## Content

**Vibrations**

**Introduction ****– ****Free response of SDOF systems**

1.1 Terminology

1.2 Equation of motion

1.3 Unforced response of SDOF system with no damping

1.4 Free vibration of a SDOF system with damping

1.5 Energy method for equation of motion

**Forced vibration of SDOF systems**

2.1 General solution

2.2 Dynamic magnification

2.3 Resonance frequency

2.4 Q factor

2.5 Vibration isolation

2.6 Support motion

**Transient response of SDOF systems**

3.1 Impulse function

3.2 Impulse response of SDOF systems

3.3 Convolution integral

3.4 Vibration instrumentation: accelerometer and vibrometer

**Unforced MDOF systems**

4.1 Example of MDOF system with 2 DOF

4.2 Natural frequencies

4.3 Modeshapes

4.4 Undamped free vibration of an N-degree of freedom system

4.5 Orthogonality of modeshape vectors

4.6 Diagonalisation of MDOF system and principal coordinates

4.7 Lagrange’s equations

**Harmonic force applied to a MDOF system**

5.1 Forced vibration of an undamped MDOF system 5.2 Receptance and mobility

5.3 Viscous damping

**Vibration in continuous systems**

6.1 Longitudinal (axial) vibration of a rod

6.2 Lateral vibration on a string in tension

6.3 Bending waves on a thin beam

6.4 Unforced flexural vibration of a thin beam

**Control**

**Introduction to Digital Control Systems**

1.1 Review and Classification of Control Systems

1.2 Analogue and Digital Control Systems

1.3 Components of a Control System

1.4 Sampling Theorem

**Mathematics of Digital Control Engineering**

2.1 Continuous Systems and Transfer Function Revision 2.2 Discrete Time Systems and Linear Difference Equations 2.3 z Transform

2.4 Transfer Function

2.5 Inverse z Transform

**Discrete Time Systems**

3.1 z Domain Transfer Function

3.2 Stability Criteria

3.3 Time Domain Response

3.4 Frequency Response

**Discrete Control Systems**

4.1 Equivalent Continuous Time Design

4.2 Realization and Implementation

4.3 Discrete PID Controller Design

4.4 Digital Control Applications

**Acoustics**

**Introduction to Acoustics:**

Basic nature of sound; particle displacement; particle velocity; acoustic pressure; condensation; sound velocity in gasses and fluids.

**Propagation of sound waves in solids and fluids:**

Derivation of the wave equation for a homogeneous, infinite medium in Cartesian co-ordinates; simple solution to the wave equation; the acoustic energy of plane waves; longitudinal and shear waves in infinite solids; torsional waves; quasi-longitudinal and flexural waves in bars and plates; dispersion curves.

**Interaction between vibrating structures and sound:**

The wave equation in spherical co-ordinates; general solution to the spherical wave equation; the monopole; source strength; the radiating dipole; vibrating piston in an infinite baffle; far-field directivity patterns; radiation from an arbitrary vibrating body; the Kirchoff-Helmholtz equation; radiation from an infinite plate; radiation efficiency; sound radiation from a finite plate; edge modes and corner modes; fluid loading of vibrating structures; radiation resistance and reactance.

**Propagation through partitions:**

Transmission and reflection coefficients for pressure, intensity and power; rigid and pressure release boundaries; normal transmission through two boundaries; transmission loss for a bounded, homogeneous, single panel; the field-incidence mass law.

The reverberant and direct fields; reverberation time; Sabine formula; sound intensity in an enclosure; room constant; the directivity factor.