In this paper, we have studied the new solitary wave solutions of the beta-fractional derivative form of the Peyrard-Bishop DNA model (PB-DNAM). These solutions are responsible for analysing the nonlinear interaction between the adjacent displacements of the DNA strand. To get these solutions, we have applied the generalized Riccati equation expansion method. Under different parametric conditions and fractional values, the obtained solutions show different wave patterns including w-shape, bright, combined dark-bright, periodic wave solutions, bell shape, m-shape, w-shape along with two bright solutions and m-shape along with two dark solutions. These physical characteristics are analyzed thoroughly by graphical representations. The solutions show the successful application of the proposed method which will be helpful in finding analytical solutions to other nonlinear problems.
{"title":"New Dynamic Multi-Wave Solutions Of The Fractional Peyrard-Bishop Dna Model","authors":"Ananya Tripathy, S. Sahoo","doi":"10.1115/1.4063223","DOIUrl":"https://doi.org/10.1115/1.4063223","url":null,"abstract":"\u0000 In this paper, we have studied the new solitary wave solutions of the beta-fractional derivative form of the Peyrard-Bishop DNA model (PB-DNAM). These solutions are responsible for analysing the nonlinear interaction between the adjacent displacements of the DNA strand. To get these solutions, we have applied the generalized Riccati equation expansion method. Under different parametric conditions and fractional values, the obtained solutions show different wave patterns including w-shape, bright, combined dark-bright, periodic wave solutions, bell shape, m-shape, w-shape along with two bright solutions and m-shape along with two dark solutions. These physical characteristics are analyzed thoroughly by graphical representations. The solutions show the successful application of the proposed method which will be helpful in finding analytical solutions to other nonlinear problems.","PeriodicalId":54858,"journal":{"name":"Journal of Computational and Nonlinear Dynamics","volume":"1 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2023-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88560628","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Tomoyuki Suzuki, K. Hirohata, Yasutaka Ito, Takehiro Hato, A. Kano
In this paper, we propose a sparse modeling method for automatically creating a surrogate model for nonlinear time-variant systems from a very small number of time series data with nonconstant time steps. We developed three machine learning methods–namely, (1) a data preprocessing method for considering the correlation between errors, (2) a sequential thresholded non-negative least-squares method based on term size criteria, and (3) a solution space search method involving similarity model classification–to apply sparse identification of nonlinear dynamical systems, as first proposed in 2016, to temperature prediction simulations. The proposed method has the potential for wide application to fields where the concept of equivalent circuits can be applied. The effectiveness of the proposed method was verified using time series data obtained by thermo-fluid analysis of a power module. Two types of cooling systems were verified: forced air cooling and natural air cooling. The model created from the thermo-fluid analysis results with fewer than the number of input parameters, predicted multiple test data, including extrapolation, with a mean error of less than 1 K. Because the proposed method can be applied using a very small number of data, has a high extrapolation accuracy, and is easy to interpret, it is expected not only that design parameters can be fine-tuned and actual loads can be taken into account, but also that condition-based maintenance can be realized through real-time simulation.
{"title":"Physics-Informed Machine Learning For Surrogate Modeling Of Heat Transfer Phenomena","authors":"Tomoyuki Suzuki, K. Hirohata, Yasutaka Ito, Takehiro Hato, A. Kano","doi":"10.1115/1.4063224","DOIUrl":"https://doi.org/10.1115/1.4063224","url":null,"abstract":"\u0000 In this paper, we propose a sparse modeling method for automatically creating a surrogate model for nonlinear time-variant systems from a very small number of time series data with nonconstant time steps. We developed three machine learning methods–namely, (1) a data preprocessing method for considering the correlation between errors, (2) a sequential thresholded non-negative least-squares method based on term size criteria, and (3) a solution space search method involving similarity model classification–to apply sparse identification of nonlinear dynamical systems, as first proposed in 2016, to temperature prediction simulations. The proposed method has the potential for wide application to fields where the concept of equivalent circuits can be applied. The effectiveness of the proposed method was verified using time series data obtained by thermo-fluid analysis of a power module. Two types of cooling systems were verified: forced air cooling and natural air cooling. The model created from the thermo-fluid analysis results with fewer than the number of input parameters, predicted multiple test data, including extrapolation, with a mean error of less than 1 K. Because the proposed method can be applied using a very small number of data, has a high extrapolation accuracy, and is easy to interpret, it is expected not only that design parameters can be fine-tuned and actual loads can be taken into account, but also that condition-based maintenance can be realized through real-time simulation.","PeriodicalId":54858,"journal":{"name":"Journal of Computational and Nonlinear Dynamics","volume":"130 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2023-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85129270","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this work we examine the nonlinear dynamics of an inverted pendulum between lateral rebounding barriers. We continue the numerical investigation started in [1] by adding the contribution of the second harmonic in the external forcing term. We investigate the behaviour of the periodic attractors by bifurcation diagrams with respect to each amplitude and by behaviour charts of single attractors in the amplitude parameters plane for fixed frequency. We study the effects of the second harmonic term on the existence domain of each attractor, on local bifurcations and on the changes in the basins of attraction. The behaviour of some robust chaotic attractor is also considered. In the evolution of the periodic attractors we have observed that the addition of the second harmonic generates a rich variety of behaviours, such as loss of stability and formation of isolas of periodic orbits. In the case of chaotic attractors, we have studied one attractor at high frequency, ω =18, and one at low frequency, ω =3. In the high frequency case we detect a transition from a scattered to a confined attractor, whereas at the lower frequency the chaotic attractor is present over a wide range of the second harmonic's amplitude. Finally, we extend the investigation of the chaotic attractors by bifurcation diagrams with respect to the frequency.
{"title":"Attractors' Analysis And Bifurcation Diagrams For An Impacting Inverted Pendulum In The Presence Of A Two-Terms Harmonic Excitation","authors":"M. Petrini, L. Demeio, S. Lenci","doi":"10.1115/1.4063034","DOIUrl":"https://doi.org/10.1115/1.4063034","url":null,"abstract":"In this work we examine the nonlinear dynamics of an inverted pendulum between lateral rebounding barriers. We continue the numerical investigation started in [1] by adding the contribution of the second harmonic in the external forcing term. We investigate the behaviour of the periodic attractors by bifurcation diagrams with respect to each amplitude and by behaviour charts of single attractors in the amplitude parameters plane for fixed frequency. We study the effects of the second harmonic term on the existence domain of each attractor, on local bifurcations and on the changes in the basins of attraction. The behaviour of some robust chaotic attractor is also considered. In the evolution of the periodic attractors we have observed that the addition of the second harmonic generates a rich variety of behaviours, such as loss of stability and formation of isolas of periodic orbits. In the case of chaotic attractors, we have studied one attractor at high frequency, ω =18, and one at low frequency, ω =3. In the high frequency case we detect a transition from a scattered to a confined attractor, whereas at the lower frequency the chaotic attractor is present over a wide range of the second harmonic's amplitude. Finally, we extend the investigation of the chaotic attractors by bifurcation diagrams with respect to the frequency.","PeriodicalId":54858,"journal":{"name":"Journal of Computational and Nonlinear Dynamics","volume":"60 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2023-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87523272","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Fractional partial differential equations are useful tools to describe transportation, anomalous and non-Brownian diffusion. In the present paper, we propose the Daftardar-Gejji and Jafari method along with its error analysis for solving systems of nonlinear time-space fractional partial differential equations (PDEs). Moreover, we solve a variety of non-trivial time-space fractional systems of PDEs. The obtained solutions either occur in exact form or in the form of a series, which converges to a closed form. The proposed method is free from linearization and discretization and does not include any tedious calculations. Moreover, it is easily employable using the Computer algebra system such as Mathematica, Maple, etc.
{"title":"Exact Solutions Of Systems Of Nonlinear Time-Space Fractional Pdes Using An Iterative Method","authors":"Manoj Kumar","doi":"10.1115/1.4062910","DOIUrl":"https://doi.org/10.1115/1.4062910","url":null,"abstract":"\u0000 Fractional partial differential equations are useful tools to describe transportation, anomalous and non-Brownian diffusion. In the present paper, we propose the Daftardar-Gejji and Jafari method along with its error analysis for solving systems of nonlinear time-space fractional partial differential equations (PDEs). Moreover, we solve a variety of non-trivial time-space fractional systems of PDEs. The obtained solutions either occur in exact form or in the form of a series, which converges to a closed form. The proposed method is free from linearization and discretization and does not include any tedious calculations. Moreover, it is easily employable using the Computer algebra system such as Mathematica, Maple, etc.","PeriodicalId":54858,"journal":{"name":"Journal of Computational and Nonlinear Dynamics","volume":"27 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2023-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89274116","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Shimmy motion may occur for an aircraft nose landing gear (NLG) during its take-off, landing and taxiing procedure, which is an undesirable motion and should be suppressed. Here, a novel torsional nonlinear energy sink (NES) based on the cam-roller mechanism is proposed and applied in the NLG to improve its shimmy performance. The torsional NES is connected with the upper and lower struts of the NLG and its mechanical characteristic is studied. A seven-dimensional dynamic model of the NLG coupled with NES is built, which considers the NLG torsional and lateral motions, and the nonlinear tire model. The numerical continuation method is applied to analyze its shimmy performance, the stable area and limit cycle oscillation (LCO) amplitude are acquired, further compared with those of the original NLG without using the NES. The results show that as the NES is used in the NLG, the torsional shimmy dominated unstable area reduces significantly and the lateral shimmy dominated unstable area decreases slightly, which results in the increase of the stable area of the NLG; the maximum LCO amplitudes for the NLG torsional and lateral shimmy become smaller, the forward speed ranges as the torsional and lateral shimmy occur become narrower, which indicates that the stable forward speed ranges of the NLG become wider; the NLG shimmy performance improves as the NES has larger torsional inertia and damping, and smaller torsional linear stiffness. Thus, the NES can suppress the NLG shimmy motion and enhance its shimmy performance effectively.
{"title":"Shimmy Suppression Of An Aircraft Nose Landing Gear Using Torsional Nonlinear Energy Sink","authors":"Y. Wang, Zhang Tao, Xianyu Jin, Yin Yin","doi":"10.1115/1.4062909","DOIUrl":"https://doi.org/10.1115/1.4062909","url":null,"abstract":"\u0000 Shimmy motion may occur for an aircraft nose landing gear (NLG) during its take-off, landing and taxiing procedure, which is an undesirable motion and should be suppressed. Here, a novel torsional nonlinear energy sink (NES) based on the cam-roller mechanism is proposed and applied in the NLG to improve its shimmy performance. The torsional NES is connected with the upper and lower struts of the NLG and its mechanical characteristic is studied. A seven-dimensional dynamic model of the NLG coupled with NES is built, which considers the NLG torsional and lateral motions, and the nonlinear tire model. The numerical continuation method is applied to analyze its shimmy performance, the stable area and limit cycle oscillation (LCO) amplitude are acquired, further compared with those of the original NLG without using the NES. The results show that as the NES is used in the NLG, the torsional shimmy dominated unstable area reduces significantly and the lateral shimmy dominated unstable area decreases slightly, which results in the increase of the stable area of the NLG; the maximum LCO amplitudes for the NLG torsional and lateral shimmy become smaller, the forward speed ranges as the torsional and lateral shimmy occur become narrower, which indicates that the stable forward speed ranges of the NLG become wider; the NLG shimmy performance improves as the NES has larger torsional inertia and damping, and smaller torsional linear stiffness. Thus, the NES can suppress the NLG shimmy motion and enhance its shimmy performance effectively.","PeriodicalId":54858,"journal":{"name":"Journal of Computational and Nonlinear Dynamics","volume":"145 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2023-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86775617","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Jialin Tian, Lanhui Mao, Yinglin Yang, Haolin Song, Jun Song
In the process of long horizontal directional well drilling, the contact between drill string and borehole wall leads to serious dragging pressure. Therefore, a Drill String Rotary Controller(DSC) for directional well is proposed, and the function test and performance test of DSC are completed through experimental platform. According to working characteristics of DSC, a coupled drill string dynamic model for directional well drilling is established. The coupling dynamic characteristics of different drill pipe sections and different modules in the axial and torsional directions are studied. The results show that in the process of directional drilling, the axial velocity of the bottom hole module is low. Under the action of formation reaction force, the drilling volume of the drill bit decreases, but it still keeps in contact with the rock. At this time, the drill string system is in a normal drilling state. When drill string is stable, the angular velocity of different drill pipes, rotary table and collars are stable at 31.16 rad / s, and the angular velocity of DSC and BHA are stable at 43.19 rad/s. It indicates the DSC works well, the drill string is balanced in the torsional direction, and there is dynamic friction between the drill pipe and the drill string, which is conducive to lower the drill string. Through theoretical and experimental research, the tool effectively solves the problem of serious drag pressure in directional drilling process, and provides a theoretical basis for directional well drilling speed increase.
{"title":"Study On Directional Drilling Coupling Dynamics Based On Drill String Rotary Controller","authors":"Jialin Tian, Lanhui Mao, Yinglin Yang, Haolin Song, Jun Song","doi":"10.1115/1.4062911","DOIUrl":"https://doi.org/10.1115/1.4062911","url":null,"abstract":"\u0000 In the process of long horizontal directional well drilling, the contact between drill string and borehole wall leads to serious dragging pressure. Therefore, a Drill String Rotary Controller(DSC) for directional well is proposed, and the function test and performance test of DSC are completed through experimental platform. According to working characteristics of DSC, a coupled drill string dynamic model for directional well drilling is established. The coupling dynamic characteristics of different drill pipe sections and different modules in the axial and torsional directions are studied. The results show that in the process of directional drilling, the axial velocity of the bottom hole module is low. Under the action of formation reaction force, the drilling volume of the drill bit decreases, but it still keeps in contact with the rock. At this time, the drill string system is in a normal drilling state. When drill string is stable, the angular velocity of different drill pipes, rotary table and collars are stable at 31.16 rad / s, and the angular velocity of DSC and BHA are stable at 43.19 rad/s. It indicates the DSC works well, the drill string is balanced in the torsional direction, and there is dynamic friction between the drill pipe and the drill string, which is conducive to lower the drill string. Through theoretical and experimental research, the tool effectively solves the problem of serious drag pressure in directional drilling process, and provides a theoretical basis for directional well drilling speed increase.","PeriodicalId":54858,"journal":{"name":"Journal of Computational and Nonlinear Dynamics","volume":"2004 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2023-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82567760","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
O. Barry, P. Belardinelli, T. Berruti, Radu Serban
{"title":"Special Issue: Selected Papers from IDETC-CIE 2022","authors":"O. Barry, P. Belardinelli, T. Berruti, Radu Serban","doi":"10.1115/1.4062725","DOIUrl":"https://doi.org/10.1115/1.4062725","url":null,"abstract":"","PeriodicalId":54858,"journal":{"name":"Journal of Computational and Nonlinear Dynamics","volume":"1 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2023-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74062068","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper is concerned with some features of the modified Caputo-type Mittag-Leffler fractional derivative operator and its associated fractional integral operator. Mainly, new types of solutions for fractional differential equations with Mittag-Leffler kernel are generated based on a numerical algorithm developed in this paper. The suggested algorithm is used to describe the solution behavior of models involving modified Caputo-type Mittag-Leffler fractional derivatives. The results described in this paper are expected to be effectively employed in the area of simulating related fractional models.
{"title":"New Solutions of the Fractional Differential Equations with Modified Mittag-Leffler Kernel","authors":"Z. Odibat, D. Baleanu","doi":"10.1115/1.4062747","DOIUrl":"https://doi.org/10.1115/1.4062747","url":null,"abstract":"\u0000 This paper is concerned with some features of the modified Caputo-type Mittag-Leffler fractional derivative operator and its associated fractional integral operator. Mainly, new types of solutions for fractional differential equations with Mittag-Leffler kernel are generated based on a numerical algorithm developed in this paper. The suggested algorithm is used to describe the solution behavior of models involving modified Caputo-type Mittag-Leffler fractional derivatives. The results described in this paper are expected to be effectively employed in the area of simulating related fractional models.","PeriodicalId":54858,"journal":{"name":"Journal of Computational and Nonlinear Dynamics","volume":"7 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2023-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89749062","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract In recent years, super-coiled polymer (SCP) actuators have been investigated as a higher yield, low-cost alternative to conventional actuators. A major challenge has been finding appropriate general and industry uses for these actuators due to their hysteretic response. This paper seeks to compare the response for SCP actuators based on different thread weights and sizes and thus suggest possible directions for their use. The actuators were produced through coiling and heat training controlled via Arduino. The responses were obtained by supplying a controlled voltage to the system. The response was filmed and processed using matlab; the resulting displacement and strain were used to observe the hysteretic characteristics. Based on the characteristics noted, different applications were recommended for these SCP actuators. It is recommended that this research into SCP actuators be furthered by developing hysteresis models for compensation, control, and exploring their use in robotic systems and tactile mechanisms.
{"title":"Comparison of the Hysteresis Response of Super-Coiled Polymer Actuators","authors":"Josh Henry, Jacqueline Bridge","doi":"10.1115/1.4062660","DOIUrl":"https://doi.org/10.1115/1.4062660","url":null,"abstract":"Abstract In recent years, super-coiled polymer (SCP) actuators have been investigated as a higher yield, low-cost alternative to conventional actuators. A major challenge has been finding appropriate general and industry uses for these actuators due to their hysteretic response. This paper seeks to compare the response for SCP actuators based on different thread weights and sizes and thus suggest possible directions for their use. The actuators were produced through coiling and heat training controlled via Arduino. The responses were obtained by supplying a controlled voltage to the system. The response was filmed and processed using matlab; the resulting displacement and strain were used to observe the hysteretic characteristics. Based on the characteristics noted, different applications were recommended for these SCP actuators. It is recommended that this research into SCP actuators be furthered by developing hysteresis models for compensation, control, and exploring their use in robotic systems and tactile mechanisms.","PeriodicalId":54858,"journal":{"name":"Journal of Computational and Nonlinear Dynamics","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135525266","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Junaidvali Shaik, Sankalp Tiwari, C. P. Vyasarayani
In the usual approach to determining the stability of a time-periodic delay differential equation (DDE), the DDE is converted into an approximate system of time-periodic ordinary differential equations (ODEs) using Galerkin approximations. Later, Floquet theory is applied to these ODEs. Alternatively, semi-discretization-like approaches can be used to construct an approximate Floquet transition matrix (FTM) for a DDE. In this paper, we develop a method to obtain the FTM directly. Our approach is analogous to the Floquet theory for ODEs: we consider one polynomial basis function at a time as the history function and stack the coefficients of the corresponding DDE solutions to construct the FTM. The largest magnitude eigenvalue of the FTM determines the stability of the DDE. Since the obtained FTM is an approximation of the actual infinite-dimensional FTM, the criterion developed for stability is approximate. We demonstrate the correctness and efficacy of our method by studying several candidate DDEs with time-periodic parameters and comparing the results with those obtained from the Galerkin approximations.
{"title":"Floquet Theory for Linear Time-Periodic Delay Differential Equations Using Orthonormal History Functions","authors":"Junaidvali Shaik, Sankalp Tiwari, C. P. Vyasarayani","doi":"10.1115/1.4062633","DOIUrl":"https://doi.org/10.1115/1.4062633","url":null,"abstract":"\u0000 In the usual approach to determining the stability of a time-periodic delay differential equation (DDE), the DDE is converted into an approximate system of time-periodic ordinary differential equations (ODEs) using Galerkin approximations. Later, Floquet theory is applied to these ODEs. Alternatively, semi-discretization-like approaches can be used to construct an approximate Floquet transition matrix (FTM) for a DDE. In this paper, we develop a method to obtain the FTM directly. Our approach is analogous to the Floquet theory for ODEs: we consider one polynomial basis function at a time as the history function and stack the coefficients of the corresponding DDE solutions to construct the FTM. The largest magnitude eigenvalue of the FTM determines the stability of the DDE. Since the obtained FTM is an approximation of the actual infinite-dimensional FTM, the criterion developed for stability is approximate. We demonstrate the correctness and efficacy of our method by studying several candidate DDEs with time-periodic parameters and comparing the results with those obtained from the Galerkin approximations.","PeriodicalId":54858,"journal":{"name":"Journal of Computational and Nonlinear Dynamics","volume":"28 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2023-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79010997","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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