Energy Flux in Thin Plates

被引：0

作者：

Thompson, Ian ^{[1
]}

Fazakerley, Grace ^{[1
]}

机构：

[1] Univ Liverpool, Dept Math Sci, Liverpool L69 7ZL, Merseyside, England

来源：

QUARTERLY JOURNAL OF MECHANICS AND APPLIED MATHEMATICS | 2022年 / 75卷 / 02期

关键词：

FLEXURAL WAVES; SEMIINFINITE LATTICE; SCATTERING; EXCITATION; ARRAY; EDGE;

D O I：

10.1093/qjmam/hbac006

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A formula for energy flux due to vibrations in a thin plate modelled by Kirchhoff theory is derived by considering a Mindlin plate and taking the low frequency (or low thickness) limit. It is shown that a term that is usually neglected in Kirchhoff theory persists close to free edges. This term does not affect the transverse displacement, but it does affect the energy flux. The new flux formula conserves energy and evaluates to zero along fixed, free and simply supported edges. An example problem, in which edge waves are excited by a point source located in a semi-infinite plate, is considered. Numerical calculations show that the energy radiated into the far field matches the energy introduced by the source.

引用

页码：127 / 146

页数：24

共 50 条

[11] Nonlinear transformation-based broadband cloaking for flexural waves in elastic thin plates [J].

Liu, M. ;

Zhu, W. D. .

JOURNAL OF SOUND AND VIBRATION, 2019, 445 :270-287

[12] Energy response of X-rays under high flux conditions using a thin APD for the energy range of 6-33 keV [J].

Masuda, T. ;

Hiraki, T. ;

Kaino, H. ;

Kishimoto, S. ;

Miyamoto, Y. ;

Okai, K. ;

Okubo, S. ;

Ozaki, R. ;

Sasao, N. ;

Suzuki, K. ;

Uetake, S. ;

Yoshimi, A. ;

Yoshimura, K. .

NUCLEAR INSTRUMENTS & METHODS IN PHYSICS RESEARCH SECTION A-ACCELERATORS SPECTROMETERS DETECTORS AND ASSOCIATED EQUIPMENT, 2019, 913 :72-77

[13] Negative refraction of flexural wave propagation on phononic thin plates based on the backward wave effect [J].

Wang, Zuowei ;

Li, Tuanjie .

WAVES IN RANDOM AND COMPLEX MEDIA, 2022, :6322-6340

[14] Cloaking bending waves propagating in thin elastic plates [J].

Farhat, Mohamed ;

Guenneau, Sebastien ;

Enoch, Stefan ;

Movchan, Alexander B. .

PHYSICAL REVIEW B, 2009, 79 (03)

[15] ABSORPTION OF p MODES BY THIN MAGNETIC FLUX TUBES [J].

Jain, Rekha ;

Hindman, Bradley W. ;

Braun, Doug C. ;

Birch, Aaron C. .

ASTROPHYSICAL JOURNAL, 2009, 695 (01) :325-335

[16] Generation of circumferential harmonic travelling waves on thin circular plates [J].

Kumar, Aman ;

DasGupta, Anirvan .

JOURNAL OF SOUND AND VIBRATION, 2020, 478 (478)

[17] Bloch-Floquet bending waves in perforated thin plates [J].

Movchan, A. B. ;

Movchan, N. V. ;

Mcphedran, R. C. .

PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 2007, 463 (2086) :2505-2518

[18] ACTIVE CLOAKING OF INCLUSIONS FOR FLEXURAL WAVES IN THIN ELASTIC PLATES [J].

O'Neill, J. ;

Selsil, Oe. ;

Mcphedran, R. C. ;

Movchan, A. B. ;

Movchan, N. V. .

QUARTERLY JOURNAL OF MECHANICS AND APPLIED MATHEMATICS, 2015, 68 (03) :263-288

[19] Omnidirectional broadband insulating device for flexural waves in thin plates [J].

Climente, Alfonso ;

Torrent, Daniel ;

Sanchez-Dehesa, Jose .

JOURNAL OF APPLIED PHYSICS, 2013, 114 (21)

[20] Analytic theory of defects in periodically structured elastic plates [J].

Poulton, C. G. ;

Movchan, A. B. ;

Movchan, N. V. ;

McPhedran, Ross C. .

PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 2012, 468 (2140) :1196-1216

← 1 2 3 4 5 →