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ADVANCED STRUCTURAL DYNAMICS AND ACOUSTICS13.811 Lecture 4
13.811Advanced Structural
Dynamics and Acoustics
AcousticsLecture 4
ADVANCED STRUCTURAL DYNAMICS AND ACOUSTICS13.811 Lecture 4
Green’s FunctionU(t)
ra
Helmholts Equation for Green’s Function
Proof
Green’s Function
ADVANCED STRUCTURAL DYNAMICS AND ACOUSTICS13.811 Lecture 4
Green’s FunctionSpectral Representations
Cylindrical Coordinates
Normalized Pressure – p(1m) = 1
Radiating Spectrum
Far Field Directivity Function
Simple Point Source
1
ADVANCED STRUCTURAL DYNAMICS AND ACOUSTICS13.811 Lecture 4
Green’s FunctionSpectral Representations
Cartesian Coordinates
Far Field Directivity Function
Normalized Pressure – p(1m) = 1
Ewald Sphere
1
Simple Point Source
ADVANCED STRUCTURAL DYNAMICS AND ACOUSTICS13.811 Lecture 4
Directivity FunctionLloyd-Mirror Pattern
Directivity Maxima and Minima
Directivity Function
θ
ADVANCED STRUCTURAL DYNAMICS AND ACOUSTICS13.811 Lecture 4
Directivity FunctionRectangular Baffled Piston
Lx
Ly
x
y
z
sinc(k L/2)
Directivity Function - Definition
Fourier Transform
Radiated Fieldx
ADVANCED STRUCTURAL DYNAMICS AND ACOUSTICS13.811 Lecture 4
Ewald Sphere ConstructionSquare Baffled Piston
LL xLy ==
f = ω/2π =kc/2π=4c/L
Directivity Function
ADVANCED STRUCTURAL DYNAMICS AND ACOUSTICS13.811 Lecture 4
Ewald Sphere ConstructionSquare Baffled Piston
L xLy ==
f = ω/2π =kc/2π=20c/L
L
Directivity Function
k = 40π/L
ADVANCED STRUCTURAL DYNAMICS AND ACOUSTICS13.811 Lecture 4
Square Baffled Platewith Traveling Wave
L
L
x
z
y
Directivity Function - Definition
Fourier Transform
Radiated Field
ADVANCED STRUCTURAL DYNAMICS AND ACOUSTICS13.811 Lecture 4
Ewald Sphere ConstructionSquare Baffled Piston
L xLy L==
f = ω/2π =kc/2π=15c/πL
Directivity Function
Square Baffled Platewith Traveling Wave – θ = 30o
0
ADVANCED STRUCTURAL DYNAMICS AND ACOUSTICS13.811 Lecture 4
Ewald Sphere ConstructionSquare Baffled Piston
L xLy L==
f = ω/2π =kc/2π=15c/πL
Directivity Function
Square Baffled Platewith Traveling Wave – θ = 90o
0
ADVANCED STRUCTURAL DYNAMICS AND ACOUSTICS13.811 Lecture 4
Directivity FunctionCircular Baffled Piston
x
z
Hankel Transform
Radiated Pressure Field
y
Directivity Function - Definition
Source Strength - Volume Injection
a
ADVANCED STRUCTURAL DYNAMICS AND ACOUSTICS13.811 Lecture 4
Ewald Sphere ConstructionCircular Baffled Piston
f = ω/2π =kc/2π=5c/aπ (ka = 10)
Directivity Function
