Title: Dispersion Analysis and Cutoff Frequency Characteristics of Harmonic Waves in a Viscoelastic-Filled Cylindrical Shell under Varying Geometric Ratios
Authors: Kholyigitova Mohigul Naim qizi
Volume: 10
Issue: 8
Pages: 48-51
Publication Date: 2026/08/28
Abstract:
This study presents a comprehensive dispersion analysis of harmonic waves propagating in a cylindrical shell filled with a Voigt viscoelastic medium. The investigation focuses on the dependence of cutoff frequencies, phase velocities, and wave attenuation on the key geometric ratios: shell thickness-to-radius ratio h/R, filler thickness-to-radius ratio a/R, and shell length-to-radius ratio L/R. The governing equations are formulated using the Donnell-Mushtari-Vlasov (DMV) shell theory for the outer elastic shell and the three-dimensional Navier equations with complex Lamé coefficients for the viscoelastic filler. Harmonic wave solutions lead to a transcendental dispersion equation whose roots are computed iteratively using the Newton-Raphson method with Bessel-function basis functions. Parametric calculations reveal that increasing a/R from 0.2 to 0.9 reduces the n = 2 cutoff frequency by up to 41%, while increasing h/R from 0.02 to 0.10 raises all cutoff frequencies by 15-22%. The viscosity coefficient ? is shown to introduce complex-valued wave numbers whose imaginary parts, interpreted as spatial attenuation rates, follow a power-law relationship with frequency. Mode shapes for circumferential orders n = 0 through n = 3 are computed and classified. The results provide design guidelines for vibration isolation and acoustic emission monitoring in filled cylindrical structures.