One-dimensional propagation of longitudinal elastic waves through functionally graded materials

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F18%3A00322476" target="_blank" >RIV/68407700:21230/18:00322476 - isvavai.cz</a>

Výsledek na webu

<a href="https://www.sciencedirect.com/science/article/pii/S0020768318301252" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0020768318301252</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.ijsolstr.2018.03.017" target="_blank" >10.1016/j.ijsolstr.2018.03.017</a>

Jazyk výsledku

angličtina

Název v původním jazyce

One-dimensional propagation of longitudinal elastic waves through functionally graded materials

Popis výsledku v původním jazyce

The one-dimensional propagation of longitudinal elastic waves along the thickness of a plate made of functionally graded materials excited by a harmonic force is reported in this article. The material properties of the plate are assumed to be graded along the thickness direction according to a trigonometric law distribution. This distribution smoothly connects the material properties of the upper and lower homogeneous materials that bounds the plate. The corresponding propagation equation is Ince-type equation that can be transformed to Heun's equation a local exact solution of which is expressed in terms of local Heun functions. The general nature of these functions is demonstrated based on four degenerate cases of Heun's equation. The transfer matrix method is used to study the elastic waves propagating in the inhomogeneous domain. The calculation of the transfer matrices requires the evaluation of the general solution in the interval containing two regular singular points. For this purpose, the modified Heun function is introduced. Based on the transfer matrices, the influence of both the asymmetry of the unit cell and various constituent materials on the transmission coefficient spectrum is studied. The transmission coefficient is also calculated for the locally periodic structures with the help of the Chebyshev polynomials. (C) 2018 Elsevier Ltd. All rights reserved.

Název v anglickém jazyce

One-dimensional propagation of longitudinal elastic waves through functionally graded materials

Popis výsledku anglicky

The one-dimensional propagation of longitudinal elastic waves along the thickness of a plate made of functionally graded materials excited by a harmonic force is reported in this article. The material properties of the plate are assumed to be graded along the thickness direction according to a trigonometric law distribution. This distribution smoothly connects the material properties of the upper and lower homogeneous materials that bounds the plate. The corresponding propagation equation is Ince-type equation that can be transformed to Heun's equation a local exact solution of which is expressed in terms of local Heun functions. The general nature of these functions is demonstrated based on four degenerate cases of Heun's equation. The transfer matrix method is used to study the elastic waves propagating in the inhomogeneous domain. The calculation of the transfer matrices requires the evaluation of the general solution in the interval containing two regular singular points. For this purpose, the modified Heun function is introduced. Based on the transfer matrices, the influence of both the asymmetry of the unit cell and various constituent materials on the transmission coefficient spectrum is studied. The transmission coefficient is also calculated for the locally periodic structures with the help of the Chebyshev polynomials. (C) 2018 Elsevier Ltd. All rights reserved.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10307 - Acoustics

Projekt

<a href="/cs/project/GA15-23079S" target="_blank" >GA15-23079S: Šíření akustických vln nelokálními disperzními zónami</a><br>

Návaznosti

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

Rok uplatnění

2018

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

146

Číslo periodika v rámci svazku

August

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

12

Strana od-do

43-54

Kód UT WoS článku

000438004200003

EID výsledku v databázi Scopus

2-s2.0-85044527506