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Existence conditions for the periodic solutions are determined in the case of the Nshaped characteristic; a description is given for the periodic waves in a harmonic approximation.


Uniform and tangential harmonic approximation of continuous functions on arbitrary sets


The correlation function of the magnetization is calculated with the aid of a selfconsistent harmonic approximation.


It is found that the isotopic dependence of the frequency of the LTO(Γ) mode in isotopically pure germanium samples can be described in the harmonic approximation (ν∝m1/2).


A nonquadratic dispersion law was taken into account in the framework of the selfconsistent harmonic approximation (SCHA).

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 The paper gives a prelimary study on a few types of automatic vibrating loading devices about its vibrating system design,selection of parameters,and calculation of productivity. The criterions of the motion of the loaded pieceses is discused,and a crite rion formula is deduced.The equations of motion of the elastic syslem of a vibrating device,stimulated by eccentric rotating mass.are given together with experimental researches. An analysis of the nonlinear equation of motion of the loaded pieceses based... The paper gives a prelimary study on a few types of automatic vibrating loading devices about its vibrating system design,selection of parameters,and calculation of productivity. The criterions of the motion of the loaded pieceses is discused,and a crite rion formula is deduced.The equations of motion of the elastic syslem of a vibrating device,stimulated by eccentric rotating mass.are given together with experimental researches. An analysis of the nonlinear equation of motion of the loaded pieceses based on the principle of harmonic approximation is proposed for two diferent types of vibrating sources.An engineering approximating formula for the calculation of the mean velocily of the loaded pieces is presented together with experimental data.The application of electronic analoque computer to study the motion of the loaded pieces is suggested together with the principle block diagram.  本文对振动式自动上料装置的振动系统结构设计方法,参数合理选择,生产率的计算方法进行了初步理论与实验研究。文中讨论了判定另件运动规律的方法,提出了合理的判断计算公式,分析了利用偏心式振动系统的振动与程式,并进行了实验论证。文中以谐波近似法从理论上分析了同步振源及不同步振源中另件非线性振动时的平均速度,提出了计算生产率的近似方法,并进行了初步理论与实验论证。最后还提出了利用电子模拟方法研究振动式自动上料装置的初步概念。  It is very difficult to investigate a nonlinear system, especially a system with many degrees of freedom. If the nonlinear system can be replaced with an equivalent linearized system, the investigation will be simplified. But up till now, no generally accepted method has been found for linearizing a nonlinear system with above two degrees of freedom [2]. In reference [3], a method is used for equivalent linearization of the two orthogonal squeeze film forces, but the method is limited to two degrees of freedom.... It is very difficult to investigate a nonlinear system, especially a system with many degrees of freedom. If the nonlinear system can be replaced with an equivalent linearized system, the investigation will be simplified. But up till now, no generally accepted method has been found for linearizing a nonlinear system with above two degrees of freedom [2]. In reference [3], a method is used for equivalent linearization of the two orthogonal squeeze film forces, but the method is limited to two degrees of freedom. In this paper, the results of [3] are extended to the general case of n degrees of freedom and n components of nonlinear forces, and the expressions of equivalent linear coefficients are derived. Nonlinear forces can be linearized in this paper by using the method of Fourier expansion, the method of active and reactive powers or the method of mean square error. All three methods lead to the same results. The n components of nonlinear forces can all be expressed formally as the sum of an average force, a linear spring force and a linear damping force. Moreover, the linearized force is just the Fourier expansion of the real nonlinear force approximated to the first harmonic; and their average active powers, reactive powers and average values are equal over a period of motion. Besides, the mean square error of the equivalent linearized force is minimum over a period. This paper also gives the flowchart for calculating the steady state responses of a nonlinear system with many degrees of freedom by using the method of equivalent linearization. The computing time can be saved greatly and the analyzing process can be simplified obviously because the problem of solving differential equations is replaced by solving algebraic equations. This point of view has been confirmed by a numerical example concerning a flexible rotorbearing system with uncentralised squeeze film damper.  对受到一组非线性力Fi(X,X),[X=(x_1,x_2,…,x_n)~T,i=1,2,…,n]作用的n自由度系统,假设系统的响应为主谐波振动,本文导出了关于F_i(i=1,2,…,n)的一种等效线性化表达式。从而将非线性力f_i等效为一个平均力,一个线性弹簧力和一个线性阻尼力之和。这种等效线性力恰是实际的非线性力在一次谐波近似下的付里埃展式,它与实际的非线性力在振动一周中的平均有功功率及平均无功功率相等,平均值也相等。而且,它与实际的非线性力在一周中的均方差也最小。本文给出了用这种方法求解柔性转子——非同心型挤压油膜阻尼器系统稳态响应的算例,计算表明这种方法可大大节省计算机时。  The new findings of this paper are: a set of nonlinear algebraic equationsfor solving the offset response of a flexible rotoruncentralised SFDB (squeezefilm damper bearing) system is derived, so that the coupled motion of rotordisk and bearing journal is separated and the computing time is saved greatly.Before giving a detailed introduction of these findings, believed to be new, itis necessary to have a brief summary of the previous researches about thissubject. Because of the high nonlinearity of squeeze film... The new findings of this paper are: a set of nonlinear algebraic equationsfor solving the offset response of a flexible rotoruncentralised SFDB (squeezefilm damper bearing) system is derived, so that the coupled motion of rotordisk and bearing journal is separated and the computing time is saved greatly.Before giving a detailed introduction of these findings, believed to be new, itis necessary to have a brief summary of the previous researches about thissubject. Because of the high nonlinearity of squeeze film force, many problemsabout rotorSFDB system have not been th(?)r(?)ughly analysed. The offsetsynchronous response of the system can only be solved by direct integrationmethod, thus it needs large quantity of time and the motion coupling of rotordisk and bearing journal increases the complication of analyses. For nonlinearsystem, if the nonlinear force can be linearized, undoubtedly the responseanalyses will be simplified. But up till now, only for centralised SFDB, canthe nonlinear film force be linearized with steady state circular response; noeffective linearizing method exists for the offset response of uncentralisedSFDB. In order to simplify the response analyses of flexible rotoruncentralisedSFDB system, the Equivalent Linearizing Method advanced in references [5] and[6] is used in this paper for solving the offset synchronous response of thesystem; the nonlinear fluid film forces are linearized with offset synchronousresponse and a set of nonlinear algebraic equations for solving the offsetresponse is obtained. In this set of equations, the motion of rotor disk can berepresented by the motion of bearing journal, so that the system's degrees offreedom are decreased. Besides, as the problem of solving differential equationsis replaced by solving algebraic equations, the computing time can be savedobviously and the analyses are simplified. Numerical results show that theequivalent solution is very near the real solution in the first harmonic appr oximation, and that the equivalent linearizing method can save computing timegreatly compared with direct integrating method.  本文用等效线性化法导出了求解柔性转子——非同心型挤压油膜阻尼器系统偏置协调响应的一组非线性代数方程,从而分离了转盘及轴颈的运动。数值计算表明,等效解与真实解在一次谐波近似下相当接近,而等效线性化法可明显节省计算机时。   << 更多相关文摘 
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