scholarly journals Digital Filter Frequency Response And Eigenfunctions: An Opportunity To Reinforce Linear System Concepts

2020 ◽  
Author(s):  
Gregory M. Dick
Keyword(s):  
Linear System ◽  
Frequency Response ◽  
Digital Filter ◽  
Filter Frequency

Digital-filter frequency response

1969 ◽  
Vol 5 (10) ◽  
pp. 210-211
Author(s):  
A.C. Davies
Keyword(s):  
Frequency Response ◽  
Digital Filter ◽  
Filter Frequency

Nonlinear Modeling of Cracked Beams for Impedance Based Structural Health Monitoring

2017 ◽  
Author(s):  
Naserodin Sepehry ◽  
Firooz Bakhtiari-Nejad ◽  
Mahnaz Shamshirsaz ◽  
Weidong Zhu
Keyword(s):  
Structural Health Monitoring ◽  
Linear System ◽  
Frequency Response ◽  
Frequency Domain ◽  
Health Monitoring ◽  
Impedance Method ◽  
Breathing Crack ◽  
Electromechanical Impedance ◽  
Structural Health ◽  
System Equations

One of the main objectives of the structural health monitoring by piezoelectric wafer active sensor (PWAS) using electromechanical impedance method is continuously damage detection applications. In present work impedance method of beam structure is considered and the effect of early crack using breathing crack modeling is studied. In order to model the effect of a crack in beam, the beam is connected with a rotational spring in crack location. The Rayleigh–Ritz method is used to generate ordinary differential equation of cracked beam. Firstly, only open crack is considered that this is leads to linear system equation. In linear system, time domain system equations are converted to frequency domain, and then impedance of PWAS in frequency domain is calculated. Secondly, the breathing crack is modeled to be fully open or fully closed. This phenomenon leads to the nonlinear system equations. These nonlinear equations are solved using pseudo-arc length continuation scheme and collocation method for any harmonic voltage applied to actuator. Then impedance of PWAS is calculated. Two methods are used to detect early crack using breathing crack modeling on PWAS impedance. At the first, frequency response of breathing crack in the frequency range with its sub-harmonics is calculated. Second, only frequency response of one harmonic is computed with its super-harmonics. Finally, the detection method of linear is compared with nonlinear model.

Elasto-Plastic Modeling of Beams for Impedance Based Structural Health Monitoring

2018 ◽  
Author(s):  
Naserodin Sepehry ◽  
Firooz Bakhtiari-Nejad ◽  
Weidong Zhu
Keyword(s):  
Structural Health Monitoring ◽  
Linear System ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Frequency Response ◽  
Health Monitoring ◽  
Difference Method ◽  
Impedance Method ◽  
Structural Health ◽  
System Equations

The structural health monitoring by piezoelectric wafer active sensor (PWAS) using electromechanical impedance method used for monitoring of structure. In present work impedance method of elasto-plastic beam structure is studied. In order to model the effect of a plastic in beam, the moment-curvature relationship for elasto-plastic region for loading and unloading is used. The finite difference method is used to discretize beam with piezoelectric. The piezoelectric actuator is modeled by equivalent moment. Then output current of piezoelectric sensor is calculated. Firstly, elastic modeling of beam is considered that this is leads to linear system equation. In linear system, time domain system equations are calculated and Fourier transform of current output obtained, and then impedance of PWAS in frequency domain is calculated. Secondly, the elasto-plastic of beam is modeled. This phenomenon leads to the nonlinear system equations. These nonlinear equations are solved using finite difference method for any harmonic voltage applied to actuator. Then impedance of PWAS is calculated. Two methods are used to detect elasto-plastic modeling on PWAS impedance. At the first, frequency response of elastic beam as intact model is compared with elasto-plastic results in a desired frequency range. Second, only frequency response of one harmonic is computed with its super-harmonics. Finally, the detection method of linear is compared with nonlinear model.

Generalized GL Fractional Derivative and Its Laplace and Fourier Transform

2009 ◽  
Author(s):  
Manuel D. Ortigueira ◽  
Juan J. Trujillo
Keyword(s):  
Fourier Transform ◽  
Linear System ◽  
Fractional Derivative ◽  
Frequency Response ◽  
Fourier Transforms ◽  
Laplace And Fourier Transforms ◽  
Riesz Fractional Derivative ◽  
Laplace And Fourier Transform

It is well known the difficulties that the Riesz fractional derivative present, as the spatial fractional derivative involved in many models of the dynamics of anomalous processes. The generalized Gru¨nwal-Letnikov fractional derivative is analysed in this paper. Its Laplace and Fourier Transforms are computed and some current results criticized. It is shown that only the forward derivative of a sinusoid exists. This result is used to define the frequency response of a fractional linear system.

Bifurcation Induced by Mass Variation in Piecewise Linear System

2012 ◽  
Vol 226-228 ◽  
pp. 531-535
Author(s):  
Yue Hua Li ◽  
Shi Dong Chen
Keyword(s):  
Linear System ◽  
Frequency Response ◽  
Averaging Method ◽  
Piecewise Linear ◽  
Singularity Theory ◽  
Excitation Amplitude ◽  
Mass Variation ◽  
Piecewise Linear System ◽  
Amplitude Frequency Response ◽  
Two Parameters

This paper investigates the bifurcations of the periodic solutions in the piecewise linear systems. Firstly the equation about amplitude-frequency response is deduced by the averaging method. Then the bifurcation classification is conducted by applying the singularity theory. The effects of the two parameters, the mass and the excitation amplitude, are discussed. The balance position will be changed when the quality changed, So the system is divided into two kinds of state. The results show that the parameter plane is divided into thirteen regions where bifurcation types are different. At last, discussing the amplitude- frequency response of different regions. this paper provides some theoretical guidance for system of considering load variation, and it is significant to help research the change in amplitude-frequency characteristic of piecewise linear system.

Optimizing Piecewise Linear Isolator for Steady State Vibration

2003 ◽  
Author(s):  
A. Narimani ◽  
M. F. Golnaraghi ◽  
R. N. Jazar
Keyword(s):  
Linear System ◽  
Cost Function ◽  
Frequency Response ◽  
Averaging Method ◽  
Piecewise Linear ◽  
Relative Displacement ◽  
Experimental Frequency ◽  
Piecewise Linear System ◽  
Transmitted Force ◽  
The Cost

In this work we have studied the effect of stoppers in quarter car model. While in rough roads these stoppers prevent the system from excessive displacement around the resonance frequency. Although stoppers prevent the undesired motion they increase the transmitted force that is undesirable in suspension systems. In order to optimize between the relative displacement and transmitted force an analytical model is considered. The piecewise linear system is the model of presented nonlinearity which cannot be considered small. Therefore standard perturbation methods are not able to provide an analytical solution. For this case we have adopted an averaging method which leads to frequency response of the piecewise linear system at resonance. In order to confirm the results obtained by averaging method an experimental device is fabricated and frequency response of the system is measured. The experimental frequency response is in very good agreement with analytical approach and numerical simulations. Sensitivity analysis methods are used to minimize the cost function of maximum relative displacement in frequency domain. The range of the parameters that minimizes the cost function where certain amount of clearance exists in the system are obtained.

Transfer Function Coefficients Calculation of the High Pass Frequency-Dependent Second-Order Components Using Special Phase Frequency Response Values

2021 ◽  
Vol 105 ◽  
pp. 161-166
Author(s):  
Hanna Ukhina ◽  
Ivan Afanasyev ◽  
Valerii Sytnikov ◽  
Oleg Streltsov ◽  
Pavel Stupen
Keyword(s):  
Transfer Function ◽  
Frequency Response ◽  
Digital Filter ◽  
Second Order ◽  
Robotic Systems ◽  
Frequency Dependent ◽  
Digital Frequency ◽  
Order Components ◽  
High Pass

In this work, adjustable second-order digital frequency-dependent components that are used in robotic systems are considered. The obtained approximations of the PFR dependence on the ripple level allow us to find the digital filter transfer function denominator coefficients' values that result contributes to a more rapid rearrangement of their responses in robotic systems.

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