共查询到20条相似文献,搜索用时 31 毫秒
1.
Auxiliary principle and three-step iterative algorithms for generalized set-valued strongly nonlinear mixed variational-like inequalities 总被引:1,自引:0,他引:1
An auxiliary principle technique to study a class of generalized set-valued strongly nonlinear mixed variational-like inequalities is extended. The existence and uniqueness of the solution of the auxiliary problem for the generalized set-valued strongly nonlinear mixed variational-like inequalities are proved, a novel and innovative three-step iterative algorithm to compute approximate solution is constructed, and the existence of the solution of the generalized set-valued strongly nonlinear mixed variational-like inequality is shown using the auxiliary principle technique. The convergence of three-step iterative sequences generated by the algorithm is also proved. 相似文献
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A generalized hyperbolic perturbation method is presented for homoclinic solutions of strongly nonlinear autonomous oscillators,in which the perturbation procedure is improved for those systems whose exact homoclinic generating solutions cannot be explicitly derived.The generalized hyperbolic functions are employed as the basis functions in the present procedure to extend the validity of the hyperbolic perturbation method.Several strongly nonlinear oscillators with quadratic,cubic,and quartic nonlinearity are studied in detail to illustrate the efficiency and accuracy of the present method. 相似文献
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GENERALIZEDSTRONGLYNONLINEARQUASI-COMPLEMENTARITYPROBLEMSLiHong-mei(李红梅)DingXie-ping(丁协平)(SichuanNormalUniversity),Chengdu(Re... 相似文献
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在经典Padé逼近理论的基础上进行了相应推广,提出了广义Padé逼近方法,并针对强非线性自治振子同宿轨的求解问题,利用双曲函数构造了一种新的广义Padé逼近式. 首先,该广义Padé逼近式有着较简单的泰勒展开式,与现有的Padé逼近式相比,在计算同阶逼近时,计算量更少;其次,该方法在强非线性时,依然有着较高的精度;第三,该方法并不局限于某些特定的系统,而是有着较广的适用范围. 因此对于广义Padé逼近方法的研究具有一定的实际意义和理论价值. 相似文献
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Iterative algorithms for finding approximate solutions of completely generalized strongly nonlinear quasivariational inequalities 总被引:1,自引:0,他引:1
曾六川 《应用数学和力学(英文版)》1994,15(11):1069-1080
ITERATIVEALGORITHMSFORFINDINGAPPROXIMATESOLUTIONSOFCOMPLETELYGENERALIZEDSTRONGLYNONLINEARQUASIVARIATIONALINEQUALITIESZengLu-c... 相似文献
8.
In this paper, we introduce a new kind of generalized strongly nonlinear quasi-complementarity problems in Hilbert space and discuss the existence of solutions for this kind of problems and the convergence of sequences generated by algorithms. The results presented in this paper improve and extend a number of known results.The Project Supported by National Natural Science Foundation of China 相似文献
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广义非线性强度理论在岩石材料中的应用 总被引:8,自引:0,他引:8
在已提出的广义非线性强度理论的基础上,结合岩石材料的力学特性,建立了岩石广
义非线性强度理论,该理论在$\pi$平面上的破坏函数为介于SMP准则和Mises准则
之间的光滑曲线,在子午面上的破坏函数为幂函数曲线. 通过已有不同岩石的真三
轴试验数据对岩石广义非线性强度理论的验证表明,岩石广义非线性强度理论可以
广泛地适用于各类岩石,描述其$\pi$平面上及子午面上的非线性强度特性;并利
用5种不同类型岩石的真三轴试验结果对岩石广义非线性强度理论和Hoek-Brown准
则进行比较,反映了所提岩石广义非线性强度理论的优越性. 相似文献
10.
A stochastic minimax semi-active control strategy for multi-degrees-of-freedom (MDOF) strongly nonlinear systems under combined harmonic and wide-band noise excitations is proposed. First, a stochastic averaging procedure is introduced for controlled uncertain strongly nonlinear systems using generalized harmonic functions and the control forces produced by Magneto-rheological (MR) dampers are split into the passive part and the active part. Then, a worst-case optimal control strategy is derived by solving a stochastic differential game problem. The worst-case disturbances and the optimal semi-active controls are obtained by solving the Hamilton–Jacobi–Isaacs (HJI) equations with the constraints of disturbance bounds and MR damper dynamics. Finally, the responses of optimally controlled MDOF nonlinear systems are predicted by solving the Fokker–Planck–Kolmogorov (FPK) equation associated with the fully averaged Itô equations. Two examples are worked out in detail to illustrate the proposed control strategy. The effectiveness of the proposed control strategy is verified by using the results from Monte Carlo simulation. 相似文献
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强非线性振动系统的渐近解法 总被引:4,自引:0,他引:4
本文推广文[1]中方法于求解广泛一类强非线性振动系统,导出了适于近似定性分析和定量计算的简便公式。作为例子研究了修正的Vander Pol振子,最后给出数字Poincaré映射结果,从近似定性分析和定量计算两方面证明了本文求得的方法的有效性。 相似文献
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丁协平 《应用数学和力学(英文版)》1999,20(10):1087-1098
IntroductionVariationalinequalitytheoryandcomplementarityproblemtheoryhavebecomeveryeffectiveandpowerfultoolsforstudyingawiderangeofproblemsarisinginmechanics,mathematicalprogramming,optimizationandcontrol,equilibriumtheoryofeconomics,managementscien… 相似文献
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In this paper, a new notion of a generalized H-η-accretive operator is introduced and studied, which provides a unifying framework for the generalized m-accretive operator and the H-η-monotone operator in Banach spaces. A resolvent operator associated with the generalized H-η-accretive operator is defined, and its Lipschitz continuity is shown. As an application, the solvability for a class of variational inclusions involving the generalized H-η-accretive operators in Banach spaces is considered. By using the technique of the resolvent mapping, an iterative algorithm for solving the variational inclusion in Banach spaces is constructed. Under some suitable conditions, it is proven that the solution for the variational inclusion and the convergence of the iterative sequence generated by the algorithm exist. 相似文献
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M. A. Bisyarin 《Journal of Applied Mechanics and Technical Physics》2007,48(6):824-833
This paper considers the propagation of a weakly nonlinear acoustic pulse in a slightly curved waveguide layer which is strongly inhomogeneous in the transverse direction and weakly inhomogeneous in the longitudinal direction. The basic system of hydrodynamic equations reduces to a nonlinear wave equation, whose coefficients are determined using the equations of state of the medium. It is established that as the adiabatic exponent passes through the value γ = 3/2, the nature of the pulse propagation changes: for large values of γ, the medium is focusing, and for smaller values, it is defocusing. It is shown that the pulse propagation process is characterized by three scales: the high-frequency filling is modulated by the envelope, whose evolution, in turn, is determined by the moderate-rate evolution of the envelope phase and slow amplitude variation. A generalized nonlinear Schrödinger equation with the coefficients dependent on the longitudinal coordinate is derived for the pulse envelope. An explicit soliton solution of this equation is constructed for some types of longitudinal inhomogeneity. 相似文献
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Multi-symplectic method for generalized Boussinesq equation 总被引:1,自引:0,他引:1
The generalized Boussinesq equation that represents a group of important nonlinear equations possesses many interesting properties. Multi-symplectic formulations of the generalized Boussinesq equation in the Hamilton space are introduced in this paper. And then an implicit multi-symplectic scheme equivalent to the multi-symplectic Box scheme is constructed to solve the partial differential equations (PDEs) derived from the generalized Boussinesq equation. Finally, the numerical experiments on the soliton solutions of the generalized Boussinesq equation are reported. The results show that the multi-symplectic method is an efficient algorithm with excellent long-time numerical behaviors for nonlinear partial differential equations. 相似文献
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The upper-branch linear and nonlinear stability of compressible boundary-layer flows is studied using the approach of Smith and Bodonyi (1982) for a similar incompressible problem. Both pressure gradient boundary layers and Blasius flow are considered with and without heat transfer and the neutral eigenrelations incorporating compressibility effects are explicitly obtained. The compressible nonlinear viscous critical-layer equations are derived and solved numerically and the results indicate some solutions with positive phase shift across the critical layer. Various limiting cases are investigated including the case of much larger disturbance amplitudes and this indicates the structure for the strongly nonlinear critical layer of the Benney-Bergeron (1969) type. Finally, we also show how a match with the inviscid neutral inflexional modes arising from the generalized inflexion-point criterion is achieved.J. Cole is grateful to the Science and Engineering Research Council of Great Britain for financial support. J. Gajjar gratefully acknowledges the support of ICOMP, NASA Lewis Research Center, Cleveland, Ohio, where part of this work was done, and he is also grateful to the Computation Center at Iowa State University for a grant which enabled the numerical work in the paper to be completed. The permanent address of the authors is the Mathematics Department, Exeter University, Exeter EX4 4QE, England. 相似文献
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Marta Pellicer 《Journal of Dynamics and Differential Equations》2010,22(3):399-411
In Pellicer (Nonlinear Anal. 69:3110–3127, 2008) we showed the existence of exponentially attracting invariant manifolds for
a nonlinear strongly damped viscoelastic problem. In that paper we used an special result, that we did not prove there, concerning
certain uniform bounds for families of semigroups generated by restrictions of nonselfadjoint linear operators. The fact of
applying this to nonselfadjoint operators represented the main novelty and difficulty of Pellicer (2008). In the present paper
we prove this special result that was used in Pellicer (2008). This is done using the notion of generalized convergence between
operators. 相似文献
19.
A popular means to mitigate excessive structural vibrations is the attachment of a lightweight spring-mass element, known as a vibration absorber or tuned mass damper. Designing new types of vibration absorbers that outperform the classical linear tuned mass damper is a challenging ongoing research field. This paper focuses on the absorber with a strongly nonlinear spring characteristic. A critical aspect in the design procedure of such nonlinear vibration absorber is the existence of energy thresholds below which no efficient vibration reduction is possible. This paper extends the concept of an energy threshold to a more general parameter threshold representing several threshold values. Two important contributions are obtained. First, one single bifurcation analysis covers every combination of the system parameters. Second, the results are generalized to linear main systems under impulsive load and harmonic load, nonlinear main systems, and general nonlinear spring characteristics. 相似文献