By applying the second order Melnikov function, the chaos behaviors of a bistable piezoelectric cantilever power generation system are analyzed. Firstly, the conditions for emerging chaos of the system are derived by ...By applying the second order Melnikov function, the chaos behaviors of a bistable piezoelectric cantilever power generation system are analyzed. Firstly, the conditions for emerging chaos of the system are derived by the second order Melnikov function. Secondly, the effects of each item in chaos threshold expression are analyzed. The excitation frequency and resistance values, which have the most influence on chaos threshold value, are found. The result from the second order Melnikov function is more accurate compared with that from the first order Melnikov function. Finally, the attraction basins of large amplitude motions under different exciting frequency, exciting amplitude, and resistance parameters are given.展开更多
The second kind of modified Bessel function of order zero is the solutions of many problems in engineering. Modified Bessel equation is transformed by exponential transformation and expanded by J.P.Boyd's rational...The second kind of modified Bessel function of order zero is the solutions of many problems in engineering. Modified Bessel equation is transformed by exponential transformation and expanded by J.P.Boyd's rational Chebyshev basis.展开更多
This paper investigates the existence of solutions of periodic boundary value problems for nonlinear second order functional differential equations. By establishing comparison results, criteria on the existence of max...This paper investigates the existence of solutions of periodic boundary value problems for nonlinear second order functional differential equations. By establishing comparison results, criteria on the existence of maximal and minimal solutions are obtained.展开更多
GH4169 superalloy stress relaxation test was investigated to study its characteristics of stress relaxation curves at various temperatures( 550,650,and 750 ℃). These curves presented jointly two distinct stages,the s...GH4169 superalloy stress relaxation test was investigated to study its characteristics of stress relaxation curves at various temperatures( 550,650,and 750 ℃). These curves presented jointly two distinct stages,the stage of inner stress relaxing quickly,and the stage of inner stress relaxing slowly and closing to the stress relaxation limit. And these curves obtained could be fitted by second order exponential decay function well. Based on the experimental stress relaxation curves,the relationship between stress relaxation rate and time were derived, which showed that the higher relaxation temperature and the greater initial rate of stress relaxation. The whole process presented two different stages,the stage of stress relaxation rate falling rapidly and the stage of stress relaxation rate slowing down and tending to be constant. The relation curve between creep strain rate and stress of GH4169 superalloy can be divided into three stages,low stress stage,transition stage,and high stress stage.Both the high stage and the low stage present linear correlation.展开更多
In this paper we discuss the types and criteria of nonoscillatory solutions for the fol-lowing second order neutral functional differential equation with nonpositive coefficients
基金supported by the National Natural Science Foundation of China (Grant 11172199)
文摘By applying the second order Melnikov function, the chaos behaviors of a bistable piezoelectric cantilever power generation system are analyzed. Firstly, the conditions for emerging chaos of the system are derived by the second order Melnikov function. Secondly, the effects of each item in chaos threshold expression are analyzed. The excitation frequency and resistance values, which have the most influence on chaos threshold value, are found. The result from the second order Melnikov function is more accurate compared with that from the first order Melnikov function. Finally, the attraction basins of large amplitude motions under different exciting frequency, exciting amplitude, and resistance parameters are given.
文摘The second kind of modified Bessel function of order zero is the solutions of many problems in engineering. Modified Bessel equation is transformed by exponential transformation and expanded by J.P.Boyd's rational Chebyshev basis.
基金Supported by NNSF-China (No.10071043)the YNSF of Shandong Province (No.Y2000A06)
文摘This paper investigates the existence of solutions of periodic boundary value problems for nonlinear second order functional differential equations. By establishing comparison results, criteria on the existence of maximal and minimal solutions are obtained.
文摘GH4169 superalloy stress relaxation test was investigated to study its characteristics of stress relaxation curves at various temperatures( 550,650,and 750 ℃). These curves presented jointly two distinct stages,the stage of inner stress relaxing quickly,and the stage of inner stress relaxing slowly and closing to the stress relaxation limit. And these curves obtained could be fitted by second order exponential decay function well. Based on the experimental stress relaxation curves,the relationship between stress relaxation rate and time were derived, which showed that the higher relaxation temperature and the greater initial rate of stress relaxation. The whole process presented two different stages,the stage of stress relaxation rate falling rapidly and the stage of stress relaxation rate slowing down and tending to be constant. The relation curve between creep strain rate and stress of GH4169 superalloy can be divided into three stages,low stress stage,transition stage,and high stress stage.Both the high stage and the low stage present linear correlation.
文摘In this paper we discuss the types and criteria of nonoscillatory solutions for the fol-lowing second order neutral functional differential equation with nonpositive coefficients
