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On meso-scale approximations for vibrations of membranes with lower-dimensional clusters of inertial inclusions
St. Petersburg Mathematical Journal ( IF 0.7 ) Pub Date : 2021-05-11 , DOI: 10.1090/spmj/1661 V. G. Maz′ya , A. B. Movchan , M. J. Nieves
St. Petersburg Mathematical Journal ( IF 0.7 ) Pub Date : 2021-05-11 , DOI: 10.1090/spmj/1661 V. G. Maz′ya , A. B. Movchan , M. J. Nieves
Abstract:Formal asymptotic algorithms are considered for a class of meso-scale approximations for problems of vibration of elastic membranes that contain clusters of small inertial inclusions distributed along contours of predefined smooth shapes. Effective transmission conditions have been identified for inertial structured interfaces, and approximations to solutions of eigenvalue problems have been derived for domains containing lower-dimensional clusters of inclusions.
中文翻译：
具有惯性夹杂物的低维簇的膜振动的中尺度近似
摘要：针对一类中尺度近似，针对包含沿预定平滑形状轮廓分布的小惯性内含物簇的弹性膜的振动问题，考虑了形式渐近算法。对于惯性结构化界面已经确定了有效的传输条件，对于包含低维包含物簇的域，已经得出了特征值问题的近似解。
更新日期：2021-05-22
中文翻译：
具有惯性夹杂物的低维簇的膜振动的中尺度近似
摘要：针对一类中尺度近似，针对包含沿预定平滑形状轮廓分布的小惯性内含物簇的弹性膜的振动问题，考虑了形式渐近算法。对于惯性结构化界面已经确定了有效的传输条件，对于包含低维包含物簇的域，已经得出了特征值问题的近似解。
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