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

Result code in 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>
Result on the web
<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>

Result language
angličtina
Original language name
Exact solutions of the Euler–Bernoulli equation for selected polynomially non-uniform beams used for acoustic black holes
Original language description
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.
Czech name
—
Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10307 - Acoustics

Project
<a href="/en/project/GA22-33896S" target="_blank" >GA22-33896S: Advanced methods of sound and elastic wave field control: acoustic black holes, metamaterials and functionally graded materials</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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