Relevant bibliographies by topics / Generalised Harmonic Models

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

Academic literature on the topic 'Generalised Harmonic Models'

Author: Grafiati
Published: 6 September 2023

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Journal articles on the topic "Generalised Harmonic Models"

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Carpinelli, G. "Generalised convertor models for iterative harmonic analysis in power systems." IEE Proceedings - Generation, Transmission and Distribution 141, no. 5 (1994): 445. http://dx.doi.org/10.1049/ip-gtd:19941212.

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Lehar, S. "Generalised Model of Illusory Grouping Accounts for Collinear, Orthogonal, and Vertex Grouping Percepts." Perception 25, no. 1_suppl (August 1996): 91. http://dx.doi.org/10.1068/v96l0704.

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A number of illusory phenomena, for example the Kanizsa illusion, exhibit boundary completion by collinearity between visible inducing edges. These phenomena have been addressed by models such as Grossberg's boundary contour system (BCS) (1985 Psychological Review92 173 – 211), which incorporates collinearity cells with receptive fields specialised to detect and enhance collinearity. Other illusory phenomena like the Ehrenstein illusion exhibit boundary completion orthogonal to the oriented inducers. The BCS model explains such orthogonal grouping by disinhibition, due to competition between collinearity cells of orthogonal orientations. There are many illusory grouping phenomena, however, which exhibit boundary completion through sharp corners in a variety of configurations, producing illusory ‘V’ or ‘Y’ vertices. Examples are seen in the diamond percept of the four-line Ehrenstein illusion, the triangular grouping percept of three dots arranged in a triangular configuration, as well as in the hexagonal percept of a grid of dots in a honeycomb pattern. These completions cannot be explained by models based on collinearity. Lehar's orientational harmonic model (1994, PhD thesis, Boston University) offers a single generalised grouping mechanism capable of collinear, orthogonal, and sharp vertex grouping. The proposed mechanism is a harmonic resonance, or pattern of standing waves in the orientational representation which promotes orientational periodicity. Computer simulations show that the model can account for a large number of diverse illusory phenomena using a single simple mechanism, and predicts the specific conditions under which a grouping of one type yields to a different grouping type.
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PALUMBO, P., and L. PIRODDI. "HARMONIC ANALYSIS OF NON-LINEAR STRUCTURES BY MEANS OF GENERALISED FREQUENCY RESPONSE FUNCTIONS COUPLED WITH NARX MODELS." Mechanical Systems and Signal Processing 14, no. 2 (March 2000): 243–65. http://dx.doi.org/10.1006/mssp.1999.1264.

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Loo, Tee-How, Avik De, Sanjay Mandal, and P. K. Sahoo. "How a projectively flat geometry regulates F(R)-gravity theory?" Physica Scripta 96, no. 12 (December 1, 2021): 125034. http://dx.doi.org/10.1088/1402-4896/ac3a51.

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Abstract In the present paper we examine a projectively flat spacetime solution of F(R)-gravity theory. It is seen that once we deploy projective flatness in the geometry of the spacetime, the matter field has constant energy density and isotropic pressure. We then make the condition weaker and discuss the effects of projectively harmonic spacetime geometry in F(R)-gravity theory and show that the spacetime in this case reduces to a generalised Robertson-Walker spacetime with a shear, vorticity, acceleration free perfect fluid with a specific form of expansion scalar presented in terms of the scale factor. Role of conharmonic curvature tensor in the spacetime geometry is also briefly discussed. Some analysis of the obtained results are conducted in terms of couple of F(R)-gravity models.
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Yao, Yuan, and Longyun Kang. "The Virtual Harmonic Power Droop Strategy to Mitigate the Output Harmonic Voltage of the Inverter." Energies 11, no. 9 (August 22, 2018): 2196. http://dx.doi.org/10.3390/en11092196.

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The harmonic voltage issue becomes a challenge for a distributed generation system. Considering that droop control is the most common control algorithm used in the distributed system, a virtual harmonic power droop strategy which aims to mitigate the harmonic voltage is proposed in this paper. First, the conventional droop control is analyzed. Based on that concept, the virtual power algorithm is introduced. Second, the output harmonic voltage issue and the mathematical model of the inverter are presented. In addition, the second-order generalized integrator is briefly discussed. Third, taking into consideration the algorithms and models presented, a virtual harmonic power droop strategy is proposed to implement the harmonic voltage mitigation. In this algorithm, signals in fundamental frequency and harmonic frequency are separated with the help of second-order generalized integrators. Unlike the conventional voltage–current dual loop structure which is used to mitigate system harmonics, this method only needs the virtual power feedback to mitigate the harmonic voltage. Based on these features, the system’s control structure is simplified. Simulation and experimental results verified the harmonic voltage mitigation ability of the proposed strategy.
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Mahadik, Mujeeb Khan Habib, Hassan Bahrami, Mofazzal Hossain, and Tsar Mitchel. "Production decline analysis and forecasting in tight-gas reservoirs." APPEA Journal 52, no. 1 (2012): 573. http://dx.doi.org/10.1071/aj11045.

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Exponential decline curve analysis is widely used to estimate recoverable reserves due to its simplicity. In most cases, however, an exponential model cannot provide a satisfactory match of overall production history. The generalised form of a hyperbolic decline model is more powerful in matching production history than the other decline models, but it is difficult to apply in practical production data analysis since it requires predicting two unknowns as decline constants. Although a hyperbolic model may provide a good fit to early-time production decline data; it may overestimate the late-time production, especially for hydraulic fractured wells in a tight-gas reservoir. In fact, the exponential decline model might be more reliable for forecasting the late-time production. This paper presents a practical approach to production decline analysis for non-fractured and fractured wells in a tight-gas reservoir using numerical simulation. Some production rate functions and type curves are introduced to obtain the best matching values of hyperbolic, exponential and harmonic production decline constants. The simulated production rate decline data for various well and reservoir parameters are used to indicate the optimum time duration of use of each decline model and to show the time when the production decline starts following the exponential model. The proposed approach is applied in production data analysis and forecasting for a tight-gas field in WA. The results showed good agreement with the production forecast obtained from a reservoir simulation.
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XIE, GUANGLONG, and BUHAN ZHANG. "PROBABILISTIC HARMONIC ANALYSIS OF WIND GENERATORS BASED ON GENERALIZED GAMMA MIXTURE MODELS." Modern Physics Letters B 27, no. 03 (December 13, 2012): 1350020. http://dx.doi.org/10.1142/s0217984913500206.

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Grid-connected wind generators pose the power quality problems such as harmonic propagation and summation, and these problems are hard to solve by deterministic harmonic analysis due to the random harmonic current emissions. In this paper, probabilistic harmonic analysis is utilized to approximate harmonic currents of wind generators. Generalized gamma mixture models based on Gaussian mixture models, phasor clustering and generalized gamma models, are proposed to approximate the probability density functions of harmonic propagation and summation. And the simulation network built on PSCAD/EMTDC is utilized to verify the proposed models and method.
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Ray, A., T. K. Dey, and S. K. Ghatak. "Low Field Second Harmonic Response and AC Susceptibility of (Bi,Pb)-2223 Pellet in a Generalized Critical State Model." International Journal of Modern Physics B 17, no. 21 (August 20, 2003): 3831–46. http://dx.doi.org/10.1142/s0217979203021848.

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The AC susceptibility and second harmonic response of bulk high Tc superconductor (Bi,Pb) -2223 is measured in presence of small AC field excitation and DC magnetic field superimposed on it. This response increases with the increase in DC field whereas decreases at a higher excitation amplitude. Critical state models are used to explain the nonlinear magnetic response in HTSCs. With a generalized field dependence of critical current Jc : Jc(B) = J0/(1 + B/B0)n, the fundamental AC susceptibility and low field second harmonics response are calculated for different n values. It is found that the theoretical consideration adopted here explains the observed AC susceptibility and low field second harmonic response qualitatively reasonably well within the Anderson–Kim regime (n = 1).
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Sitepu, Husin. "Texture and structural refinement using neutron diffraction data from molybdite (MoO3) and calcite (CaCO3) powders and a Ni-rich Ni50.7Ti49.30 alloy." Powder Diffraction 24, no. 4 (December 2009): 315–26. http://dx.doi.org/10.1154/1.3257906.

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Preferred orientation or texture is a common feature of experimental powder patterns. The mathematics of two commonly used models for preferred orientation—the March-Dollase and the generalized spherical-harmonic models—is reviewed. Both models were applied individually to neutron powder data from uniaxially pressed molybdite (MoO3) and calcite (CaCO3) powders in Rietveld analyses, as well as the as-received powders. The structural refinement results are compared to single-crystal structures. The results indicate that reasonable refinement of crystal structures can be obtained using either the March model or generalized spherical-harmonic description. However, the generalized spherical-harmonic description provided better Rietveld fits than the March model for the molybdite and calcite. Therefore, the generalized spherical-harmonic description is recommended for correction of preferred orientation in neutron diffraction analysis for both crystal structure refinement and phase composition analysis. Subsequently, the generalized spherical-harmonic description is extended to crystal structure refinement of annealed and the aged polycrystalline Ni-rich Ni50.7Ti49.30 shape memory alloys.
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Van Nimmen, Katrien, Benedicte Vanwanseele, and Peter Van den Broeck. "Reconstruction of the Vertical Dynamic Running Load from the Registered Body Motion." Vibration 5, no. 3 (July 25, 2022): 464–82. http://dx.doi.org/10.3390/vibration5030026.

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In view of in-field applications, this paper introduces a methodology that uses the registered body motion to reconstruct the vertical dynamic running load. The principle of the reconstruction methodology is to use the time-variant pacing rate that is identified from the body motion together with a generalized single-step load model available in the literature. The methodology is reasonably robust against measurement noise. The performance of the methodology is evaluated by application to an experimental dataset where the running load and the body motion were registered simultaneously. The results show that a very good fit is found with the measured forces, with coefficients of determination of 95% in the time domain and 98% for the amplitude spectrum. Considering a 90% confidence interval, the fundamental harmonic is shown to be reconstructed with a maximum error of 12%. With nearly 90% of the energy concentrated around the fundamental harmonic, this harmonic is the dominant component of the running load. Due to the large inter-person variability in the single-step load pattern, a generalized single-step load model does not arrive at a good fit for the higher harmonics: the reproduction errors easily exceed 50% for a 90% confidence interval. Finally, the methodology is applied to reproduce the dynamic running load induced during full-scale tests on a flexible footbridge. The tests are designed such that the structural response is governed by the (near-)resonant contribution of the fundamental harmonic of the running load. The results show that even when a 12% uncertainty bound is taken into account, the structural response is significantly over-estimated by the numerical simulations (up to 50%). These results suggest a non-negligible impact of other phenomena, such as human–structure interaction, that are not accounted for in current load models.
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Dissertations / Theses on the topic "Generalised Harmonic Models"

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Jang, Haedong. "NONLINEAR EMBEDDING FOR HIGH EFFICIENCY RF POWER AMPLIFIER DESIGN AND APPLICATION TO GENERALIZED ASYMMETRIC DOHERTY AMPLIFIERS." The Ohio State University, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=osu1406269587.

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Uttam, Vishwabandhu. "A Unified Modeling Approach for Design and Performance Improvement of Triple Active Bridge Converter." Thesis, 2023. https://etd.iisc.ac.in/handle/2005/6107.

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Triple Active Bridge (TAB) converter is a multi-port DC-DC converter. This converter is an extension of the popular Dual Active Bridge converter. It features desirable traits of the DAB converter, such as high power density, galvanic isolation, and bi-directional power flow between any of the ports. As in other multi-port converters, redundant power conversion is minimized through component sharing among the ports in a TAB converter. All the switches in a TAB converter can undergo soft-switching over a wide range of operating points, reducing switching losses and the size of auxiliary components. The multiple degrees of freedom in modulating a TAB converter offer several design and operational flexibilities. However, this converter has yet to come into the limelight despite these advantages. One of the reasons is the lack of a unified analytical framework for the design and operation of this converter. The existing models for the TAB converter are limited in scope and cannot be easily used for the design and operational optimization of the converter. This work focuses on developing simple, unified models for analyzing the TAB converter. Firstly, the popular Fundamental Harmonic Approximated (FHA) large-signal and small- signal models are evaluated to understand their limitations. Improved large-signal and small-signal Generalised Harmonic Models (GHM) are developed by incorporating the impact of higher-order harmonics. While the GHM is shown to be superior for small-signal analysis of the converter and the design of a closed-loop control system, it is not suitable to analyze the soft-switching bounds of the TAB converter. To overcome the limitations of GHM, a Unified Model that incorporates the impact of the magnetising inductance of the three-winding transformer is proposed. The Unified Model can accurately predict the AC port currents at the switching instants and is used to study the soft-switching bounds of the TAB converter. The GHM and Unified Model are validated through extensive switching circuit simulations and experimental results from a 1 kW hardware prototype developed in the laboratory. Further, a new design algorithm for the TAB converter is proposed. The proposed algorithm leverages the FHA model’s simplicity and the Unified Model’s accuracy. Finally, a new modulation scheme based on Penta Phase Shift with five degrees of freedom is proposed to achieve soft-switching across the operational range of the TAB converter.
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Cajiao, Velez Felipe. "Engineering and Control of Quantum Processes by Short Laser Pulses." Doctoral thesis, 2016. https://depotuw.ceon.pl/handle/item/1854.

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Mugisha, Stella. "Applied mathematical modelling with new parameters and applications to some real life problems." Thesis, 2018. http://hdl.handle.net/10500/24973.

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Some Epidemic models with fractional derivatives were proved to be well-defined, well-posed and more accurate [34, 51, 116], compared to models with the conventional derivative. An Ebola epidemic model with non-linear transmission is fully analyzed. The model is expressed with the conventional time derivative with a new parameter included, which happens to be fractional (that derivative is called the 􀀀derivative). We proved that the model is well-de ned and well-posed. Moreover, conditions for boundedness and dissipativity of the trajectories are established. Exploiting the generalized Routh-Hurwitz Criteria, existence and stability analysis of equilibrium points for the Ebola model are performed to show that they are strongly dependent on the non-linear transmission. In particular, conditions for existence and stability of a unique endemic equilibrium to the Ebola system are given. Numerical simulations are provided for particular expressions of the non-linear transmission, with model's parameters taking di erent values. The resulting simulations are in concordance with the usual threshold behavior. The results obtained here may be signi cant for the ght and prevention against Ebola haemorrhagic fever that has so far exterminated hundreds of families and is still a ecting many people in West-Africa and other parts of the world. The full comprehension and handling of the phenomenon of shattering, sometime happening during the process of polymer chain degradation [129, 142], remains unsolved when using the traditional evolution equations describing the degradation. This traditional model has been proved to be very hard to handle as it involves evolution of two intertwined quantities. Moreover, the explicit form of its solution is, in general, impossible to obtain. We explore the possibility of generalizing evolution equation modeling the polymer chain degradation and analyze the model with the conventional time derivative with a new parameter. We consider the general case where the breakup rate depends on the size of the chain breaking up. In the process, the alternative version of Sumudu integral transform is used to provide an explicit form of the general solution representing the evolution of polymer sizes distribution. In particular, we show that this evolution exhibits existence of complex periodic properties due to the presence of cosine and sine functions governing the solutions. Numerical simulations are performed for some particular cases and prove that the system describing the polymer chain degradation contains complex and simple harmonic poles whose e ects are given by these functions or a combination of them. This result may be crucial in the ongoing research to better handle and explain the phenomenon of shattering. Lastly, it has become a conjecture that power series like Mittag-Le er functions and their variants naturally govern solutions to most of generalized fractional evolution models such as kinetic, di usion or relaxation equations. The question is to say whether or not this is always true! Whence, three generalized evolution equations with an additional fractional parameter are solved analytically with conventional techniques. These are processes related to stationary state system, relaxation and di usion. In the analysis, we exploit the Sumudu transform to show that investigation on the stationary state system leads to results of invariability. However, unlike other models, the generalized di usion and relaxation models are proven not to be governed by Mittag-Le er functions or any of their variants, but rather by a parameterized exponential function, new in the literature, more accurate and easier to handle. Graphical representations are performed and also show how that parameter, called ; can be used to control the stationarity of such generalized models.
Mathematical Sciences
Ph. D. (Applied Mathematics)
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Book chapters on the topic "Generalised Harmonic Models"

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Steeb, Willi-Hans. "Harmonic Oscillator." In Hilbert Spaces, Wavelets, Generalised Functions and Modern Quantum Mechanics, 123–34. Dordrecht: Springer Netherlands, 1998. http://dx.doi.org/10.1007/978-94-011-5332-4_12.

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Dey, Santanu, and Kalpesh J. Haria. "Generalized Repeated Interaction Model and Transfer Functions." In Operator Theory in Harmonic and Non-commutative Analysis, 111–35. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-06266-2_6.

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Kazarian, K. S. "Generalized Fourier Series by the Double Trigonometric System." In Modern Methods in Operator Theory and Harmonic Analysis, 67–79. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-26748-3_5.

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Karapetyants, Alexey, and Joel E. Restrepo. "Boundedness of Projection Operator in Generalized Holomorphic and Harmonic Spaces of Functions of Hölder Type." In Modern Methods in Operator Theory and Harmonic Analysis, 57–66. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-26748-3_4.

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Cesari, Stefano. "Prison Treatment Programs From an International Perspective." In Handbook of Research on Trends and Issues in Crime Prevention, Rehabilitation, and Victim Support, 359–74. IGI Global, 2020. http://dx.doi.org/10.4018/978-1-7998-1286-9.ch021.

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The generalized use of imprisonment to meet the need for security witnessed by the high rates of incarceration in countries such as the United States makes it necessary to question sentences, seeking to shape them so that they actually pursue the purposes indicated by international resources. In harmony with the model proposed by international resources for which detention can actually constitute a period capable of facilitating re-entry into society, in the chapter, some local experiences regarding the treatment of prisoners will be discussed. The reduction of recourse to the precautionary measure of deprivation of liberty is a good practice to limit the detained population. As for the methods of treatment within the prison walls, a penitentiary model based on the empowerment of the prisoner and on the recovery of his or her social, family, and work dimensions seems the only way to legitimize the deprivation of freedom beyond a logic of mere suppression.
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Conference papers on the topic "Generalised Harmonic Models"

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Peel, D. J., R. Stanway, and W. A. Bullough. "The ER Long-Stroke Damper: Experimental Verification of Mathematical Models." In ASME 1997 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 1997. http://dx.doi.org/10.1115/imece1997-0492.

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Abstract Traditionally, procedures of modelling the performance of electro-rheological (ER) devices have been severely hampered by the absence of robust methods for characterising the behaviour of the ER fluids themselves. Recent publications by the authors have described a non-dimensional characterisation procedure. Not only does this new approach drastically reduce the number of variables but through a generalised analysis enables tire steady flow characteristics of different types and sizes of devices to be related. In this paper, the authors describe the extension of the characterisation technique to consider the behaviour of a controllable vibration damper which uses ER fluid as the working medium. A critical comparison is made between the model predictions and the observed behaviour of a test facility specially constructed to examine the response of an ER damper to harmonic displacement excitation. Emphasis is placed upon the influence of fluid inertia and compressibility on dynamic response and upon phenomena which are observed at the reversal of fluid motion; suggestions are made for further work.
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H. Dadmarzi, Fatemeh, Maxime Thys, and Erin E. Bachynski. "Validation of Hydrodynamic Loads on a Large-Diameter Monopile in Regular Waves." In ASME 2019 38th International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2019. http://dx.doi.org/10.1115/omae2019-95929.

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Abstract Validated hydrodynamic load models for large-diameter support structures are increasingly important as the industry moves towards larger offshore wind turbines. Experiments at 1:50 scale with stiff, vertical, bottom-fixed, extra-large (9m and 11m diameter full-scale) monopiles in steep waves are conducted. The tests are carried out at two water depths, 27 m and 33 m. A range of regular waves, with varying period and amplitude, are used. The first, second, and third harmonics of the total wave loads, where measurements are available, are calculated with different methods. For the first harmonic of the force (and consequently the mudline moment), MacCamy-Fuchs gives the best agreement with experiments, especially for the larger diameter model. For the second harmonic, for the shortest waves the generalized FNV theory and Morison equation overpredict the forces, while for the longest (and largest) waves, the opposite is observed. The third harmonic of the force is generally overpredicted by the calculations.
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CASTRO, ALLAN GREGORI DE, PAULO ROBERTO UBALDO GUAZZELLI, STEFAN THIAGO CURY ALVES DOS SANTOS, WILLIAM CéSAR DE ANDRADE PEREIRA, CARLOS MATHEUS RODRIGUES DE OLIVEIRA, GEYVERSON TEIXEIRA DE PAULA, and JOSé ROBERTO BOFFINO DE ALMEIDA MONTEIRO. "Finite Control-Set Model Predictive Torque Control of Nonsinusoidal PMSM: a Generalized Approach for Torque Ripple Mitigation and MTPA Operation." In Seminar on Power Electronics and Control (SEPOC 2021). sepoc, 2021. http://dx.doi.org/10.53316/sepoc2021.024.

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Permanent Magnet Synchronous Motors (PMSMs) may present spatial harmonics depending on the design guidelines or imprecisions on the manufacturing process. The interaction of conventional sinusoidal current feeding strategies with these spatial harmonics can produce a considerable torque ripple. This paper deals with a modified Finite Control-Set Model Predictive Torque Control (FCS-MPTC) loop as an active torque ripple minimization solution for PMSMs with spatial harmonics. The proposed approach designs a novel cost function, based on the cross product reactive instantaneous power theory. The benefits of the proposed generalized approach include providing smooth torque production and the Maximum Torque per Ampère (MTPA) operation on PMSMs with a number of spatial harmonic sources, including those on zero-sequence. The effectiveness of the presented control strategy is demonstrated comparatively to conventional sinusoidal current feeding strategy on a PMSM drive employing a three-phase four-leg two level voltage source inverter under both steady and transient state.
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Mickens, Ronald E. "Generalized Harmonic Oscillators: Velocity Dependent Frequencies." In ASME 2001 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2001. http://dx.doi.org/10.1115/detc2001/vib-21417.

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Abstract Preliminary results are given on a new class of nonlinear oscillator equations that generalize those of the usual linear harmonic case. These equations take the form ẋ = f(x)y and ẏ = −g(y)x, where f(x) and g(y) are continuous with first derivatives, and f(0) > 0, g(0) > 0. Of interest is the fact that these equations have a first-integral, i.e., there exists a function H(x,y) such that along a particular trajectory in the (x,y) phase space, H(x,y) = constant. We work out several general results related to this system of equations and illustrate them with several special cases that correspond to models of physical systems. The work reported here was supported in part by research grants from DOE and the MBRS-SCORE Program at Clark Atlanta University.
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Fabre, C., N. Pettiaux, and P. Mandel. "Squeezing spectrum in second-harmonic generation in the self-pulsing domain." In OSA Annual Meeting. Washington, D.C.: Optica Publishing Group, 1990. http://dx.doi.org/10.1364/oam.1990.thb1.

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We consider the process of second-harmonic generation (SHG) in a cavity that is resonant for both the fundamental- and second-harmonic modes. It has been previously shown that such a system displays a phase instability leading to self-pulsing and that one gets important intensity squeezing on both the fundamental- and second-harmonic mode for pump intensities close to but below, this instability threshold. Such a squeezing has been recently observed. We have analytically calculated the intensity-noise spectrum of the frequency-doubled field above such an instability threshold, using a semiclassical input-output technique for the treatment of quantum fluctuations.1 Such a method, introduced to deal with fluctuations around a stable solution, has been generalized to the self-pulsing domain. As expected, the instability brings excess noise to the output beams, especially around the zero-frequency, the self-oscillation frequency, and its harmonics. Remarkably, some regions exist in which where the noise increase is small; squeezing still occurs in this frequency range far in the instability domain.
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Xu, Yufeng, and Om P. Agrawal. "Numerical Solutions of Generalized Oscillator Equations." In ASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/detc2013-12705.

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Harmonic oscillators play a fundamental role in many areas of science and engineering, such as classical mechanics, electronics, quantum physics, and others. As a result, harmonic oscillators have been studied extensively. Classical harmonic oscillators are defined using integer order derivatives. In recent years, fractional derivatives have been used to model the behaviors of damped systems more accurately. In this paper, we use three operators called K-, A- and B-operators to define the equation of motion of an oscillator. In contrast to fractional integral and derivative operators which use fractional power kernels or their variations in their definitions, the K-, A- and B-operators allow the kernel to be arbitrary. In the case when the kernel is a power kernel, these operators reduce to fractional integral and derivative operators. Thus, they are more general than the fractional integral and derivative operators. Because of the general nature of the K-, A- and B-operators, the harmonic oscillators are called the generalized harmonic oscillators. The equations of motion of a generalized harmonic oscillator are obtained using a generalized Euler-Lagrange equation presented recently. In general, the resulting equations cannot be solved in closed form. A numerical scheme is presented to solve these equations. To verify the effectiveness of the numerical scheme, a problem is considered for which a closed form solution could be found. Numerical solution for the problem is compared with the analytical solution. It is demonstrated that the numerical scheme is convergent, and the order of convergence is 2. For a special kernel, this scheme reduces to a scheme presented recently in the literature.
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Uttam, Vishwabandhu, Venkateswara Rao Kudaravalli, and Vishnu Mahadeva Iyer. "Generalised Harmonic Model for a Triple Active Bridge DC-DC Converter." In 2022 IEEE Energy Conversion Congress and Exposition (ECCE). IEEE, 2022. http://dx.doi.org/10.1109/ecce50734.2022.9947769.

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Khorrami, Hamid, Ramin Sedaghati, and Subhash Rakheja. "Developing a Generalized Harmonic Balance Method for Accurate Identification of Crack Depth in a Continuous Shaft-Disc System." In ASME 2015 Conference on Smart Materials, Adaptive Structures and Intelligent Systems. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/smasis2015-8954.

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In this work, the effect of a crack on the vibrational properties of a shaft-disc system has been studied applying a generalized harmonic balance method. In the reviewed literature, the reported methods to find the unbalance response of a continuous shaft-disc system provide only the first harmonic component of the response; whereas, the presented method gives the super-harmonic components as well. The shaft-disk system consists of a flexible shaft with a single rigid disc mounted on rigid short bearing supports. The shaft contains a transverse breathing crack (fatigue crack). The main concept for crack detection in vibration-based methods is basically the investigation of crack-induced changes in the selected vibrational properties. Shaft critical speeds and harmonic and super-harmonic components of the unbalance lateral response have been used as typical vibrational properties for crack detection in a rotating shaft system. A generalized harmonic balance method has been developed to efficiently investigate changes in vibrational properties due to the effect of crack properties, depth and location. The results of the developed analytical model have been compared with those obtained from the finite element model and close agreement has been observed.
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Achar, B. N. Narahari, Tanya Prozny, and John W. Hanneken. "Linear Chain of Coupled Fractional Oscillators: Response Dynamics and Its Continuum Limit." In ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/detc2007-35403.

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The standard model of a chain of simple harmonic oscillators of Condensed Matter Physics is generalized to a model of linear chain of coupled fractional oscillators in fractional dynamics. The set of integral equations of motion pertaining to the chain of harmonic oscillators is generalized by taking the integrals to be of arbitrary order according to the methods of fractional calculus to yield the equations of motion of a chain of coupled fractional oscillators. The solution is obtained by using Laplace transforms. The continuum limit of the equations is shown to yield the fractional diffusion-wave equation in one dimension. The solution and numerical application of the set of equations and the continuum limit there of are discussed.
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10

Wang, Fengxia. "Parametric Stability Analysis of Nonlinear Rotating Blades." In ASME 2011 International Mechanical Engineering Congress and Exposition. ASMEDC, 2011. http://dx.doi.org/10.1115/imece2011-63903.

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The role of the “geometric stiffening” nonlinearities played in the stability analysis of a rotating beam is investigated. It is a well established fact that nonlinear theory must be employed to capture geometric stiffening effect, which has been extensively investigated. In this work, two models are built for a rotating blade with periodically perturbed rotation rate, one is the “effective load” linear model and the other is “geometric stiffening” nonlinear model. Both of these two models are discretisized via Galerkin’s method and a set of parametric excited gyroscopic equations are obtained. The dynamic stability of these two models are studied and compared by the generalized harmonic balance method.
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Reports on the topic "Generalised Harmonic Models"

1

Tang, J. The generalized spin-boson model for electron-transfer reactions involving two harmonic potentials with a different force constant. Office of Scientific and Technical Information (OSTI), January 1994. http://dx.doi.org/10.2172/10117016.

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