Relevant bibliographies by topics / Chebyshev excitation

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  1. Journal articles
  2. Dissertations / Theses
  3. Book chapters
  4. Conference papers

Academic literature on the topic 'Chebyshev excitation'

Author: Grafiati
Published: 6 September 2023

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Journal articles on the topic "Chebyshev excitation"

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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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Dissertations / Theses on the topic "Chebyshev excitation"

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CHOU, CHUNG-I., and 周中一. "Design of CPW-Fed Slot Antenna Array with Chebyshev Excitation." Thesis, 2003. http://ndltd.ncl.edu.tw/handle/00841177175910526597.

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碩士
國立臺灣大學
電信工程學研究所
91
A coplanar waveguide fed slot antenna array with Chebyshev excitation is investigated in this dissertation. Different radiation patterns will be induced by antenna array with different kinds of excitation. The main purpose of this thesis is to induce a CPW fed slot antenna array with Chebyshev excitation such that all sidelobe levels are equal to -20 dB. In the design of antenna, we calculate the self admittance of a single isolated slot antenna with the computer simulation software “Ensemble”. The mutual admittance between the slot antennas can be calculated from the formulas derived for the complementary strip dipoles based on reciprocity theorem and via Booker’s relation. After self admittances and mutual admittances are obtained, a CPW fed slot antenna array with Chebyshev excitation can be designed with suitable matching network. Finally, in order to clarify our design, a five-element CPW fed slot antenna array with Chebyshev excitation is designed and fabricated. Form simulated and experimental results, the design of the slot antenna array is proved to be practical and correct.
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Yi-Chun, Chen. "Design of CPW-Fed Coupling Slot Antenna Array with Chebyshev Excitation." 2006. http://www.cetd.com.tw/ec/thesisdetail.aspx?etdun=U0001-2107200607435700.

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Chen, Yi-Chun, and 陳奕君. "Design of CPW-Fed Coupling Slot Antenna Array with Chebyshev Excitation." Thesis, 2006. http://ndltd.ncl.edu.tw/handle/73367515224504364794.

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碩士
國立臺灣大學
電信工程學研究所
94
Different radiation patterns will be induced by different excitation distribution in the antenna array. A coplanar waveguide fed coupling slot antenna array with Chebyshev excitation with equal side lobe level is investigated in this thesis. Conventionally, to consider the mutual coupling between each element in an antenna array, we need to calculate the active impedance or admittance by calculating electric field or magnetic field first. This thesis proposes a systematic method combined with commercial software package to derive the active impedance. The major advantage is that it removes the need for calculation by field theory. After the active impedances are obtained, a CPW fed coupling slot antenna array can be designed with proper impedance matching. Finally, a 4-element and 6-element CPW fed coupling slot antenna array with Chebyshev excitation are designed and fabricated to clarify the design method. From the simulated and experimental results, the design of the coupling slot antenna array is proved to be practical.
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Book chapters on the topic "Chebyshev excitation"

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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." In Few-Body Problems in Physics ’02, 127–30. Vienna: Springer Vienna, 2003. http://dx.doi.org/10.1007/978-3-7091-6728-1_29.

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Conference papers on the topic "Chebyshev excitation"

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Butcher, Eric A., and Oleg A. Bobrenkov. "The Chebyshev Spectral Continuous Time Approximation for Periodic Delay Differential Equations." In ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2009. http://dx.doi.org/10.1115/detc2009-86641.

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In this paper, the approximation technique proposed in [1] for converting a system of constant-coefficient delay differential equations (DDEs) into a system of ordinary differential equations (ODEs) using pseudospectral differencing is applied to both constant and periodic systems of DDEs. Specifically, the use of Chebyshev spectral collocation is proposed in order to obtain the “spectral accuracy” convergence behavior shown in [1]. The proposed technique is used to study the stability of first and second order constant coefficient DDEs with one or two fixed delays with or without cubic nonlinearity and parametric sinusoidal excitation, as well as of the delayed Mathieu’s equation. In all the examples, the results of the approximation by the proposed method show good agreement with either analytical results, or the results obtained before by other reliable approximation methods. In particular, the greater accuracy and convergence properties of this method compared to the finite difference-based continuous time approximation proposed recently in [2] is shown.
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Alijani, F., and M. Amabili. "Large Amplitude Vibrations of Completely Free Rectangular Plates." In ASME 2012 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/imece2012-89724.

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Nonlinear forced vibrations of completely free rectangular plates are studied using multi-modal Lagrangian approach. Nonlinear higher-order shear deformation theory is used and the nonlinear response to transverse harmonic excitation in the frequency neighborhood of the fundamental mode is investigated. Geometric imperfections are taken into account. The analysis is carried out in two steps. First, the plate displacements and rotations are expanded in terms of Chebyshev polynomials and a linear analysis is conducted to obtain the natural frequencies and mode shapes. Then, the energy functional is discretized by using the natural modes of vibration and a system of nonlinear ordinary differential equations with cubic and quadratic nonlinear terms is obtained. A pseudo arc-length continuation and collocation scheme is employed to carry out a bifurcation analysis. The effect of number of modes retained in the approximation, thickness ratio and geometric imperfections on the trend of nonlinearity is discussed.
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Alijani, F., and M. Amabili. "Large Amplitude Vibrations of Laminated Rectangular Plates With Free Edges." In ASME 2013 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/imece2013-62254.

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Nonlinear forced vibrations of completely free laminated composite rectangular plates are studied using multi-modal Lagrangian approach. Nonlinear higher-order shear deformation theory is used and the nonlinear response to transverse harmonic excitation in the frequency neighborhood of the fundamental mode is investigated. The numerical analysis is conducted in two steps. First, the plate displacements and rotations are expanded in terms of Chebyshev polynomials and a linear analysis is performed to obtain the natural frequencies and mode shapes. Then, the energy functional is discretized by using the natural modes of vibration and a system of nonlinear ordinary differential equations with cubic and quadratic nonlinear terms is obtained. A pseudo arc-length continuation and collocation scheme is employed to carry out a bifurcation analysis. A consistent reduced-order model necessary to capture the nonlinear dynamics of the plate is developed and the effect of number of modes retained in the numerical model is discussed.
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Sarkar, Dripta, Emiliano Renzi, and Frederic Dias. "Wave Power Extraction by an Oscillating Wave Surge Converter in Random Seas." In ASME 2013 32nd International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/omae2013-10188.

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This paper investigates the behaviour of a bottom hinged flap-type wave energy converter (WEC), namely the Oscillating Wave Surge Converter (OWSC), in random seas. The semi-analytical model of Renzi and Dias (2013b) for an OWSC in the open ocean is considered to analyze the performance of the device in random incident waves. The modelling is performed within the framework of a linear potential flow theory, by means of Green’s integral theorem. The resultant hypersingular integral equation for the velocity potential obtained from the above formulation is solved using a series expansion in terms of Chebyshev polynomials of the second kind. The behaviour of the device is investigated for six different sea states, generally representative of the wave climate in the North Atlantic Ocean at the European Marine Energy Centre test site. A Bretschneider spectrum is considered in order to reproduce the sea climate. The analysis is made for sea states where the spectral energy contribution from large periods, which cause excitation of body resonance of the flap — not modelled by the linear theory — is almost negligible. The power take-off damping is optimised for each individual sea state to calculate the captured power. The investigation is undertaken for two flaps of different widths, resembling the Oyster1 and the new Oyster800 version of the Oyster WEC, respectively. Comparison is made between the performances of the two converters. The effect of varying the width and the characteristic parameters of the flap on the capture factor in random seas is then discussed. The results of the analysis show that the performance of the device is fairly consistent for the sea states considered. Also an enhancement in the overall average capture factor is shown for the latest version of the wave energy conversion device.
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Spires, J. M., and S. C. Sinha. "Response of Linear Time-Periodic Systems Subjected to Stochastic Excitations: A Chebyshev Polynomial Approach." In ASME 1995 Design Engineering Technical Conferences collocated with the ASME 1995 15th International Computers in Engineering Conference and the ASME 1995 9th Annual Engineering Database Symposium. American Society of Mechanical Engineers, 1995. http://dx.doi.org/10.1115/detc1995-0336.

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Abstract In many situations engineering systems modeled by a system of linear second order differential equations with periodic damping and stiffness matrices are subjected to stochastic 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 has been shown that the Liapunov-Floquet transformation matrix 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 mean square response and transient autocorrelation response of periodic systems subjected to stochastic forcing vectors. Two formulations are presented. In the first formulation, the mean square response of the original system is computed directly. In the second formulation, the original system is transformed to a time-invariant form. The autocorrelation response is found by determining the response of the time-invariant system. Both formulations utilize the convolution integral to form an expression for the response. This expression can be evaluated numerically, symbolically, or through Chebyshev polynomial expansion. Results for some time-invariant and periodic systems are included, as illustrative examples.
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Wei, Sha, Qinkai Han, Zhipeng Feng, Yanhua Shen, and Fulei Chu. "Dynamic Response Analysis of Wind Turbine Planetary Gear System With Interval Stiffness Parameters." In ASME 2014 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/detc2014-34269.

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Planetary gear transmission system is one of the primary parts of the wind turbine drive train. Due to the assembly state, lubrication conditions and wear, the mesh stiffness of the planetary gear system is an uncertain parameter. In this paper, taking the uncertainty of mesh stiffness into account, the dynamic responses of a wind turbine gear system subjected to wind loads and transmission error excitations are studied. Firstly, a lumped-parameter model is extended to include both the planetary and parallel gears. Then the fluctuation ranges of dynamic mesh forces are predicted quantitatively and intuitively based on the combined Chebyshev interval inclusion function and numerical integration method. Finally, examples of gear trains with different interval mesh stiffnesses are simulated and the results show that tooth separations are becoming more obvious at the resonant speed by considering the fluctuating mesh stiffness of the second parallel gear stage. The nonlinear tooth separations are degenerated obviously as the fluctuation error of the mesh stiffness of the second parallel gear set is increased.
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