Modal analysis of continuous structures

• Free vibration and modes of vibration.

• Forced vibration, modal decomposition.

• Experimental modal analysis.

Modal analysis at high frequencies

• Difficulties at high frequencies, high frequency approximations.

• Mean square response, kinetic energy.

• Frequency average input power and mobility of infinite system.

Elastic wave motion in rods and beams

• Longitudinal, torsional, flexural wave equations.

• Wave solution, dispersion diagrams.

• Energy flow in propagating waves, group velocity, damping.

Forcing, reflection and transmission in beams

• Receptance of infinite or semi-infinite beam excited by force or moment, input power.

• Reflection of wave at different types of boundary.

• Interaction of wave in beam with a discontinuity.

• Prediction of natural frequencies by wave approach.

• Mode count and modal density of 1D systems.

Waves in plates

• Bending and in-plane waves.
• Reflection at an edge, modal density, transmission at boundaries.

Statistical energy analysis

• Introduction: power and energy, power balance, coupling power proportionality.
• SEA equations, weak and strong coupling.
• Energy equations of a simple oscillator, coupled oscillators and multi-modal systems.
• Wave transmission and coupling loss factors,
• SEA modeling
• Experimental SEA.