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	1. Stochastic P-bifurcations In Tri-stable van der Pol- Duffing Oscillator
	Hao Ying,Wu zhiqiang
	Mechanics 20 December 2012
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	Abstract:This paper aims to investigate the stochastic P-bifurcations in the tri-stable van der Pol-Duffing oscillator with Gauss white noise. By using the stochastic averaging method, the stationary probability density function of amplitude is obtained. Then based on the singularity theory of the deterministic system, the explicit parameter conditions for P-bifurcation are deduced, eleven types of qualitatively different probability density curves are founded. Finally the effects of three coefficients, one for linear damping and two for random excitation strength, are discussed. The results are verified by Monte-Carlo numerical simulations. The method used here is also suitable for other systems' P-bifurcation analysis.
	TO cite this article:Hao Ying,Wu zhiqiang. Stochastic P-bifurcations In Tri-stable van der Pol- Duffing Oscillator[OL].[20 December 2012] http://en.paper.edu.cn/en_releasepaper/content/4503911


	2. A bounded optimal control for maximizing the reliability of randomly excited nonlinear oscillators with fractional derivative damping
	CHEN Licong,ZHU Weiqiu
	Mechanics 18 July 2012
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	Abstract:In this paper, a bounded optimal control for maximizing the reliability of randomly excited nonlinear oscillators with fractional derivative damping is proposed. First, the partially averaged Itô equations for the energy processes are derived by using the stochastic averaging method. Then, the dynamical programming equations for the control problems of maximizing the reliability function and maximizing the mean first passage time are established from the partially averaged Itô equations by using the dynamical programming principle and solved to obtain the optimal control law. The conditional reliability function and mean first passage time of the optimal control system are obtained by solving the backward Kolmogorov equation and Pontryagin equation associated with the fully averaged Itô equations, respectively. The application of the proposed procedure and effectiveness of the control strategy are illustrated by using two examples. In addition, the effect of fractional derivative order on the reliability of optimally controlled system is examined.
	TO cite this article:CHEN Licong,ZHU Weiqiu. A bounded optimal control for maximizing the reliability of randomly excited nonlinear oscillators with fractional derivative damping[OL].[18 July 2012] http://en.paper.edu.cn/en_releasepaper/content/4485187

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	3. Independent modal variable structure fuzzy active vibration control of cylindrical thin shells laminated with photostrictive actuators
	HE Rongbo,ZHENG Shijie,WANG Hongtao
	Mechanics 09 March 2012
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	Abstract:This paper presents an investigation into sliding mode fuzzy active vibration control of cylindrical thin shells laminated with photostrictive actuators. A phenomenon that the photostrictive actuators can not induce negative membrane control forces was pointed out and a novel multi-layer actuator configuration was presented to remedy this deficiency. Due to the switching actuation and nonlinear dynamic characteristics of photostrictive actuator, sliding mode fuzzy active controller was proposed to suppress the vibration. In order to further increase the range of sliding mode to facilitate vibration suppression, the function of the optimal switching surface was derived. Continuous function was applied to replace sign function to reduce the variable structure control chattering. Numerical simulation results demonstrated that the proposed actuator configuration provided better performance and effect to shell actuation and control. It was also suggested that the proposed control strategy could effectively suppresses vibration.
	TO cite this article:HE Rongbo,ZHENG Shijie,WANG Hongtao. Independent modal variable structure fuzzy active vibration control of cylindrical thin shells laminated with photostrictive actuators[OL].[ 9 March 2012] http://en.paper.edu.cn/en_releasepaper/content/4470780


	4. First-passage problem of 5DOF strongly nonlinear oscillators under wide-band stochastic excitation
	Wu Yongjun,Gao Yangyan,Zhang Lei
	Mechanics 04 November 2011
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	Abstract:First-passage problem of 5DOF strongly nonlinear oscillators under wide-band stochastic excitations is studied theoretically in this paper. By using stochastic averaging method, the equations of motion of the original system are reduced to a set of averaged Itô stochastic differential equations about the amplitudes. The 6-dimensional backward Kolmogorov equation and the 5-dimensional Pontryagin equation are established. These two high-dimensional partial differential equations are solved by using finite difference method to yield the conditional reliability function and mean first-passage time, respectively. The accuracy of the theoretical method is verified by Monte Carlo digital simulation.
	TO cite this article:Wu Yongjun,Gao Yangyan,Zhang Lei. First-passage problem of 5DOF strongly nonlinear oscillators under wide-band stochastic excitation[OL].[ 4 November 2011] http://en.paper.edu.cn/en_releasepaper/content/4448523


	5. Propagation of thickness-twist waves in an inhomogeneous piezoelectric plate with an imperfect bonded interface
	Li Peng,Jin Feng
	Mechanics 22 November 2010
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	Abstract:The propagation of thickness-twist waves in an inhomogeneous piezoelectric plate with an imperfect bonded interface is investigated. Based on the spring-type relation, the imperfect bonded interface is dealt with, and the exact solution is obtained from the equations of the linear theory of piezoelectricity. The amplitude ratio between the incident wave and the reflected wave, the displacement component and the stress component are all obtained and plotted. The conclusion that the effect of mechanical imperfection is more evident than that of the electrical imperfection can be obtained by theoretical analysis and numerical examples. It is shown that there will no reflected waves when the frequency of the incident wave and the mechanical imperfection satisfy a particular relation.
	TO cite this article:Li Peng,Jin Feng. Propagation of thickness-twist waves in an inhomogeneous piezoelectric plate with an imperfect bonded interface[J].


	6. The propagation of B-G waves in a functional graded transversely isotropic electro-magneto-elastic half-space
	Li Peng,Jin Feng
	Mechanics 22 November 2010
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	Abstract:The B-G waves are investigated in a functionally graded transversely isotropic electro-magneto-elastic substrate in which all the parameters change exponentially along the depth direction, and the dispersion equations with respect to the phase velocity are obtained for both electromagnetically open and short conditions. It is shown that the B-G waves are dispersive owning to the inhomogeneity of the material, which is different from the pure substrate. The effect of the graded coefficient on the B-G waves are different in different electromagnetically circumstances. Meanwhile, the electro-magneto-mechanical coupling factor can be improved and the penetration depth of the B-G waves decreases, which are all because of the intervention of the functional graded material. The outcome is widely applicable and could be expected to be utilized in the design of SAW devices with high performance.
	TO cite this article:Li Peng,Jin Feng. The propagation of B-G waves in a functional graded transversely isotropic electro-magneto-elastic half-space[J].


	7. Point-by-Point Scanning Piezoelectric Phased Array for detecting damage for SHM
	Li Xingang ,Wang Zhenqing ,Huang Zhanwen
	Mechanics 24 February 2009
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	Abstract:The aim of the present work is to develop a system of smart devices that could be permanently attached on the surface of the structure for monitoring cracks in most aerospace structures in isolated environments. It is shown that temporal and spatial focusing can be achieved through synthetic time-reversal array method for a linear phase array of sensors and actuators. A Piezoelectric phased array system performs a point-by-point scan in which focusing allow the inspection of large areas. Damage to the structure can be inferred if there is a significant change in the transient response of the structure using the analysis of the amplitude of the received signal. The location of this damaged area can be determined using the analysis of the time it reaches the transducer. By the method of synthesis of received signal time delay from multiple sensors, we can considerably enhance the signal strength, thus reducing the negative effects of noises to solve the tough problem of processing the echo signal. The results suggest an accuracy better than 1 mm in finding the location of crack tips.
	TO cite this article:Li Xingang ,Wang Zhenqing ,Huang Zhanwen . Point-by-Point Scanning Piezoelectric Phased Array for detecting damage for SHM [OL].[24 February 2009] http://en.paper.edu.cn/en_releasepaper/content/29526


	8. Relationship between the homotopy analysis method and harmonic balance method
	Y.M. Chen,J.K. Liu
	Mechanics 09 February 2009
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	Abstract:The relationship between the homotopy analysis method (HAM) and harmonic balance (HB) method is studied. The HAM is employed to obtain the periodic solutions of conservative and self-excited systems, respectively. Different from the usual procedures in the existing literature, the HAM is modified by retaining only several lower harmonics. It is proved that as long as the solution obtained by the modified approach is convergent, it must converge to one HB solution. The Duffing equation, the van der Pol equation and the flutter equation of a two-dimensional airfoil are taken as three illustrative examples to validate the proposed theory.
	TO cite this article:Y.M. Chen,J.K. Liu. Relationship between the homotopy analysis method and harmonic balance method[OL].[ 9 February 2009] http://en.paper.edu.cn/en_releasepaper/content/28594


	9. Uniformly valid frequency solution of the limit cycle of the Duffing-van der Pol equation
	Y.M. Chen,J.K. Liu
	Mechanics 05 January 2009
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	Abstract:The limit cycle of the Duffing-van der Pol equation is studied. First, an equivalent equation is obtained by considering the product of the frequency of the limit cycle and the coefficient as an independent parameter . Then, the frequency is obtained as a function of and by solving the equivalent equation via the homotopy analysis method. This function provides us with an algebraic equation in . Solving this algebraic equation, an analytical approximation for the frequency is obtained. Numerical examples show that the attained approximation is very accurate and more importantly uniformly valid for all positive values of .
	TO cite this article:Y.M. Chen,J.K. Liu. Uniformly valid frequency solution of the limit cycle of the Duffing-van der Pol equation[OL].[ 5 January 2009] http://en.paper.edu.cn/en_releasepaper/content/27342


	10. A modified variational iteration method for nonlinear oscillators
	Chen Yanmao,Liu Jike
	Mechanics 05 January 2009
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	Abstract:A modified variational iteration method (VIM) is proposed for nonlinear oscillators. Different from the existing VIM, the algebraic equation deduced at each iteration stage is always linear when the proposed procedure is applied to conservative oscillators. Taking the Duffing and the van der Pol equations as illustrative examples, very excellent approximations can be easily. In addition, it is proved the modified VIM is equivalent to a modified Mickens iteration. Furthermore, the modified VIM is extended by introducing an auxiliary parameter exemplified by two special examples. This parameter provides us with a convenient way to control the convergence of approximation series and adjust convergence rate when necessary. Consequently, the extended method is valid for both weakly and strongly nonlinear oscillators with either small or large amplitude.
	TO cite this article:Chen Yanmao,Liu Jike. A modified variational iteration method for nonlinear oscillators[OL].[ 5 January 2009] http://en.paper.edu.cn/en_releasepaper/content/27331

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