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  • 1990-1994  (3)
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Publisher
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Year
  • 1
    Electronic Resource
    Electronic Resource
    Solution of dynamic problems for perforated structures by the method of averaging (1991)
    Springer
    Journal of mathematical sciences 57 (1991), S. 3410-3412 
    Details
    ISSN: 1573-8795
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We consider transverse oscillations of a membrane with a square network of perforations whose contour is clamped and whose aperture edges are free. We apply the method of averaging in conjunction with variational methods for solving “cell problems. “ The eigenfunctions and characteristic frequencies of oscillation are represented as asymptotic series in powers of a small parameter that characterizes the period of the lattice. The problem is solved in stages: first the “cell problem,” then the principal parts of the eigenfunctions and characteristic frequencies are determined from the averaged equation. To determine the first correction to the frequency we use the averaged equation for the next approximation and the selfadjoint property of the original operator.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01880207
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Application of the averaging method to the study of oscillations of a perforated plate (1993)
    Springer
    Journal of mathematical sciences 65 (1993), S. 1503-1507 
    Details
    ISSN: 1573-8795
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A dynamical problem for a perforated membrane with free holes is considered. A solution is obtained with the help of the averaging method and the use of two-scaling decompositions. To solve local problems, we apply the variational Bubnov-Galerkin method. The first correction to the frequency is determined from the averaging equation of order ɛ1 and the property that the initial differential operator is self-adjoint. A comparison with respect to rigidity is given of the results obtained with the known.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01097652
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Solution of dynamic problems for perforated structures by the method of averaging (1991)
    Springer
    Journal of mathematical sciences 57 (1991), S. 3410-3412 
    Details
    ISSN: 1573-8795
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We consider transverse oscillations of a membrane with a square network of perforations whose contour is clamped and whose aperture edges are free. We apply the method of averaging in conjunction with variational methods for solving “cell problems.” The eigenfunctions and characteristic frequencies of oscillation are represented as asymptotic series in powers of a small parameter that characterizes the period of the lattice. The problem is solved in stages: first the “cell problem,” then the principal parts of the eigenfunctions and characteristic frequencies are determined from the averaged equation. To determine the first correction to the frequency we use the averaged equation for the next approximation and the self-adjoint property of the original operator.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01097714
    Location Call Number Expected Availability
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    Paper (German National Licenses)
    Fulltext
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