Acoustics, Vibration, and Waves

5.

Vibration of Continuous Systems

5.1.

Transverse Vibration of Strings

5.1.1.

The Wave Equation for a String

5.1.1.1.

Derivation from Newton's Laws

5.1.1.2.

Assumptions and Limitations

5.1.2.

Boundary Conditions for Strings

5.1.2.1.

5.1.2.2.

5.1.2.3.

Mixed Boundary Conditions

5.1.3.

Normal Modes and Frequencies

5.1.3.1.

5.1.3.2.

Frequency Calculation

5.1.3.3.

Harmonic Series

5.1.4.

String Excitation Methods

5.1.4.1.

Plucked Strings

5.1.4.2.

5.1.4.3.

5.1.5.

Energy Distribution in Vibrating Strings

5.1.6.

Damping in Strings

5.1.7.

Nonlinear Effects

5.2.

Longitudinal Vibration of Bars and Rods

5.2.1.

Wave Equation for Rods

5.2.2.

Material Properties

5.2.2.1.

Young's Modulus

5.2.2.2.

5.2.3.

Boundary Conditions and Normal Modes

5.2.3.1.

5.2.3.2.

Fixed-Free Rods

5.2.3.3.

Fixed-Fixed Rods

5.2.4.

Frequency Calculation for Rods

5.2.5.

5.2.5.1.

Ultrasonic Horns

5.2.5.2.

5.3.

Transverse Vibration of Beams

5.3.1.

Euler-Bernoulli Beam Theory

5.3.1.1.

5.3.1.2.

Governing Equation

5.3.2.

Bending Waves in Beams

5.3.3.

Boundary Conditions

5.3.3.1.

Simply Supported

5.3.3.2.

5.3.3.3.

5.3.3.4.

5.3.4.

Modal Frequencies and Mode Shapes

5.3.5.

Timoshenko Beam Theory

5.3.6.

Damping in Beams

5.3.6.1.

Material Damping

5.3.6.2.

Structural Damping

5.4.

Vibration of Membranes and Plates

5.4.1.

Two-Dimensional Wave Equation

5.4.2.

Boundary Conditions for Membranes

5.4.2.1.

Circular Membranes

5.4.2.2.

Rectangular Membranes

5.4.2.3.

Irregular Shapes

5.4.3.

Nodal Lines and Chladni Patterns

5.4.4.

Mode Shapes and Frequencies

5.4.4.1.

Rectangular Membranes

5.4.4.2.

Circular Membranes

5.4.5.

Vibrating Plates

5.4.5.1.

Thin Plate Theory

5.4.5.2.

Thick Plate Theory

5.4.5.3.

Modes of Plates

5.4.5.4.

Frequency Calculation

5.4.6.

5.4.6.1.

Drums and Percussion

5.4.6.2.

Loudspeaker Diaphragms

Previous

4. Acoustics: The Science of Sound

Go to top

Next

6. Architectural and Room Acoustics