Time-Varying Frequency Formula for the Purely Nonlinear Damped Oscillator

2014 ◽  
Author(s):  
Mohammad A. AL-Shudeifat
Keyword(s):  
Instantaneous Frequency ◽  
Nonlinear Oscillator ◽  
Analytical Formula ◽  
Initial Energy ◽  
Physical Parameters ◽  
Frequency Change ◽  
Nonlinear Frequency ◽  
Time Varying ◽  
Time Varying Frequency ◽  
Damped Oscillator

The frequency of the purely nonlinear and non-conservative oscillator is a time-varying quantity due to the presence of damping. For the nonlinear oscillator addressed here, only cubic-power stiffness nonlinearity is considered. The nonlinear frequency of the conservative nonlinear oscillator is dependent on the initial energy induced into the system. However, for the non-conservative and purely nonlinear oscillator, the instantaneous frequency is dependent on the instantaneous energy of the system. Consequently, the exact amplitude decay formula obtained in a recent publication for such oscillator is accurately applied here to obtain an accurate analytical formula for the time-varying frequency of the considered system. Excellent agreement between the results obtained by the new time-varying frequency formula presented here and both numerical simulation and wavelet transform has been clearly observed. This analytical formula is found to be accurate in identifying the instantaneous frequency change of the system regardless of its physical parameters and the initial input energies.

scholarly journals Instantaneous Frequency Identification Using Adaptive Linear Chirplet Transform and Matching Pursuit

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
Chang Xu ◽  
Cong Wang ◽  
Jingbo Gao
Keyword(s):  
Instantaneous Frequency ◽  
Matching Pursuit ◽  
Vibration Signal ◽  
High Time Resolution ◽  
Nonlinear Frequency ◽  
Time Varying ◽  
Identification Method ◽  
Chirplet Transform ◽  
Comparison Results ◽  
Frequency Identification

An instantaneous frequency identification method of vibration signal based on linear chirplet transform and Wigner-Ville distribution is presented. This method has an obvious advantage in identifying closely spaced and time-varying frequencies. The matching pursuit algorithm is employed to select optimal chirplets, and a modified version of chirplet transform is presented to estimate nonlinear varying frequencies. Because of the high time resolution, the modified chirplet transform is superior to the original method. The proposed method is applied to time-varying systems with both linear and nonlinear varying stiffness and systems with closely spaced modes. A wavelet-based identification method is simulated to compare with the proposed method, with the comparison results showing that the chirplet-based method is effective and accurate in identifying both time-varying and closely spaced frequencies. A bat echolocation signal is used to verify the effectiveness of the modified chirplet transform. The result shows that it will significantly increase the accuracy of nonlinear frequency trajectory identification.

scholarly journals Estimating the Instantaneous Frequency of Linear and Nonlinear Frequency Modulated Radar Signals—A Comparative Study

Sensors ◽  
2021 ◽  
Vol 21 (8) ◽  
pp. 2840
Author(s):  
Hubert Milczarek ◽  
Czesław Leśnik ◽  
Igor Djurović ◽  
Adam Kawalec
Keyword(s):  
Instantaneous Frequency ◽  
Early Warning Systems ◽  
Vital Role ◽  
Estimation Methods ◽  
Radar Signal ◽  
Nonlinear Frequency ◽  
Modulation Recognition ◽  
Electronic Warfare ◽  
Time Frequency ◽  
Radar Signals

Automatic modulation recognition plays a vital role in electronic warfare. Modern electronic intelligence and electronic support measures systems are able to automatically distinguish the modulation type of an intercepted radar signal by means of real-time intra-pulse analysis. This extra information can facilitate deinterleaving process as well as be utilized in early warning systems or give better insight into the performance of hostile radars. Existing modulation recognition algorithms usually extract signal features from one of the rudimentary waveform characteristics, namely instantaneous frequency (IF). Currently, there are a small number of studies concerning IF estimation methods, specifically for radar signals, whereas estimator accuracy may adversely affect the performance of the whole classification process. In this paper, five popular methods of evaluating the IF–law of frequency modulated radar signals are compared. The considered algorithms incorporate the two most prevalent estimation techniques, i.e., phase finite differences and time-frequency representations. The novel approach based on the generalized quasi-maximum likelihood (QML) method is also proposed. The results of simulation experiments show that the proposed QML estimator is significantly more accurate than the other considered techniques. Furthermore, for the first time in the publicly available literature, multipath influence on IF estimates has been investigated.

scholarly journals Confinement of Vibrations in Variable-Geometry Nonlinear Flexible Beam

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
W. Gafsi ◽  
F. Najar ◽  
S. Choura ◽  
S. El-Borgi
Keyword(s):  
Passive Control ◽  
Inverse Eigenvalue Problem ◽  
Beam Dynamics ◽  
Mode Shapes ◽  
Physical Parameters ◽  
Geometrical Parameters ◽  
Flexible Beam ◽  
Beam Model ◽  
Nonlinear Frequency ◽  
Nonlinear Beam

In this paper, we propose a novel strategy for controlling a flexible nonlinear beam with the confinement of vibrations. We focus principally on design issues related to the passive control of the beam by proper selection of its geometrical and physical parameters. Due to large deflections within the regions where the vibrations are to be confined, we admit a nonlinear model that describes with precision the beam dynamics. In order to design a set of physical and geometrical parameters of the beam, we first formulate an inverse eigenvalue problem. To this end, we linearize the beam model and determine the linearly assumed modes that guarantee vibration confinement in selected spatial zones and satisfy the boundary conditions of the beam to be controlled. The approximation of the physical and geometrical parameters is based on the orthogonality of the assumed linear mode shapes. To validate the strategy, we input the resulting parameters into the nonlinear integral-partial differential equation that describes the beam dynamics. The nonlinear frequency response curves of the beam are approximated using the differential quadrature method and the finite difference method. We confirm that using the linear model, the strategy of vibration confinement remains valid for the nonlinear beam.

scholarly journals The interactions between an atom and a field with a time-varying frequency

2004 ◽  
Vol 53 (7) ◽  
pp. 2139
Author(s):  
Xu Jing-Ping ◽  
Yang Ya-Ping
Keyword(s):  
Time Varying ◽  
Time Varying Frequency
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