Exact solutions of the Euler–Bernoulli equation for selected polynomially non-uniform beams used for acoustic black holes

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F25%3A00384868" target="_blank" >RIV/68407700:21230/25:00384868 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1016/j.ijsolstr.2025.113468" target="_blank" >https://doi.org/10.1016/j.ijsolstr.2025.113468</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.ijsolstr.2025.113468" target="_blank" >10.1016/j.ijsolstr.2025.113468</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Exact solutions of the Euler–Bernoulli equation for selected polynomially non-uniform beams used for acoustic black holes

Popis výsledku v původním jazyce

In this work, we present a method for obtaining exact analytical solutions to the Euler–Bernoulli equation for nonuniform beams with continuously varying rectangular cross-sections. The approach is based on factorizing the fourth-order equation into a system of second-order differential equations with variable coefficients. Focusing on polynomial expressions for the cross-sectional profile, we show that such factorization is possible only when the profile is described by a polynomial of at most third order. In the general cubic case, the resulting equation transforms into Heun’s differential equation; in degenerate cases, it reduces to the hypergeometric or Bessel equations, all of which admit closed-form solutions. To demonstrate the method’s applicability, we compute reflection coefficients for selected profiles relevant to Acoustic Black Holes and validate the analytical results using a Riccati-based numerical method, showing excellent agreement.

Název v anglickém jazyce

Exact solutions of the Euler–Bernoulli equation for selected polynomially non-uniform beams used for acoustic black holes

Popis výsledku anglicky

In this work, we present a method for obtaining exact analytical solutions to the Euler–Bernoulli equation for nonuniform beams with continuously varying rectangular cross-sections. The approach is based on factorizing the fourth-order equation into a system of second-order differential equations with variable coefficients. Focusing on polynomial expressions for the cross-sectional profile, we show that such factorization is possible only when the profile is described by a polynomial of at most third order. In the general cubic case, the resulting equation transforms into Heun’s differential equation; in degenerate cases, it reduces to the hypergeometric or Bessel equations, all of which admit closed-form solutions. To demonstrate the method’s applicability, we compute reflection coefficients for selected profiles relevant to Acoustic Black Holes and validate the analytical results using a Riccati-based numerical method, showing excellent agreement.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10307 - Acoustics

Projekt

<a href="/cs/project/GA22-33896S" target="_blank" >GA22-33896S: Pokročilé metody řízení zvukových a elastických vlnových polí: akustické černé díry, metamateriály a funkčně gradované materiály</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2025

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

International Journal of Solids and Structures

ISSN

0020-7683

e-ISSN

1879-2146

Svazek periodika

320

Číslo periodika v rámci svazku

September

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

10

Strana od-do

—

Kód UT WoS článku

001509604500001

EID výsledku v databázi Scopus

2-s2.0-105007312095