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Journal articles on the topic 'Chebyshev excitation'
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1
Petrovic, Nenad, Velibor Pjevalica, and Vladimir Vujicic. "The theorem about the transformer excitation current waveform mapping into the dynamic hysteresis loop branch for the sinusoidal magnetic flux case." Serbian Journal of Electrical Engineering 12, no. 1 (2015): 33–52. http://dx.doi.org/10.2298/sjee1501033p.
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This paper analyses aspects of the approximation theory application on the certain subsets of the measured samples of the transformer excitation current and the sinusoidal magnetic flux. The presented analysis is performed for single-phase transformer case, Epstein frame case and toroidal core case. In the paper the theorem of direct mapping the transformer excitation current in the stationary regime is proposed. The excitation current is mapped to the dynamic hysteresis loop branch (in further text DHLB) by an appropriate cosine transformation. This theorem provides the necessary and satisfactory conditions for above described mapping. The theorem highlights that the transformer excitation current under the sinusoidal magnetic flux has qualitatively equivalent information about magnetic core properties as the DHLB. Furthermore, the theorem establishes direct relationship between the number of the transformer excitation current harmonics and their coefficients with the degree of the DHLB interpolation polynomial and its coefficients. The DHLB interpolation polynomial is calculated over the measured subsets of samples representing Chebyshev nodes of the first and the second kind. These nonequidistant Chebyshev nodes provides uniform convergence of the interpolation polynomial to the experimentally obtained DHLB with an excellent approximation accuracy and are applicable on the approximation of the static hysteresis loops and the DC magnetization curves as well.
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Xu, Bin, Bai-Chuan Deng, Jing Li, and Jia He. "Structural nonlinearity and mass identification with a nonparametric model using limited acceleration measurements." Advances in Structural Engineering 22, no. 4 (August 13, 2018): 1018–31. http://dx.doi.org/10.1177/1369433218792083.
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Structural nonlinearity identification is critical for post-event damage detection or condition evaluation of engineering structures after strong dynamic excitation such as earthquake where structural nonlinear behaviour should be considered. Structural nonlinear restoring force provides direct indicator describing structural damage initiation and development procedure. Considering the availability of structural dynamic response measurement and the difficulty in defining a parametric model for structural nonlinearity and in estimating structure mass accurately in practice, in this article, a time-domain structural nonlinear restoring force and mass identification approach for multi-degree-of-freedom structures under incomplete excitation using limited acceleration measurements but without using any parametric models of structural nonlinear restoring force is proposed. At first, a memory fading extended Kalman filter with a weighted globl iteration (MF-EKF-WGI) is used to identify the location of nonlinearities and then a Chebyshev polynomial nonparametric model is introduced to model the nonlinear restoring force. The unscented Kalman filter is used to identify the structural responses and the parameters of the Chebyshev polynomial to describe structural nonlinearity. Numerical and experimental studies with a four-storey frame model structure equipped with a magnetorheological damper, which is employed to mimic structural nonlinear behaviour, under impact excitations are carried out to validate the performance of the proposed approach using acceleration measurements at certain degrees of freedom. Numerical and experimental results show that the proposed approach is capable of identifying both structural nonlinear restoring force and mass with acceptable accuracy even with a very rough initial mass estimation. The proposed time-domain identification approach can be used to detect structural damage initiation and development process and to evaluate energy consumption quantitatively of engineering structures under dynamic loadings.
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Yuan, Suwei, Haichao Zhu, Jiuxiao Hou, and Jinlong Liao. "Acoustic characteristics of a cylindrical shell coupled to an acoustic cavity under complex excitations." AIP Advances 12, no. 11 (November 1, 2022): 115212. http://dx.doi.org/10.1063/5.0125655.
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In this research, we analyze the acoustic–vibration coupling of liquid-filled cylindrical shells under complex excitations. A calculation model to determine the acoustic characteristics and steady-state response of a cylindrical shell coupled to an acoustic cavity is proposed. The displacement and sound pressure of the cylindrical shell are described by a Chebyshev–Fourier series in three dimensions. The uncertain expansion coefficient is determined with a Rayleigh–Ritz model. The accuracy and convergence of this method are compared with those of the finite element method. The spring constraint is applied to simulate arbitrary boundary parameters. The impact of these parameters on the coupled natural frequency is analyzed. Finally, the steady-state response of a coupled system for various excitation parameters is analyzed.
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DELTUVA, A., K. CHMIELEWSKI, and P. U. SAUER. "NUCLEON-DEUTERON SCATTERING WITH Δ-ISOBAR EXCITATION: NEW TECHNICAL DEVELOPMENTS." Modern Physics Letters A 18, no. 02n06 (February 28, 2003): 426–35. http://dx.doi.org/10.1142/s0217732303010624.
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A new technique for solving three-particle scattering equations is developed. It is based on the two-dimensional Chebyshev expansion of the two-baryon transition matrix. Its validity and its effectiveness is demonstrated. Furthermore, a new perturbative technique for simulating exact scattering results is developed. It has the potential for understanding three-particle reaction mechanisms in detail. The dynamics of the examples is based on a two-baryon potential which allows for the excitation or a nucleon to a Δ-isobar; the coupled-channel potential yields an effective three-nucleon force in the three-nucleon system. The purely nucleonic reference potential is the charge-dependent Bonn potential.
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Ma, Haitao, Eric A. Butcher, and Ed Bueler. "Chebyshev Expansion of Linear and Piecewise Linear Dynamic Systems With Time Delay and Periodic Coefficients Under Control Excitations." Journal of Dynamic Systems, Measurement, and Control 125, no. 2 (June 1, 2003): 236–43. http://dx.doi.org/10.1115/1.1570449.
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In this paper, a new efficient method is proposed to obtain the transient response of linear or piecewise linear dynamic systems with time delay and periodic coefficients under arbitrary control excitations via Chebyshev polynomial expansion. Since the time domain can be divided into intervals with length equal to the delay period, at each such interval the fundamental solution matrix for the corresponding periodic ordinary differential equation (without delay) is constructed in terms of shifted Chebyshev polynomials by using a previous technique that reduces the problem to a set of linear algebraic equations. By employing a convolution integral formula, the solution for each interval can be directly obtained in terms of the fundamental solution matrix. In addition, by combining the properties of the periodic system and Floquet theory, the computational processes are simplified and become very efficient. An alternate version, which does not employ Floquet theory, is also presented. Several examples of time-periodic delay systems, when the excitation period is equal to or larger than the delay period and for linear and piecewise linear systems, are studied. The numerical results obtained via this method are compared with those obtained from Matlab DDE23 software (Shampine, L. F., and Thompson, S., 2001, “Solving DDEs in MATLAB,” Appl. Numer. Math., 37(4), pp. 441–458.) An error bound analysis is also included. It is found that this method efficiently provides accurate results that find general application in areas such as machine tool vibrations and parametric control of robotic systems.
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Zhou, Ding, Jianshi Fang, Hongwei Wang, and Xiaopeng Zhang. "Three-Dimensional Dynamics Analysis of Rotating Functionally Gradient Beams Based on Timoshenko Beam Theory." International Journal of Applied Mechanics 11, no. 04 (May 2019): 1950040. http://dx.doi.org/10.1142/s1758825119500406.
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Through the Timoshenko beam theory (TBT), the 3D dynamics of a rotary functional gradient (FG) cantilever beam are investigated. Material capabilities alter continuously throughout the thickness obeying the power law. It is assumed that the Poisson’s ratio does not change. Based on the von Kármán nonlinearity, the governing equation is determined through the Hamilton principle, which includes the Coriolis effects. The couplings among the axial, flapwise and chordwise deformations caused by the usage of the functionally graded materials (FGMs) are revealed. Chebyshev polynomials are utilized to construct trial functions of deformations in the Rayleigh–Ritz method. The centrifugal strengthening effect caused by the rotational motion is described through the nonlinear axial shortening deformations derived from transverse deformations. The influences of the dimensionless angular velocity, FG index and slenderness ratio on vibration characteristics are studied. It is proved that the FG index significantly affects the dynamic response of deformation. For high-frequency external excitation cases, selection of Chebyshev polynomials as trial functions is more stable and effective than other polynomials.
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Hussein, Manaf K., Riyadh A. Abbas, and Ali A. Tayeb. "PATTERN SYNTHEISS OF LINEAR PHASE ARRAY USING ARTIFICIAL NEAURAL NETWORK BASED ON PARTICLE SWARM OPTIMIZATION." Kufa Journal of Engineering 5, no. 1 (January 15, 2014): 71–84. http://dx.doi.org/10.30572/2018/kje/511238.
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This paper focuses on the antenna synthesis of uniformly spaced linear phase array using artificial neural network (ANN) based on Particle Swarm Optimization (PSO). The weights of the Artificial Neural Networks (ANN) are trained by Particle Swarm Optimization (PSO). Subsequently the Particle Swarm Optimization (PSO) algorithm is applied in order to select the "global best" ANNs for the future investment decisions and to adapt the weights of other networks towards the weights of the best network. Chebyshev method is used to compare with this approach. Although, Chebyshev method is able to generate perfectly leveled side lobes, PSONN does not have the phenomena of up-swing in edges amplitude of the excitation and grating lobes does not appear in PSONN when the distances between elements are increased. The basic rule is to alter the weights (current distributions of elements) such that the error between the output values and the target values (desired values) is minimized. In this paper, single layer feed forward neural network with PSO training is used.
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Lei, Youming, and Yanyan Wang. "Period-Doubling Bifurcation of Stochastic Fractional-Order Duffing System via Chebyshev Polynomial Approximation." Shock and Vibration 2017 (2017): 1–12. http://dx.doi.org/10.1155/2017/4162363.
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Fractional-order calculus is more competent than integer-order one when modeling systems with properties of nonlocality and memory effect. And many real world problems related to uncertainties can be modeled with stochastic fractional-order systems with random parameters. Therefore, it is necessary to analyze the dynamical behaviors in those systems concerning both memory and uncertainties. The period-doubling bifurcation of stochastic fractional-order Duffing (SFOD for short) system with a bounded random parameter subject to harmonic excitation is studied in this paper. Firstly, Chebyshev polynomial approximation in conjunction with the predictor-corrector approach is used to numerically solve the SFOD system that can be reduced to the equivalent deterministic system. Then, the global and local analysis of period-doubling bifurcation are presented, respectively. It is shown that both the fractional-order and the intensity of the random parameter can be taken as bifurcation parameters, which are peculiar to the stochastic fractional-order system, comparing with the stochastic integer-order system or the deterministic fractional-order system. Moreover, the Chebyshev polynomial approximation is proved to be an effective approach for studying the period-doubling bifurcation of the SFOD system.
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Lopez-Alba, Elias, Christopher M. Sebastian, William JR Christian, and Eann A. Patterson. "The use of charge-coupled device cameras for characterizing the mean deflected shape of an aerospace panel during broadband excitation." Journal of Strain Analysis for Engineering Design 54, no. 1 (November 28, 2018): 13–23. http://dx.doi.org/10.1177/0309324718812542.
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In vibration experiments demanding long-duration measurements, traditional point-wise techniques are often employed, despite the availability of high-speed digital image correlation. This is due to the high volume of images generated by the latter technique, which limit acquisition times and lengthen post-processing times. In this experimental investigation, it is demonstrated that standard frame rate charge-coupled device cameras yield results for the mean deflected shape of a reinforced aerospace panel subject to a random broadband excitation between 0 and 800 Hz that are not statistically different to those from high-speed cameras. The images from both types of camera were processed using digital image correlation to generate out-of-plane displacement maps, which were then decomposed using Chebyshev descriptors for ease of comparison and to determine the mean deflected shape. The results indicate that, with appropriate sampling rates and durations, standard frame rate charge-coupled device cameras can be used to study broadband random excitation behavior of structures when mean behavior needs to be characterized over long time scales compared to the excitation wavelengths. This is contrary to accepted procedures, but offers comparable accuracy with substantially reduced computational resources compared to using high-speed cameras, as well as effectively unlimited data acquisition periods, which is useful in condition monitoring, for example.
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Tumin, Anatoli. "Receptivity of pipe Poiseuille flow." Journal of Fluid Mechanics 315 (May 25, 1996): 119–37. http://dx.doi.org/10.1017/s0022112096002364.
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The receptivity problem is considered for pipe flow with periodic blow–suction through a narrow gap in the pipe wall. Axisymmetric and non-axisymmetric modes (1, 2, and 3) are analysed. The method of solution is based on global eigenvalue analysis for spatially growing disturbances in circular pipe Poiseuille flow. The numerical procedure is formulated in terms of the collocation method with the Chebyshev polynomials application. The receptivity problem is solved with an expansion of the solution in a biorthogonal eigenfunction system, and it was found that there is an excitation of many eigenmodes, which should be taken into account. The result explains the non-similar character of the amplitude distribution in the downstream direction that was observed in experiments.
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Khan, Waseem, Saleem Shahid, Waleed Iqbal, Ahsan Sarwar Rana, Hijab Zahra, Moath Alathbah, and Syed Muzahir Abbas. "Semi-Coprime Array with Staggered Beam-Steering of Sub-Arrays." Sensors 23, no. 12 (June 10, 2023): 5484. http://dx.doi.org/10.3390/s23125484.
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A split-aperture array (SAA) is an array of sensors or antenna elements in which the array is split into two or more sub-arrays (SAs). Recently proposed SAAs, namely coprime and semi-coprime arrays, offer to attain a small half-power beamwidth (HPBW) with a small number of elements, compared to most conventional unified-aperture arrays, at the cost of reduced peak-to-side-lobe ratio (PSLR). To reduce HPBW and increase PSLR, non-uniform inter-element spacing and excitation amplitudes have proven helpful. However, all the existing arrays and beam-formers suffer increased HPBW, degraded PSLR or both when the main beam is steered away from the broadside. In this paper, we propose staggered beam-steering of SAs, a novel technique for decreasing HPBW. In this technique, we steer the main beams of the SAs of a semi-coprime array to angles slightly different from the desired steering angle. In conjunction with staggered beam-steering of SAs, we have utilized Chebyshev weights to suppress the side lobes. The results show that the beam-widening effect of Chebyshev weights can be mitigated considerably by staggered beam-steering of the SAs. Ultimately, the unified beam-pattern of the whole array offers HPBW and PSLR better than the existing SAAs, uniform and non-uniform linear arrays, especially when the desired steering angle is away from the broadside direction.
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Zhao, Ye, Bin Xu, Baichuan Deng, Shirley J. Dyke, Jia He, and Hanbin Ge. "Various damper forces and dynamic excitation nonparametric identification with a double Chebyshev polynomial using limited fused measurements." Measurement 193 (April 2022): 110940. http://dx.doi.org/10.1016/j.measurement.2022.110940.
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Droigk, Christine, Marco Maass, and Alfred Mertins. "Direct multi-dimensional Chebyshev polynomial based reconstruction for magnetic particle imaging." Physics in Medicine & Biology 67, no. 4 (February 16, 2022): 045014. http://dx.doi.org/10.1088/1361-6560/ac4c2e.
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Abstract Magnetic Particle Imaging is a tomographic imaging technique that measures the voltage induced due to magnetization changes of magnetic nanoparticle distributions. The relationship between the received signal and the distribution of the nanoparticels is described by the system function. A common method for image reconstruction is using a measured system function to create a system matrix and set up a regularized linear system of equations. Since the measurement of the system matrix is time-consuming, different methods for acceleration have been proposed. These include modeling the system matrix or using a direct reconstruction method in time, known as X-space reconstruction. In this work, based on the simplified Langevin model of paramagnetism and certain approximations, a direct reconstruction technique for Magnetic Particle Imaging in the frequency domain with two- and three-dimensional Lissajous trajectory excitation is presented. The approach uses Chebyshev polynomials of second kind. During reconstruction, they are weighted with the frequency components of the voltage signal and additional factors and then summed up. To obtain the final nanoparticle distribution, this result is rescaled and deconvolved. It is shown that the approach works for both simulated data and real measurements. The obtained image quality is comparable to a modeled system matrix approach using the same simplified physical assumptions and no relaxation effects. The reconstruction of a 31 × 31 × 31 volume takes less than a second and is up to 25 times faster than the state-of-the-art Kaczmarz reconstruction. Besides, the derivation of the proposed method shows some new theoretical aspects of the system function and its well-known observed similarity to tensor products of Chebyshev polynomials of second kind.
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Qin, Shi Qiang, Qian Hui Pu, and Zhou Shi. "Dynamic Test Signal Analysis and Modal Parameters Identification of High-Pier Long-Span Rail Bridge Based on HHT." Advanced Materials Research 163-167 (December 2010): 2880–86. http://dx.doi.org/10.4028/www.scientific.net/amr.163-167.2880.
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Dynamic loading test is exerted on a railway continuous beam bridge with a main span of 100m and a pier of 99m high, and dynamic responses are tested under natural excitation. Chebyshev digital filter is used to signal for low-pass filter according to the frequency distribution in FFT spectrum. A series of IMFs are obtained from the Hilbert-Huang Transform of a measured lateral displacement response, which shows: EMD is a self-adaptive signal analysis method that can effectively process non-stationary signal; IMFs can clearly show local features of complicated signal. Modal parameters of the bridge are identified based on HHT and Random Decrement Technique (RDT), the comparison of the identified results obtained from FFT, HHT-RDT and Finite Element Method is made, which show that HHT-RDT is an effective method to identify modal parameters of large bridge structures.
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Chan, Ricky, and Peter Wong. "A Passive Rotary System for Seismic Risk Mitigation of Steel Structures." Australasian Journal of Construction Economics and Building - Conference Series 2, no. 2 (April 14, 2014): 72. http://dx.doi.org/10.5130/ajceb-cs.v2i2.3893.
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This paper presents a novel bracing system designed for earthquake risk mitigation for steel structures. It involves a rotary system which a Chebyshev linkage connected to the ground and the building frame. Upon earthquake excitation, movement of structure floor slabs causes a rotational motion in the disc. Displacement-based dampers are installed between the rotary system and the ground which damp the structural vibrations. The system amplifies the travel of the dampers and efficiency is enhanced. In addition, the cross-brace members are always in tension, permitting the use of very slender sections. The paper first reviews the governing equations of the system, followed by a physical model demonstration. A 3-degree-of-system model with the proposed rotary system was subjected to simulated ground shaking. Acceleration on top floor was measured. Results demonstrated that proposed system effectively supresses the vibrational characteristics of the structure, and represents a viable and inexpensive solution to mitigate seismic risks.Keywords: Earthquake engineering, passive energy dissipation
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Peruzzi, NJ, FR Chavarette, JM Balthazar, AM Tusset, ALPM Perticarrari, and RMFL Brasil. "The dynamic behavior of a parametrically excited time-periodic MEMS taking into account parametric errors." Journal of Vibration and Control 22, no. 20 (August 8, 2016): 4101–10. http://dx.doi.org/10.1177/1077546315573913.
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Micro-electromechanical systems (MEMS) are micro scale devices that are able to convert electrical energy into mechanical energy or vice versa. In this paper, the mathematical model of an electronic circuit of a resonant MEMS mass sensor, with time-periodic parametric excitation, was analyzed and controlled by Chebyshev polynomial expansion of the Picard interaction and Lyapunov-Floquet transformation, and by Optimal Linear Feedback Control (OLFC). Both controls consider the union of feedback and feedforward controls. The feedback control obtained by Picard interaction and Lyapunov-Floquet transformation is the first strategy and the optimal control theory the second strategy. Numerical simulations show the efficiency of the two control methods, as well as the sensitivity of each control strategy to parametric errors. Without parametric errors, both control strategies were effective in maintaining the system in the desired orbit. On the other hand, in the presence of parametric errors, the OLFC technique was more robust.
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Guo, Yan, Wei Tang, Guanghua Hou, Fei Pan, Yubo Wang, and Wei Wang. "Research on Precipitation Forecast Based on LSTM–CP Combined Model." Sustainability 13, no. 21 (October 20, 2021): 11596. http://dx.doi.org/10.3390/su132111596.
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The tremendous progress made in the field of deep learning allows us to accurately predict precipitation and avoid major and long-term disruptions to the entire socio-economic system caused by floods. This paper presents an LSTM–CP combined model formed by the Long Short-Term Memory (LSTM) network and Chebyshev polynomial (CP) as applied to the precipitation forecast of Yibin City. Firstly, the data are fed into the LSTM network to extract the time-series features. Then, the sequence features obtained are input into the BP (Back Propagation) neural network with CP as the excitation function. Finally, the prediction results are obtained. By theoretical analysis and experimental comparison, the LSTM–CP combined model proposed in this paper has fewer parameters, shorter running time, and relatively smaller prediction error than the LSTM network. Meanwhile, compared with the SVR model, ARIMA model, and MLP model, the prediction accuracy of the LSTM–CP combination model is significantly improved, which can aid relevant departments in making disaster response measures in advance to reduce disaster losses and promote sustainable development by providing them data support.
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Ma, Li, Minghui Yao, Wei Zhang, and Dongxing Cao. "Linear Vibration of the Rotary Plate Under Combined Excitations in Subsonic Airflow." International Journal of Applied Mechanics 12, no. 08 (September 2020): 2050088. http://dx.doi.org/10.1142/s175882512050088x.
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Due to strong nonlinear, unsteady characteristics and the fluid–structure interaction effect, vibration analysis of blades under the excitation of the airflow is still one of the technical difficulties. In this paper, the accurate subsonic aerodynamic force is obtained through numerical simulation, and the aerodynamic coupling model of the rotary blade is established. The distribution of the aerodynamic force of the compressor blade under the unsteady airflow is focused on. The blade is modeled as presetting a presetting pre-twisted rotary cantilever plate. Dynamic frequencies of the plate, calculated by Chebyshev–Ritz method, are compared with frequencies calculated using the finite element method (FEM). Effects of different parameters on natural frequencies of the rotary plate are discussed. Based on von-Karman nonlinear geometric relation and the first-order shear deformation theory, nonlinear dynamic equations of the pre-twisted rotary plate under the combination of the centrifugal force and the aerodynamic are derived by utilizing Hamilton’s principle. Second-order ordinary differential equations are derived by applying the Galerkin method. Analytical solution of the dynamic deformation of the plate is presented and is compared with that produced by FEM. Results indicate the accuracy of the explicit presentation of the aerodynamic of the low-pressure compressor blade. Effects of the rotary speed, the thickness, the pre-twisted angle and the presetting angle on vibration characteristics of the warping blade are studied. Mode shape shift and frequency loci veering are discussed.
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Sun, Ying, Ding Zhou, Jiadong Wang, Zhenyuan Gu, and Wangping Qian. "Sloshing of Liquid in a Cylindrical Tank with Multiple Baffles and Considering Soil-Structure Interaction." Applied Sciences 12, no. 22 (November 21, 2022): 11841. http://dx.doi.org/10.3390/app122211841.
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In this study, the liquid sloshing in a cylindrical tank considering soil–structure interaction and undergoing horizontal excitation is investigated analytically. Multiple rigid annular baffles are positioned on the rigid wall to mitigate the liquid sloshing. Firstly, combined with the subdomain partition method for sloshing, the complex liquid domain is partitioned into simple subdomains with the single condition for boundary. Based on continuity conditions of velocity and pressure as well as the linear sloshing equation for free surface, the exact solution for convective velocity potential is derived with high accuracy. By yielding the similar hydrodynamic shear and moment as those of the original system, a mechanical model is developed to describe continuous sloshing, and parameters of the model are given in detail. Then, by means of the least squares approach, the Chebyshev polynomials are utilized to fit impedances for the circular surface foundation. A lumped parameter model is employed to represent influences of soil on the superstructure. Finally, by using the substructure method, a coupling model of the soil–tank system is developed to simplify the dynamic analysis. Comparison investigations are carried out to verify the effectiveness of the model. Detailed sloshing characteristics and dynamic responses of sloshing are analyzed with regard to different baffle sizes and positions as well as soil parameters, respectively. The novelty of the present study is that an equivalent analytical model for the soil–foundation–tank–liquid system with multiple baffles is firstly obtained and it allows the dynamic behaviors of the coupling system to be investigated with high computation efficiency and acceptable accuracy.
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Bukaros, A., A. Herega, V. Sergeiev, T. Obnyavko, and K. Konkov. "STATE OBSERVER OF THE COMBAT VEHICLE ELECTRIC DRIVES." Collection of scientific works of Odesa Military Academy, no. 17 (August 31, 2022): 116–24. http://dx.doi.org/10.37129/2313-7509.2022.17.116-124.
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The paper substantiates the use of adaptive state observers of combat vehicles guiding electric drives instead of imperfect rotation speed sensors of executive motors, as which tachogenerators are traditionally used. The synthesis is carried out, the structure and mathematical description of the Luenberger observer of the direct current executive motor with independent excitation by the modal method are obtained. The performance of the synthesized observer is confirmed by checking the fulfillment of the observability condition. An expression for determining the geometric mean root, which makes it possible to simplify the structure of the observer and to evaluate not only the rotation speed, but also the load torque on the motor shaft is proposed. For definite structure of the observer, expressions for the coefficients of the Luenberger matrix are obtained. The modernized Luenberger observer was studied by simulation in the Matlab/Simulink environment. The parameters of the DC executive motor D-135 of the vertical guidance system of the 9K35 anti-aircraft missile system were used as the initial data of the model. The simulation results with the accepted binomial distribution of the roots of the characteristic polynomial proved the efficiency of the proposed structure of the observer. The estimation of the electric drive coordinates occurred aperiodically, without fluctuations, however, it had a relatively large error due to the underestimated speed of the observer. To eliminate this shortcoming, the distribution of the roots of the characteristic polynomial of the observer according to the Chebyshev linear form was proposed. With this distribution of roots, the performance of the Luenberger observer increased significantly, which limited the error in tracking the coordinates of the electric drive to 4%. The prospects for further research of the proposed method for the synthesis of state observers of the executive motors of the combat vehicles guidance systems are outlined. Keywords: Luenberger observer, executive motor, guidance system, combat vehicle.
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Spires, J. M., and S. C. Sinha. "On The Response of Linear Time-Periodic Systems Subjected to Deterministic and Stochastic Excitations." Journal of Vibration and Control 2, no. 2 (April 1996): 219–49. http://dx.doi.org/10.1177/107754639600200205.
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In many situations, engineering systems modeled by a set of linear, second-order differential equations, with periodic damping and stiffness matrices, are subjected to external excitations. It has been shown that the fundamental solution matrix for such systems can be efficiently computed using a Chebyshev polynomial series solution technique. Further, it is shown that the Liapunov-Floquet transformation matrix associated with the system can be computed, and the original time-periodic system can be put into a time- invariant form. In this paper, these techniques are applied in finding the transient response of periodic systems subjected to deterministic and stochastic forces. Two formulations are presented. In the first formulation, the response of the original system is computed directly. In the second formulation, first the original system is transformed to a time-invariant form, and then the response is found by determining the response of the time-invariant system. Both formulations use the convolution integral to form an expression for the response. This expression can be evaluated numerically, symbolically, or through a Chebyshev polynomial expansion technique. Results for some time-invariant and periodic systems are included, as illustrative examples.
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Napoli, Francesco, Lara Pajewski, Roberto Vescovo, and Marian Marciniak. "Multi-Objective Evolutionary Optimization of Aperiodic Symmetrical Linear Arrays." Journal of Telecommunications and Information Technology, no. 3 (2017): 79–87. http://dx.doi.org/10.26636/jtit.2017.118517.
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In this paper, a multi-objective approach is applied to the design of aperiodic linear arrays of antennas. The adopted procedure is based on a standard Matlab implementation of the Controlled Elitist Non-Dominated Sorting Genetic Algorithm II. Broadside symmetrical arrays of isotropic radiators are considered with both uniform and non-uniform excitations. The work focuses on whether, and in which design conditions, the aperiodic solutions obtained by the adopted standard multi-objective evolutionary procedure can approximate or outperform the Pareto-optimal front for the uniformspacing case computable by the Dolph-Chebyshev method.
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Jerez-Hanckes, Carlos, and José Pinto. "High-order Galerkin method for Helmholtz and Laplace problems on multiple open arcs." ESAIM: Mathematical Modelling and Numerical Analysis 54, no. 6 (October 12, 2020): 1975–2009. http://dx.doi.org/10.1051/m2an/2020017.
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We present a spectral Galerkin numerical scheme for solving Helmholtz and Laplace problems with Dirichlet boundary conditions on a finite collection of open arcs in two-dimensional space. A boundary integral method is employed, giving rise to a first kind Fredholm equation whose variational form is discretized using weighted Chebyshev polynomials. Well-posedness of the discrete problems is established as well as algebraic or even exponential convergence rates depending on the regularities of both arcs and excitations. Our numerical experiments show the robustness of the method with respect to number of arcs and large wavenumber range. Moreover, we present a suitable compression algorithm that further accelerates computational times.
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KACHALAI NARSIMMAN, Mohan, Yogesh Kumar CHOUKIKER, Srinivasa Rao ZINKA, and Kannadassan DHANARAJ. "Effect of uniform and Dolph--Chebyshev excitations on the performance of circular array antennas." TURKISH JOURNAL OF ELECTRICAL ENGINEERING & COMPUTER SCIENCES 25 (2017): 3660–72. http://dx.doi.org/10.3906/elk-1604-222.
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Yenneti, Laxmi Lavanya, Aruna Singam, and Sasibhushana Rao Gottapu. "Conflicting Parameter Pair Optimization for Linear Aperiodic Antenna Array using Chebyshev Taper based Genetic Algorithm." International Journal on Recent and Innovation Trends in Computing and Communication 11, no. 1 (February 15, 2023): 161–66. http://dx.doi.org/10.17762/ijritcc.v11i1.6086.
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In this study, the peak side lobe level (PSLL) in the radiation pattern of a linear antenna array (LAA) is lowered without affecting its first null beam width (FNBW). Antenna array synthesis is commonly applied to achieve high directivity, low side lobes, high gain and desired null positions in the output radiation pattern. But output parameters like PSLL, null positions and beam width conflict with each other, i.e. as one parameter improves, the other deteriorates. To avoid this problem, a multi-objective optimization algorithm can be implemented, in which both the conflicting parameters can be simultaneously optimized. This work proposes a multi-objective algorithm, which takes advantages of the well-known Chebyshev tapering and genetic algorithm (GA), to lower the PSLL without broadening the beam further. Array elements are fed using Chebyshev tapered excitations while GA is incorporated to optimize the elemental spacing. The results of 28-element LAA are compared with those of multi-objective Cauchy mutated cat swarm optimization (MO-CMCSO) existing in literature, which has also been proven to be superior to multi-objective cat swarm optimization (MO-CSO) and multi-objective particle swarm optimization (MO-PSO). Results indicate that the proposed algorithm performs better by further reducing the PSLL from -21.57 dB (MO-CMCSO) to -28.18 dB, while maintaining the same FNBW of 7.4 degrees.
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Wu, Shi Hao, Ye Gao Qu, and Hong Xing Hua. "A Domain Decomposition Method for Forced Vibration Analysis of Joined Conical-Cylindrical-Spherical Shell." Applied Mechanics and Materials 184-185 (June 2012): 3–10. http://dx.doi.org/10.4028/www.scientific.net/amm.184-185.3.
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Based upon the Reissner-Naghdi-Berry shell theory, a semi-analytical domain decomposition method is presented to analyze the forced vibration of a joined conical-cylindrical-spherical shell with general boundary conditions. The joined shell was divided into some conical, cylindrical and spherical shell segments along the axis of revolution. The constraint equations derived from interface continuity conditions between two adjacent shell segments were introduced into the energy functional of the joined shell. Displacement variables of each shell segment are expressed as a mixed double series in the forms of Fourier series in the circumferential direction and Chebyshev orthogonal polynomial in the longitudinal direction. The forced vibration response of the joined shells subjected to various harmonic excitations and boundary conditions was calculated and compared with those FEM results obtained by finite element software ANSYS to confirm the reliability and accuracy of this analytical solution.
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Sood, Khagindra, Rajeev Jyoti, and Shashi Bhushan Sharma. "Linear array modules with prescribed excitations using waveguide shunt slot-fed microstrip patch elements." International Journal of Microwave and Wireless Technologies 5, no. 5 (June 3, 2013): 637–44. http://dx.doi.org/10.1017/s1759078713000548.
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A waveguide shunt slot-fed microstrip patch antenna (WGMPA) element is proposed and analyzed with method of moments (MOM) using entire-domain basis functions. The developed analysis has been utilized to obtain parametric observation of power-coupling versus transverse offset of feeding slot from the waveguide axis. Expressions for the radiation pattern as a summation of contributions of individual basis functions are reported. The proposed element is amenable to building-up series-fed linear arrays by a simple cascading of elements at the through-end of the feeding waveguide. The authors propose that arbitrary amplitude excitations may be applied to such linear arrays for desired tailored array pattern characteristics. The required transverse offsets for each array element may be computed using the reported parametric result. As a demonstration of concept, two distributions are designed – uniform amplitudes and Dolph–Chebyshev for reduced side lobes. Computed element patterns from MOM are used with an array factor formulation for arbitrary element positions. Both modules show radiation characteristics closely matching the expected directivity and sidelobe envelopes. Analysis validation is achieved using a proven finite element method (FEM)-based solver; the comparison is close and is reported. Efficacy of the waveguide shunt-slot fed patch element for building linear array modules with prescribed amplitude distributions is thus established.
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Jiang, Bin, Daiqian Xie, and Hua Guo. "Calculation of multiple initial state selected reaction probabilities from Chebyshev flux-flux correlation functions: Influence of reactant internal excitations on H + H2O → OH + H2." Journal of Chemical Physics 135, no. 8 (August 28, 2011): 084112. http://dx.doi.org/10.1063/1.3626525.
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Wang, Jian, and Jun Zhang. "Effects of random interval parameters on spur gear vibration." Journal of Vibration and Control, September 16, 2020, 107754632095952. http://dx.doi.org/10.1177/1077546320959529.
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Gear driving devices are commonly used in mechanical transmission systems. Due to the inevitable random errors in manufacturing, installation, and operation, the dynamics of a gear transmission system will fluctuate randomly. To reveal the dynamic characteristics, an interval parameters dynamic model of a single-stage spur gear pair is established, in which the uncertainties of displacement excitation, load excitation, and stiffness excitation are included, and their formulations are derived in detail by using interval mathematics. The established interval parameters dynamic model is solved by combining the Chebyshev inclusion function method and the Runge–Kutta method. Finally, the influence of the random interval parameters of meshing stiffness, input torque, and transmission error as well as backlash on the vibration velocity interval and transmission reliability of the gear transmission system are studied. The analysis results show that the three types of excitations have different effects on the dynamic characteristics. To be specific, the effects of uncertain parameters on the dynamic characteristics can be ordered as meshing stiffness, input torque, backlash, and transmission error in sequence from the strongest to the weakest. The present study may serve as a sound theoretical basis and can provide references for the design and vibration control of spur gear transmission systems.
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Deltuva, A., K. Chmielewski, and P. U. Sauer. "Nucleon-deuteron scattering with Δ-isobar excitation: Chebyshev expansion of two-baryon transition matrix." Physical Review C 67, no. 3 (March 3, 2003). http://dx.doi.org/10.1103/physrevc.67.034001.
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"A spectral method for the depth-separated solution of a wavenumber integration model for horizontally stratified fluid acoustic waveguides." Physics of Fluids 35, no. 5 (May 1, 2023). http://dx.doi.org/10.1063/5.0150221.
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The wavenumber integration model is the most precise approach for assessing arbitrary horizontally stratified media within the sphere of computational ocean acoustics. Unlike the normal-mode approach, it considers not only discrete spectra but also continuous spectral components, resulting in fewer model approximation errors for horizontally stratified media. Traditionally, the depth-separated wave equation in the wavenumber integration model has been solved using analytical and semianalytical methods, and numerical solutions have been primarily based on the finite difference and finite element methods. This paper proposes an algorithm for solving the depth equation via the Chebyshev–Tau spectral method, combined with a domain decomposition strategy, resulting in the development of a numerical program named WISpec. The algorithm can simulate the sound field excitation not only from a point source but also from an infinite line source. To that end, the depth equations for each layer are first discretized through the Chebyshev–Tau spectral method and subsequently solved simultaneously by incorporating boundary and interface conditions. Representative numerical experiments are presented to validate the accuracy and speed of WISpec. The high degree of consistency of results obtained from different software tools running the same configuration provides ample evidence that the numerical algorithm described in this paper is accurate, reliable, and numerically stable.
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Xu, Bin, Ye Zhao, Baichuan Deng, and Chen Wang. "NONPARAMETRIC NONLINEARITY IDENTIFICATION WITH AN UPDATED EKF APPROACH USING DYNAMIC RESPONSE FUSION." Proceedings of International Structural Engineering and Construction 7, no. 2 (November 2020). http://dx.doi.org/10.14455/isec.2020.7(2).str-19.
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Most parametric nonlinear behavior identification methods require an assumed mathematical model to describe the hysteretic behavior of structural members or substructures. Due to the individuality of various construction materials and structural systems, it is challenging to forecast the real nonlinear performance of a structure member or a substructure under dynamic loadings with a general parametric model in prior. In this paper, a nonparametric nonlinear restoring force (NRF) identification approach with limited output and unknown input is proposed by employing a double Chebyshev polynomial combined with an updated Extended Kalman filter (U-EKF) approach, where the observation equation is updated without using external excitation information. Moreover, data fusion is used to deal with the drift problem in dynamic response forecasting. The proposed approach is validated numerically with multi-degree-of-freedom (MDOF) structures equipped with various nonlinear members, including MR damper (damping-dominant) and SMA damper (stiffness-dominant) employed to mimic different structural nonlinear behavior. Moreover, a four-story shear frame model, including MR damper on the fourth floor, is employed to experimentally validate the approach. Identified results show that the proposed algorithm can identify structural nonlinear behavior in a nonparametric way without using excitation as an input, which is helpful for structural damage diagnosis where nonlinearity and loading profile should be considered.
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Chattopadhyay, Anindita, Angshuman Majumdar, and Sankar Gangopadhyay. "A simple but accurate technique for prediction of confinement and normalized group delay parameters for propagation of first higher order mode in graded index fiber." Journal of Optical Communications, December 12, 2022. http://dx.doi.org/10.1515/joc-2022-0274.
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Abstract This paper deals with expressions for simple but precise analyses of fractional modal power (FMP) inside the core of optical fibers, the excitation efficiency and the normalized group delay (NGD) for the first higher order (LP11) mode in step and parabolic index fibers both with and without Kerr type non linearity. To get the analytical results, we have employed simple power series Chebyshev expansion for the LP11 mode of the above mentioned fibers. At first, the analytical expression for linear case is found out and then by applying the method of iteration the propagation parameters are estimated when there is nonlinearity of the Kerr type. Here, some typical step and parabolic profile fibers have been used for our investigation. Our findings of confinement and group delay parameters perfectly match with the precise numerical findings made by the intricate finite element method (FEM). This implies the precision of our formalism. The study of nonlinear optical transmission systems will benefit from the findings.
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Sharma, Ashu, and S. C. Sinha. "An Approximate Analysis of Quasi-Periodic Systems Via Floquét Theory." Journal of Computational and Nonlinear Dynamics 13, no. 2 (November 9, 2017). http://dx.doi.org/10.1115/1.4037797.
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Parametrically excited linear systems with oscillatory coefficients have been generally modeled by Mathieu or Hill equations (periodic coefficients) because their stability and response can be determined by Floquét theory. However, in many cases, the parametric excitation is not periodic but consists of frequencies that are incommensurate, making them quasi-periodic. Unfortunately, there is no complete theory for linear dynamic systems with quasi-periodic coefficients. Motivated by this fact, in this work, an approximate approach has been proposed to determine the stability and response of quasi-periodic systems. It is suggested here that a quasi-periodic system may be replaced by a periodic system with an appropriate large principal period and thus making it suitable for an application of the Floquét theory. Based on this premise, a systematic approach has been developed and applied to three typical quasi-periodic systems. The approximate boundaries in stability charts obtained from the proposed method are very close to the exact boundaries of original quasi-periodic equations computed numerically using maximal Lyapunov exponents. Further, the frequency spectra of solutions generated near approximate and exact boundaries are found to be almost identical ensuring a high degree of accuracy. In addition, state transition matrices (STMs) are also computed symbolically in terms of system parameters using Chebyshev polynomials and Picard iteration method. Stability diagrams based on this approach are found to be in excellent agreement with those obtained from numerical methods. The coefficients of parametric excitation terms are not necessarily small in all cases.
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Wu, Zhiwei, Chaofeng Li, Binbin Zhu, and Ying Li. "Design and performance study of a piezoelectric beam conveyor based on the standing wave principle." Smart Materials and Structures, July 11, 2023. http://dx.doi.org/10.1088/1361-665x/ace66c.
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Abstract This paper aims to develop a simple piezoelectric beam conveyor based on the standing wave principle, and explore the effect of the height of the teeth on the piezoelectric beam and the number of piezoelectric plates on the motion. Based on the Euler–Bernoulli beam theory and Lagrange equation, the Chebyshev polynomial is used as the admissble displacement function to establish the numerical model. And the ANSYS is used to verify the correctness of the numerical model calculation results. The vibration response of the tooth tip is calculated by the numerical integration method, and the effect of different excitation parameters on the motion trajectory of the tooth tip is derived. Finally, an experimental device is built to verify the effectiveness and efficiency of the device to drive the slider. The bi-directional motion of the slider is realized. And the effects of voltage amplitude, frequency, tooth height, preload force, and the driving quantity of piezoelectric plates on the slider motion speed and driving force are discussed. The conclusion is informative for the selection of teeth and preload force.
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Wang, Nan, Yibo Zhang, Kun Gao, Jian Wu, Beijia Dang, Zhizhan Kong, Haokun Wei, Feng Gao, and Shuangyang Liu. "Design of Millimeter Wave Radar Antenna Array with Flat-top Pattern." Applied Computational Electromagnetics Society Journal (ACES), May 26, 2023. http://dx.doi.org/10.13052/2022.aces.j.371201.
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In this paper, a planar millimeter wave radar array antenna with flat-top pattern is proposed for wide detection angle. Firstly, the Chebyshev synthesis method is used to design the linear array with high gain and low sidelobe pattern which works in the 24 GHz frequency band. The maximum gain of the linear array is roughly 15 dBi, and the main-sidelobe ratio is close to 20 dB. By setting the excitations and phases distribution of the planar array feeding network, a 5××4 antenna array with a flat-top pattern is obtained. The simulated and measured results show that the radar antenna array has a wide half-power beamwidth of 88 degrees, which can ensure that the automotive radar has a longer detection range and a larger monitoring angle.
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Pradhan, Hrudananda, Biswa Binayak Mangaraj, and Santanu Kumar Behera. "Chebyshev-based array for beam steering and null positioning using modified ant lion optimization." International Journal of Microwave and Wireless Technologies, March 12, 2021, 1–15. http://dx.doi.org/10.1017/s1759078721000295.
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Abstract A modified ant lion optimization (MALO) algorithm is proposed in this article, for the synthesis of Chebyshev-based arrays by optimizing amplitudes and phases of excitations, and element spacings. Modification in ant lion optimization is achieved by hybridizing it with chaotic particle swarm optimization. The optimization process is employed to obtain an array pattern with the least possible sidelobe level. Close-in sidelobe level minimization for optimum pattern synthesis is suggested. Instead of only steering the main beam towards the desired direction presented by some popular optimization methods, the beam steering along with null positioning in other specified direction is also achieved employing MALO. Considering the arrays with the same design parameters and the results of other optimization algorithms, the performance of MALO is evaluated. The results show that MALO provides considerable improvements in an array pattern compared to the arrays optimized using other optimization algorithms and the uniform array.
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Phuc, Vu Duc, Tong Van Canh, and Pham Van Lieu. "Optimal parameters of dynamic vibration absorber for linear damped rotary systems subjected to harmonic excitation." Vietnam Journal of Mechanics, July 16, 2020. http://dx.doi.org/10.15625/0866-7136/14897.
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Dynamic vibration absorber (DVA) is a simple and effective device for vibration absorption used in many practical applications. Determination of suitable parameters for DVA is of significant importance to achieve high vibration reduction effectiveness. This paper presents a method to find the optimal parameters of a DVA attached to a linear damped rotary system excited by harmonic torque. To this end, a closed-form formula for the optimum tuning parameter is derived using the fixed-point theory based on an assumption that the damped rotary systems are lightly or moderately damped. The optimal damping ratio of DVA is found by solving a set of non-linear equations established by the Chebyshev's min-max criterion. The performance of the proposed optimal DVA is compared with that obtained by existing optimal solution in literature. It is shown that the proposed optimal parameters are possible to obtain superior vibration suppression compared to existing optimal formula. Extended simulations are carried out to examine the performance of the optimally designed DVA and the sensitivity of the optimum parameters. The simulation results show that the improvement of the vibration performance on damped rotary system can be as much as 90% by using DVA.