Journal of Applied Mathematics and MechanicsJournal of Applied Mathematics and MechanicsПрикладная математика и механика0032-82353034-5758The Russian Academy of Sciences70038810.7868/S3034575825060051ArticlesСтатьиResearch ArticleAnalysis of acoustic waves in periodic functionally graded rods using the cauchy formalism methodАнализ акустических волн в периодических функционально-градиентных стержнях методом формализма КошиSaiyanS. G.СаиянС. Г.Berformert@gmail.comKuznetsovS. V.КузнецовС. В.Berformert@gmail.comNational Research Moscow State University of Civil Engineering (NRU MGSU)Национальный исследовательский Московский государственный строительный университет (НИУ МГСУ)Ishlinsky Institute for Problems in Mechanics RASИнститут Проблем Механики им. А.Ю. Ишлинского РАН15122025896VOL 89, NO6 (2025)ТОМ 89, №6 (2025)94395808012026Copyright ©; 2025, Russian Academy of SciencesCopyright ©; 2025, Российская академия наук2025Russian Academy of SciencesРоссийская академия наукhttps://cardiosomatics.ru/0032-8235/article/view/700388

This study investigates acoustic waves in one-dimensional periodic functionally graded rods using a modified Cauchy formalism previously applied to analyze the dispersion of surface acoustic waves in layered media. During the propagation of harmonic waves in a semi-infinite rod with harmonic periodicity of acoustic properties, phenomena were observed, including non-periodic spatial variation of the wave's phase velocity and amplitude, along with spatially periodic changes in kinetic energy and strain energy.

В данной работе исследуются акустические волны в одномерных периодических функционально-градиентных стержнях с использованием модифицированного формализма Коши, ранее примененного для анализа дисперсии поверхностных акустических волн в слоистых средах. При распространении гармонических волн в полу-бесконечном стержне с гармонической периодичностью акустических свойств обнаружены явления, включая непериодическое пространственное изменение дисперсии и амплитуды волны, но при этом пространственно-периодическое изменение кинетической энергии и энергии деформаций.

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