{"title":"非线性系统次谐波振荡的稳定性","authors":"S. Qiu, I. Filanovsky","doi":"10.1109/MWSCAS.1998.759450","DOIUrl":null,"url":null,"abstract":"A method for verification of subharmonic oscillation stability in nonlinear systems with a polynomial type of nonlinearity is proposed. The main harmonic and the subharmonic are represented in the exponential form and substituted into the system differential equation. Amplitudes of both harmonics are perturbed, and the subharmonic amplitude perturbation operator equation is obtained. Then, only the terms representing the first order derivatives are retained. The real and imaginary parts of the operator equation are separated to give the system of two linear differential equations for the components of subharmonic amplitude perturbation. The perturbations of the main harmonic are eliminated using the main harmonic equation. Then the characteristic equation of this system is used for verification of the subharmonic stability.","PeriodicalId":338994,"journal":{"name":"1998 Midwest Symposium on Circuits and Systems (Cat. No. 98CB36268)","volume":"4 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1998-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On stability of subharmonic oscillations in nonlinear systems\",\"authors\":\"S. Qiu, I. Filanovsky\",\"doi\":\"10.1109/MWSCAS.1998.759450\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A method for verification of subharmonic oscillation stability in nonlinear systems with a polynomial type of nonlinearity is proposed. The main harmonic and the subharmonic are represented in the exponential form and substituted into the system differential equation. Amplitudes of both harmonics are perturbed, and the subharmonic amplitude perturbation operator equation is obtained. Then, only the terms representing the first order derivatives are retained. The real and imaginary parts of the operator equation are separated to give the system of two linear differential equations for the components of subharmonic amplitude perturbation. The perturbations of the main harmonic are eliminated using the main harmonic equation. Then the characteristic equation of this system is used for verification of the subharmonic stability.\",\"PeriodicalId\":338994,\"journal\":{\"name\":\"1998 Midwest Symposium on Circuits and Systems (Cat. No. 98CB36268)\",\"volume\":\"4 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1998-08-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"1998 Midwest Symposium on Circuits and Systems (Cat. No. 98CB36268)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/MWSCAS.1998.759450\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"1998 Midwest Symposium on Circuits and Systems (Cat. No. 98CB36268)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/MWSCAS.1998.759450","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
On stability of subharmonic oscillations in nonlinear systems
A method for verification of subharmonic oscillation stability in nonlinear systems with a polynomial type of nonlinearity is proposed. The main harmonic and the subharmonic are represented in the exponential form and substituted into the system differential equation. Amplitudes of both harmonics are perturbed, and the subharmonic amplitude perturbation operator equation is obtained. Then, only the terms representing the first order derivatives are retained. The real and imaginary parts of the operator equation are separated to give the system of two linear differential equations for the components of subharmonic amplitude perturbation. The perturbations of the main harmonic are eliminated using the main harmonic equation. Then the characteristic equation of this system is used for verification of the subharmonic stability.
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