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