VIBRATIONS OF ARCHIMEDEAN SPIRALS WITH DISPLACEMENTS PERPENDICULAR TO THE PLANE OF THE CURVE
Ruziyev T.R Associate professor of Bukhara State Pedagogical Institute
Keywords:
Archimedes’ spirals, ordinary differential equations, viscoelastic properties, displacementsAbstract
The work examines vibrations of the Archimedes spiral. Differential equations of motion are integrated using the asymptotic method. To do this, the basic partial differential equations are reduced to ordinary differential equations with variable coefficients. The viscoelastic properties of materials are taken into account using complex elastic moduli. The construction of asymptotic expansions for eigenfunctions and eigenfrequencies corresponding to both types of oscillations of a repeatedly twisted flat spiral spring with fixed ends is presented. A technique has been developed for obtaining asymptotic resolving equations over a large range of changes in the variable φ and the corresponding boundary conditions. The solution is obtained in the form of series.
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