 1-3
Keyword(s):  
Left Nostril ◽  
The Third ◽  
Nasal Cycle ◽  
Air Resistance ◽  
Second Mode ◽  
Stabilizing Effect ◽  
The Right ◽  
Fourth Mode

The dominant passability of the left or right nostril in terms of nasal air resistance can be classified into 4 main modes. In the first mode, both nostrils are closed and have equal and low air passability. In the second mode, the passability of the right nostril is higher than the left. In the third mode, the passability of the left nostril is higher than the right. In the fourth mode, both nostrils are open and passability of nostrils is equal and high. The first and fourth modes are unstable (with duration- minutes). The second and third modes are stable (with duration-hours). Author presents a yawning as physiological reflex leading to transition from unstable to stable modes.

Modal interactions in the nonlinear dynamics of a beam–cable–beam

2019 ◽  
Vol 96 (4) ◽  
pp. 2547-2566 ◽  
Author(s):  
Vincenzo Gattulli ◽  
Marco Lepidi ◽  
Francesco Potenza ◽  
Umberto Di Sabatino
Keyword(s):  
Nonlinear Dynamics ◽  
Modal Interactions

Coupling Effects on Synchronizability of Two-Layer Network's Projective Outer Synchronization

2017 ◽  
Vol 873 ◽  
pp. 353-357
Author(s):  
Bo Yu Feng ◽  
Zhi Hao Zhang
Keyword(s):  
Nonlinear Dynamics ◽  
Mathematical Model ◽  
Complex Network ◽  
Simulation Experiment ◽  
Small World ◽  
Experimental Results ◽  
Coupling Effects ◽  
Network Synchronization ◽  
Numerical Examples ◽  
Outer Synchronization

Based on nonlinear dynamics theory and knowledge of complex network, this paper expanded the range of two-layer network synchronization to projective outers synchronization. A mathematical model was constructed and feasibility of synchronization was demonstrated. Then we improved the model in order to study the function of different couplings [1]. Numerical examples are examined to compare the synchronizability of projective outer synchronization with different couplings. A rule called "outer small-world effect" was found due to simulation experiment. Finally, some instances were used to explain experimental results.

Nonlinear Dynamics of a Taut String with Material Nonlinearities

2000 ◽  
Vol 123 (1) ◽  
pp. 53-60 ◽  
Author(s):  
M. J. Leamy ◽  
O. Gottlieb
Keyword(s):  
Nonlinear Dynamics ◽  
Dynamic Response ◽  
Natural Frequency ◽  
Continuum Mechanics ◽  
Finite Deformation ◽  
Multiple Scales ◽  
String Model ◽  
Taut String ◽  
Linear Material ◽  
Nonlinear String

A spatial string model incorporating a nonlinear (and nonconservative) material law is proposed using finite deformation continuum mechanics. The resulting model is shown to reduce to the classical nonlinear string when a linear material law is used. The influence of material nonlinearities on the string’s dynamic response to excitation near a transverse natural frequency is shown to be small due to their appearance at high orders only. Material nonlinearities appear at low order in the equations for excitation near a longitudinal natural frequency, and a solution for this case is developed by applying a second order multiple scales method directly to the partial differential equations. The material nonlinearities are found to influence both the degree of nonlinearity in the response and its softening or hardening nature.

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.

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