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  • 1
    Electronic Resource
    Electronic Resource
    On the method of orthogonality conditions for solving the problem of large deflection of circular plate (1991)
    Springer
    Applied mathematics and mechanics 12 (1991), S. 617-625 
    Details
    ISSN: 1573-2754
    Keywords: circular plate ; large deflection ; method of strained parameters ; orthogonality condition ; perturbation theory
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract In this paper, we reexamine the method of successive approximation presented by Prof. Chien Wei-zang for solving the problem of large deflection of a circular plate, and find that the method could be regarded as the method of strained parameters in the singular perturbation theory. In terms of the parameter representing the ratio of the center deflection to the thickness of the plate, we make the asymptotic expansions of the deflection, membrane stress and the parameter of load as in Ref. [1], and then give the orthogonality conditions (i.e. the solvability conditions) for the resulting equations, by which the stiffness characteristics of the plate could be determined. It is pointed out that with the solutions for the small deflection problem of the circular plate and the orthogonality conditions, we can derive the third order approximate relations between the parameter of load and the center deflection and the first-term approximation of membrane stresses at the center and edge of the plate without solving the differential equations. For some special cases (i.e. under uniform load, under compound load, with different boundary conditions), we deduce the specific expressions and obtain the results in agreement with the previous ones given by Chien Wei-zang, Yeh kai-yuan and Hwang Chien in Refs. [1–4].
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02018942
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  • 2
    Electronic Resource
    Electronic Resource
    Asymptotic analysis of a class of nonlinear oscillation equation in electrical engineering (1994)
    Springer
    Applied mathematics and mechanics 15 (1994), S. 7-12 
    Details
    ISSN: 1573-2754
    Keywords: nonlinear oscillation ; limit cycle ; asymptotic analysis ; modified Krylov-Bogolyubov method
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract In the present paper, we investigate a class of nonlinear oscillation equations in electrical engineering by using the modified Krylov-Bogolyubov method presented in[1]. We obtain quantitatively the parameter range for the existence of a limit cycle and the amplitude of the limit cycle, and find that the limit cycle is unstable. All the results agree entirely with the known results given by qualitative analysis, and hence confirm the effectiveness of the above-mentioned asymptotic method.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02451022
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  • 3
    Electronic Resource
    Electronic Resource
    Surface effects of internal wave generated by a moving source in a two-layer fluid of finite depth (2003)
    Springer
    Applied mathematics and mechanics 24 (2003), S. 1025-1040 
    Details
    ISSN: 1573-2754
    Keywords: internal wave ; surface wave ; stratified fluid ; divergence field ; wave-wave interaction ; ship wave ; O353 ; 76B20
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract Based on the potential flow theory of water waves, the interaction mechanism between the free-surface and internal waves generated by a moving point source in the lower layer of a two-layer fluid was studied. By virtue of the method of Green's function, the properties of the divergence field at the free surface were obtained, which plays an important role in the SAR (Synthetic Aperture Radar) image. It is shown that the coupling interaction between the surface-wave mode and internal-wave mode must be taken into account for the cases of large density difference between two layers, the source approaching to the pynocline and the total Froude number Fr close to the critical number Fr2. The theoretical analysis is qualitatively consistent with the experimental results presented by Ma Hui-yang.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02437635
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  • 4
    Electronic Resource
    Electronic Resource
    Generalization of the method of full approximation and its applications (1991)
    Springer
    Applied mathematics and mechanics 12 (1991), S. 255-264 
    Details
    ISSN: 1573-2754
    Keywords: perturbation methods ; methods of full approximation ; asymptotic linearization ; nonlinear waves ; nonlinear oscillations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract This paper presents a generalized form of the method of full approximation. By using the concept of asymptotic linearization and making the coordinate transformations including the nonlinear functionals of dependent variables, the original nonlinear problems are linearized and their higher-order solutions are given in terms of the first-term asymptotic solutions and corresponding transformations. The analysis of a model equation and some problems of weakly nonlinear oscillations and waves with the generalized method shows that it is effective and straightforward.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02098055
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  • 5
    Electronic Resource
    Electronic Resource
    Solitary waves at the interface of a two-layer fluid (1982)
    Springer
    Applied mathematics and mechanics 3 (1982), S. 777-788 
    Details
    ISSN: 1573-2754
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract In this paper, we discuss the solitary waves at the interface of a two-layer incompressible inviscid fluid confined by two horizontal rigid walls, taking the effect of surface tension into account. First of all, we establish the basic equations suitable for the model considered, and hence derive the Korteweg-de Vries (KdV) equation satisfied by the first-order elevation of the interface with the aid of the reductive perturbation method under the approximation of weak dispersion. It is found that the KdV solitary waves may be convex upward or downward. It depends on whether the signs of the coefficients α and μ of the KdV equation are the same or not. Then we examine in detail two critical cases, in which the nonlinear effect and the dispersion effect cannot balance under the original approximation. Applying other appropriate approximations, we obtain the modified KdV equation for the critical case of first kind (α=0), and conclude that solitary waves cannot exist in the case considered as μ〉0, but may still occur as μ〈0, being in the form other than that of the KdV solitary wave.As for the critical case of second kind (μ=0), we deduce the generalized KdV equation, for which a kind of oscillatory solitary waves may occur. In addition, we discuss briefly the near-critical cases. The conclusions in this paper are in good agreement with some classical results which are extended considerably.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01895332
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  • 6
    Electronic Resource
    Electronic Resource
    The generalized Boussinesq equations and obliquely interacting solitary waves in a stratified fluid (1984)
    Springer
    Applied mathematics and mechanics 5 (1984), S. 1469-1478 
    Details
    ISSN: 1573-2754
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract In this paper, on the basis of Boussinesq's shallow water theory, we establish the basic equations governing the motion of a stratified fluid, a kind of the generalized Boussinesq equations. And then by way of them, we study the weak interaction of two pairs of obliquely colliding solitary waves, give the second-order approximate solutions for wave profiles and maximum amplitudes, as well as conclude that when the included angle between the directions of propagation of impinging solitary waves is less than 120°, the effect of oblique interaction is stronger than that of the head-on one, but when the angle concerned is greater than 120°, the former is slightly weaker than the latter.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01910437
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  • 7
    Electronic Resource
    Electronic Resource
    Quasi-periodic waves and quasi-solitary waves in stratified fluid of slowly varying depth (1989)
    Springer
    Applied mathematics and mechanics 10 (1989), S. 213-220 
    Details
    ISSN: 1573-2754
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract The nonlinear waves in a stratified fluid of slowly varying depth are investigated in this paper. The model considered here consists of a two-layer incompressible constantdensity inviscid fluid confined by a slightly uneven bottom and a horizontal rigid wall. The Korteweg-de Vries (KdV) equation with varying coefficients is derived with the aid of the reductive perturbation method. By using the method of multiple scales, the approximate solutions of this equation are obtained. It is found that the unevenness of bottom may lead to the generation of so-called quasi-periodic waves and quasisolitary waves, whose periods, propagation velocities and wave profiles vary slowly. The relations of the period of quasiperiodic waves and of the amplitude, propagation velocity of quasi-solitary waves varying with the depth of fluid are also presented. The models with two horizontal rigid walls or single-layer fluid can be regarded as particular cases of those in this paper.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02014615
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  • 8
    Electronic Resource
    Electronic Resource
    Asymptotic analysis of strongly nonlinear oscillators (1985)
    Springer
    Applied mathematics and mechanics 6 (1985), S. 409-415 
    Details
    ISSN: 1573-2754
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract In this paper, an asymptotic method is presented for the analysis of a class of strongly nonlinear autonomous oscillators. The equations governing the amplitude and phase factor are obtained, and the amplitude and stability of the corresponding limit cycles are determined.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01895378
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  • 9
    Electronic Resource
    Electronic Resource
    Homogenized equations for steady heat conduction in composite materials with dilutely-distributed impurities (1983)
    Springer
    Applied mathematics and mechanics 4 (1983), S. 167-173 
    Details
    ISSN: 1573-2754
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract In this paper, by using the two-space method, homogenized equations for steady heat conduction in the composite material cylinders with dilutely-distributed elliptic cylinders of impurities are derived, and the explicit expressions for the corresponding effective heat conductivity of those which are concerned are obtained. It is also shown that the macroscopic heat conduction is anisotropic when the cross-sections of the impurity cylinders are unidirectionally oriented and isotropic when the angular distribution of the cross-sections is uniform.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01895441
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  • 10
    Electronic Resource
    Electronic Resource
    Computer algebra-perturbation solution to a nonlinear wave equation (1995)
    Springer
    Applied mathematics and mechanics 16 (1995), S. 429-435 
    Details
    ISSN: 1573-2754
    Keywords: nonlinear wave ; perturbation ; computer algebra ; renormalization technique ; approximate analytical method of characteristics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract In this paper, the higher-order asymptotic solution to the Cauchy problem of a nonlinear wave equation is found by using a computer algebra-perturbation method. The secular terms in the solution from straightforward expansions are eliminated with the straining of characteristic, coordinates and the use of the renormalization technique, and the four-term uniformly valid solution is obtained with the symbolic computation by using a computer algebra system. The comparison of the derived asymptotic solution and the numerical solution shows that they coincide with each other for smaller ε and agree quite well for larger ε (e. g., ε=0.25)
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02459341
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