Geodesic
Mode-series expansion of solutions of elasticity problems for a~strip
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 11 (2011) no. 2, pp. 83-96

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Oscillations of a strip are considered as a plane problem of elasticity theory. Description of oscillation modes is provided. Properties of eigenvalues and eigenfunctions are studied for a boundary value problem for their amplitudes. Green's function is constructed as a kernel of the inverse operator. Completeness and expansion theorems are proved which allow one to solve problems for finite and infinite membranes under arbitrary boundary conditions. 
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     author = {L. Yu. Kossovich and V. A. Yurko and I. V. Kirillova},
     title = {Mode-series expansion of solutions of elasticity problems for a~strip},
     journal = {Izvestiya of Saratov University. Mathematics. Mechanics. Informatics},
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L. Yu. Kossovich; V. A. Yurko; I. V. Kirillova. Mode-series expansion of solutions of elasticity problems for a~strip. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 11 (2011) no. 2, pp. 83-96. http://geodesic.mathdoc.fr/item/ISU_2011_11_2_a11/