A parallel nonlinear energy sink(NES) is proposed and analyzed. The parallel NES is composed of a vibro-impact(VI) NES and a cubic NES. The dynamical equation is given, and the essential analytical investigation is ca...A parallel nonlinear energy sink(NES) is proposed and analyzed. The parallel NES is composed of a vibro-impact(VI) NES and a cubic NES. The dynamical equation is given, and the essential analytical investigation is carried out to deal with the cubic nonlinearity and impact nonlinearity. Multiple time-scale expansion is introduced, and the zeroth order is derived to give a rough outline of the system. The underlying Hamilton dynamic equation is given, and then the optimal stiffness is expressed. The clearance is regarded as a critical factor for the VI. Based on the periodical impact treatment by analytical investigation, the relationships of the cubic stiffness, the clearance, and the zeroth-order attenuation amplitude of the linear primary oscillator(LPO) are obtained.A cubic NES under the optimal condition is compared with the parallel NES. Harmonic signals, harmonic signals with noises, and the excitation generated by a second-order?lter are considered as the potential excitation forces on the system. The targeted energy transfer(TET) in the designed parallel NES is shown to be more e?cient.展开更多
A novel method based on time-dependent stochastic orthogonal bases for stochastic response surface approximation is proposed to overcome the problem of significant errors in the utilization of the generalized polynomi...A novel method based on time-dependent stochastic orthogonal bases for stochastic response surface approximation is proposed to overcome the problem of significant errors in the utilization of the generalized polynomial chaos(GPC) method that approximates the stochastic response by orthogonal polynomials. The accuracy and effectiveness of the method are illustrated by different numerical examples including both linear and nonlinear problems. The results indicate that the proposed method modifies the stochastic bases adaptively, and has a better approximation for the probability density function in contrast to the GPC method.展开更多
基金Project supported by the National Natural Science Foundation of China(Nos.11632011,11702170,11472170,51421092,and 11572189)
文摘A parallel nonlinear energy sink(NES) is proposed and analyzed. The parallel NES is composed of a vibro-impact(VI) NES and a cubic NES. The dynamical equation is given, and the essential analytical investigation is carried out to deal with the cubic nonlinearity and impact nonlinearity. Multiple time-scale expansion is introduced, and the zeroth order is derived to give a rough outline of the system. The underlying Hamilton dynamic equation is given, and then the optimal stiffness is expressed. The clearance is regarded as a critical factor for the VI. Based on the periodical impact treatment by analytical investigation, the relationships of the cubic stiffness, the clearance, and the zeroth-order attenuation amplitude of the linear primary oscillator(LPO) are obtained.A cubic NES under the optimal condition is compared with the parallel NES. Harmonic signals, harmonic signals with noises, and the excitation generated by a second-order?lter are considered as the potential excitation forces on the system. The targeted energy transfer(TET) in the designed parallel NES is shown to be more e?cient.
基金Project supported by the National Natural Science Foundation of China(Nos.11632011,11572189,and 51421092)the China Postdoctoral Science Foundation(No.2016M601585)
文摘A novel method based on time-dependent stochastic orthogonal bases for stochastic response surface approximation is proposed to overcome the problem of significant errors in the utilization of the generalized polynomial chaos(GPC) method that approximates the stochastic response by orthogonal polynomials. The accuracy and effectiveness of the method are illustrated by different numerical examples including both linear and nonlinear problems. The results indicate that the proposed method modifies the stochastic bases adaptively, and has a better approximation for the probability density function in contrast to the GPC method.
