Спектр стрічкового акустопроводу з періодично розподіленими діафрагмами. Слабий зв'язок

Abstract

The frequency’s spectrum of stripe acoustic waveguides with special structure has been investigated in the work. The waveguide is formed by translations of identical diaphragms along the structure axis. By applying conform mapping approach elementary cell of the such periodic waveguide was transformed into the canonical one with simple rectangular geometry. This method allows us to introduce correspondent periodic form-factor into wave equation directly. The main results have been obtained by using perturbative theory in the form adapted to the wave equations with periodic coefficients. They can be summed as phase velocity renormalization and splitting frequency spectrum into subbands separated by the forbidden windows. Renormalization factors and frequency’s gaps have been expressed over geometric parameters of waveguide