Due to autorotation,samaras can fly efficiently and stably to be dispersed over a great distance under various weather conditions.Here,we provide a quantitative analysis of the dynamic stability of free-falling maple ...Due to autorotation,samaras can fly efficiently and stably to be dispersed over a great distance under various weather conditions.Here,we provide a quantitative analysis of the dynamic stability of free-falling maple samara(Acer grosseri Pax)and verify whether they are dynamically stable as observed.Morphological and kinematic parameters were obtained based on the existing experimental data of the maple seed.Then the linearized equations of motion were derived,and the stability derivatives were calculated by a computational fluid dynamics method.The techniques of eigenvalue and eigenvector analysis were also used to examine the stability characteristics.It is found that there are five natural modes of motion of the maple seed:one stable oscillatory mode,one fast subsidence mode,one slow subsidence mode,and two neutral stable modes.The two neutral modes are manifested as the seed moving horizontally at a low speed under disturbance.Results show that the maple seed has dynamic stability in sustaining the steady autorotation and descent,exhibiting a minor horizontal motion when disturbed.These findings can beapplied to biomimetic aircraft.展开更多
The stochastic stability of the harmonically and randomly excited Duffing oscillator with damping modeled by a fractional derivative of Caputo's definition is analyzed.First,the system state is approximately descr...The stochastic stability of the harmonically and randomly excited Duffing oscillator with damping modeled by a fractional derivative of Caputo's definition is analyzed.First,the system state is approximately described by It equations through the stochastic averaging method based on the generalized harmonic function.Then,the associated expression for the largest Lyapunov exponent of the linearized averaged It is derived,and the necessary and sufficient condition for the asymptotic stability with probability one of the trivial solution of the original system is obtained approximately by letting the largest Lyapunov exponent be negative.The effects of fractional orders and random excitation intensities on the asymptotic stability with probability one determined by the largest Lyapunov exponent are shown graphically.展开更多
In this paper,the asymptotic stability with probability one of multi-degree-of-freedom(MDOF)nonlinear oscillators with fractional derivative damping parametrically excited by Gaussian white noises is investigated.A st...In this paper,the asymptotic stability with probability one of multi-degree-of-freedom(MDOF)nonlinear oscillators with fractional derivative damping parametrically excited by Gaussian white noises is investigated.A stochastic averaging method and the Khasminskii’s procedure are employed to evaluate the largest Lyapunov exponent,whose sign determines the stability of the system.As an example,two coupled nonlinear oscillators with fractional derivative damping is worked out to demonstrate the proposed procedure and to examine the effect of fractional order on the stochastic stability of system.In particular,the case of factional order more than 1 is studied for the first time.展开更多
This paper proves the existence of 4 families of nontrivial homotopy elements in the stablehomotopy of spheres which are represented by in the ternis of the Adams spectral sequence respectively, where and are thekno...This paper proves the existence of 4 families of nontrivial homotopy elements in the stablehomotopy of spheres which are represented by in the ternis of the Adams spectral sequence respectively, where and are theknown generators in the terms whose internal degree are 4(p - 1) + 1, 2pn+1(p-1),展开更多
基金supported by the National Natural Science Foundation of China(Grant No.11832004)。
文摘Due to autorotation,samaras can fly efficiently and stably to be dispersed over a great distance under various weather conditions.Here,we provide a quantitative analysis of the dynamic stability of free-falling maple samara(Acer grosseri Pax)and verify whether they are dynamically stable as observed.Morphological and kinematic parameters were obtained based on the existing experimental data of the maple seed.Then the linearized equations of motion were derived,and the stability derivatives were calculated by a computational fluid dynamics method.The techniques of eigenvalue and eigenvector analysis were also used to examine the stability characteristics.It is found that there are five natural modes of motion of the maple seed:one stable oscillatory mode,one fast subsidence mode,one slow subsidence mode,and two neutral stable modes.The two neutral modes are manifested as the seed moving horizontally at a low speed under disturbance.Results show that the maple seed has dynamic stability in sustaining the steady autorotation and descent,exhibiting a minor horizontal motion when disturbed.These findings can beapplied to biomimetic aircraft.
基金supported by the National Natural Science Foundation of China(Grant Nos.10932009,11072212 and 11002059)the Specialized Research Fund for the Doctoral Program of Higher Education(Grant No.20103501120003)+2 种基金the Natural Science Foundation of Fujian Province (Grant No.2010J05006)the Fundamental Research Funds for Huaqiao University(Grant No.JB-SJ1010)the Research & Development Start Funds of Huaqiao University(Grant No.09BS622)
文摘The stochastic stability of the harmonically and randomly excited Duffing oscillator with damping modeled by a fractional derivative of Caputo's definition is analyzed.First,the system state is approximately described by It equations through the stochastic averaging method based on the generalized harmonic function.Then,the associated expression for the largest Lyapunov exponent of the linearized averaged It is derived,and the necessary and sufficient condition for the asymptotic stability with probability one of the trivial solution of the original system is obtained approximately by letting the largest Lyapunov exponent be negative.The effects of fractional orders and random excitation intensities on the asymptotic stability with probability one determined by the largest Lyapunov exponent are shown graphically.
基金supported by the National Natural Science Foundation of China(Grant Nos.10932009,11072212,11272279 and 11002059)Specialized Research Fund for the Doctoral Program of Higher Education(Grant No.20103501120003)+1 种基金Fujian Province Natural Science Foundation of China(Grant No.2010J05006)Fundamental Research Funds for Huaqiao University(Grant No.JB-SJ1010)
文摘In this paper,the asymptotic stability with probability one of multi-degree-of-freedom(MDOF)nonlinear oscillators with fractional derivative damping parametrically excited by Gaussian white noises is investigated.A stochastic averaging method and the Khasminskii’s procedure are employed to evaluate the largest Lyapunov exponent,whose sign determines the stability of the system.As an example,two coupled nonlinear oscillators with fractional derivative damping is worked out to demonstrate the proposed procedure and to examine the effect of fractional order on the stochastic stability of system.In particular,the case of factional order more than 1 is studied for the first time.
文摘This paper proves the existence of 4 families of nontrivial homotopy elements in the stablehomotopy of spheres which are represented by in the ternis of the Adams spectral sequence respectively, where and are theknown generators in the terms whose internal degree are 4(p - 1) + 1, 2pn+1(p-1),
