FORCED VIBRATIONS OF ANISOTROPIC ELASTIC SOLIDS SUBJECTED TO AN ACTION OF COMPLICATED LOADS

The work studies the forced vibrations of anisotropic elastic circular plates caused by dynamic loads uniformly distributed along concentric circumferences and over ring surfaces. The method of compensating loads (MCL) is used to solve the formulated problems. A new technique is used to construct basic and compensating solutions. The Nielsen’s equation is taken into consideration. The solutions are obtained in closed form in terms of Bessel functions. Formulae of addition of cylindrical functions are used.

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ETHOD OF COMPENSATING LOADS FOR SOLVING OF ANISOTROPIC MEDIUM PROBLEMS

International Journal for Computational Civil and Structural Engineering ◽

10.22337/2587-9618-2018-14-1-71-77 ◽

2018 ◽

Vol 14 (1) ◽

pp. 71-77

Author(s):

Elena B. Koreneva

Keyword(s):

Closed Form ◽

Anisotropic Medium ◽

Bessel Functions ◽

Circular Plates ◽

Cylindrical Anisotropy

The work applies the method of compensating loads (MCL) for solution of statics and vibrations problems of plates with cylindrical anisotropy. For receiving of basic and compensating solutions Nielsen’s equation is used. The solution expressed in terms of Bessel functions is obtained. Such way can be used in con-sideration of symmetric, antisymmetric and unsymmetric flexure of orthotropic circular plates resting on an elastic Winkler’s subgrade. The similar method can be also utilized for examination of the symmetric vibrations of the orthotropic circular plates as well as for the cases of vibrations with one or a few nodal diameters. The solutions are obtained in closed form in terms of the cylindrical functions.

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The evaluation of integrals occurring in the theory of molecular structure. Parts I & II

Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences ◽

10.1098/rsta.1951.0003 ◽

1951 ◽

Vol 243 (864) ◽

pp. 221-249 ◽

Cited By ~ 332

Keyword(s):

Molecular Structure ◽

Bessel Functions ◽

Molecular Theory ◽

New Technique ◽

Modified Bessel Functions ◽

Numerical Examples ◽

A New Technique

Part I : A new technique is developed for evaluating the integrals which occur in molecular theory. The method is based on the expansion of exponentials in terms of the so-called £ functions. These involve modified Bessel functions. In this part we list the properties of these £ functions needed for the two-centre integrals. A table is provided of the I ’s and K ’s used in their tabulation. An account is given of the properties of certain integrals of the £ functions and some numerical examples are provided. Part II : Methods are described for the evaluation of the two-centre, one-electron Coulomb, overlap and resonance integrals, for the two-electron Coulomb and hybrid (Coulomb-exchange) integrals, and for the penetration integrals. Formulae are listed for more than 180 distinct integrals.

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