PHY 711 Fall 2014 Lecture 27 1 PHY 7 11 Classical Mechanics and Mathematical Methods 101050 AM MWF Olin 103 Plan for Lecture 27 Membrane vibrations Chap 8 2dimensional rectangular membrane ID: 209955
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PHY 711 Fall 2014 -- Lecture 27
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PHY
7
11 Classical Mechanics and Mathematical Methods
10-10:50 AM MWF Olin 103
Plan for Lecture 27:
Membrane vibrations (Chap. 8)
2-dimensional rectangular membrane
2-dimensional circular membrane
Other examplesSlide2
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Wave motion on a two-dimensional surface – elastic membrane (transverse wave; linear regime).
u(
x,y,t
)Slide5
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Consider a rectangular boundary:
a
bSlide6
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More general boundary conditions:Slide8
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Consider a circular boundary:
RSlide9
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Consider circular boundary -- continuedSlide10
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Some properties of Bessel functionsSlide11
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http://dlmf.nist.gov
/Slide12
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Series expansions of Bessel and Neumann functionsSlide13
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Some properties of Bessel functions -- continuedSlide14
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More complicated geometry – annular membrane
a
bSlide17
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Consider circular boundary -- continuedSlide18
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a
b
Normal modes of an annular membrane -- continuedSlide19
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a
b
Normal modes of an annular membrane -- continuedSlide20
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a
b
Normal modes of an annular membrane -- continuedSlide21
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Analysis for
m=0
:Slide22
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