Uniqueness in the determination of vibration sources in polygonal plates observing the displacement over a space-time open set

Alexandre Kawano; Luís Yamaoka

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Uniqueness in the determination of vibration sources in polygonal plates observing the displacement over a space-time open set

机译：在多边形板中测定振动源的唯一性观察时空开放式置换的振动源

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摘要

In this article we deal with the identification of dynamical loading over the class of all plates with polygonal shapes that admit complete systems of trigonometric polynomials. It is proved that given an open set V in the interior of a plate with one of those shapes, using the displacement measured over V for a time interval longer than a minimum value, it is possible to identify uniquely the spatial distribution of the load acting over the plate.

机译：在本文中，我们应对所有具有多边形多项式系统的多边形形状的所有板类上的动态加载。被证明，在具有那种形状之一的板内部的窗口内部的开放组V，使用通过V的时间间隔测量的时间间隔长于最小值，可以唯一地识别负载作用的空间分布在盘子上。

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来源
《Zeitschrift fur Angewandte Mathematik und Mechanik》 |2019年第8期|共14页
作者
Alexandre Kawano; Luís Yamaoka;
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作者单位

Escola Politecnica University of Sao Paulo Sao Paulo Brazil;

Multidisciplinary Department Universidade Federal de Sao Paulo Sao Paulo Brazil;

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原文格式 PDF
正文语种 eng
中图分类应用数学;力学;
关键词
Germain Lagrange plates; inverse problems; Lipschitz boundaries; source identification;

机译：Germain Lagrange Plates;逆问题;Lipschitz边界;来源识别;

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专利

1. Uniqueness in the determination of vibration sources in polygonal plates observing the displacement over a space-time open set [J] . Alexandre Kawano, Luís Yamaoka Zeitschrift fur Angewandte Mathematik und Mechanik . 2019,第8期

机译：在多边形板中测定振动源的唯一性观察时空开放式置换的振动源
2. A uniqueness theorem for the determination of sources in the Germain-Lagrange plate equation [J] . Kawano A. Journal of Mathematical Analysis and Applications . 2013,第1期

机译：确定Germain-Lagrange平板方程式中源的唯一性定理
3. Characterisation of vibration sources on a set of plates using the RIFF technique [J] . Pezerat C., Loyau T., Guyader JL. Noise Control Engineering Journal . 2002,第2期

机译：使用RIFF技术表征一组板的振动源
4. MODELING THE FLEXURAL VIBRATIONS OF PLANAR ASSEMBLIES OF POLYGONAL PLATES USING THE IMAGE SOURCE METHOD [C] . Jacques Cuenca, Francois Gautier, Laurent Simon International congress on noise control engineering . 2010

机译：用图像源法模拟多边形板平面组合的弯曲振动。
5. Plate Vibration Displacement Curve Measurement Using PVDF [D] . Pinjan, Aniket Nandkumar 2018

机译：使用PVDF测量板的振动位移曲线
6. AN INTERFEROMETER METHOD OF OBSERVING THE VIBRATIONS OF AN OSCILLATING QUARTZ PLATE [O] . Harold Osterberg 1929

机译：干涉石英板振动的干涉法
7. AN INTERFEROMETER METHOD OF OBSERVING THE VIBRATIONS OF AN OSCILLATING QUARTZ PLATE [O] . Osterberg, Harold 1929

机译：干涉石英板振动的干涉法
8. NOTE OF VIBRATIONS OF PRISMS AND POLYGONAL PLATES [R] . R. D. MINDL1N 1958

机译：关于pRIsms和多边形板振动的注记

Uniqueness in the determination of vibration sources in polygonal plates observing the displacement over a space-time open set

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