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Cited by 19 publications
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References 27 publications
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“…[19][20][21]). The main feature of the incremental method is that all of the nonlinear terms are removed from the variation process, meaning that bifurcation is not possible, whereas the total harmonic balance method retains all of those terms to produce a set of nonlinear algebraic equations.…”
Section: Introductionmentioning
confidence: 97%
“…[19][20][21]). The main feature of the incremental method is that all of the nonlinear terms are removed from the variation process, meaning that bifurcation is not possible, whereas the total harmonic balance method retains all of those terms to produce a set of nonlinear algebraic equations.…”
Section: Introductionmentioning
confidence: 97%
“…The rational polynomials have been introduced to properly approximate both the freeplay and hysteresis nonlinearities. To overcome these computational limitations for approximation of the nonlinear forces in Li et al (2012) and Liu et al (2012), a new approach using piecewise integration is proposed in the present contribution.…”
Section: Introductionmentioning
confidence: 99%
“…With the help of the time discretization technique of the cyclic method, the incremental harmonic balance technique in conjunction with the Fourier expansion approach of hysteresis nonlinearity is used by Liu et al (2012) to simulate the dynamics of an airfoil with a pitching hysteresis nonlinearity. In and Cui et al (2015), bifurcation and LCOs of the aeroelastic systems with freeplay nonlinearity are analyzed and a predictor-corrector algorithm based on the precise integration method is proposed to determine the switching points of the piecewise nonlinearity system.…”
Section: Introductionmentioning
confidence: 99%
“…Therefore, it is much tougher to solve hysteresis systems. Maybe for this reason, it is rare to find effective solution approaches to do this job [12,22,28]. It is necessary and worthwhile to extending our newly proposed method [24,26] to study the airfoil aeroelastic system with hysteresis.…”
Section: Introductionmentioning
confidence: 99%
“…For example, Liu and Dowell [21] introduced FFT technique to handle the freeplay nonlinearities when applying the harmonic balance method to solve an airfoil aeroelastic system with a control surface. Liu et al [22] proposed a new technique to transform time domain solutions into frequency ones so that the incremental harmonic balance method is capable of analyzing the LCOs of an airfoil aeroelastic system with a hysteresis.…”
Section: Introductionmentioning
confidence: 99%