# Modal Analysis

The process of determining a set of generalized coordinates for a system such that the equations of motion are both inertially and elastically uncoupled. More commonly, it is a process of determining the natural frequencies, damping factors, and mode shapes for a structure. This is usually done either experimentally through frequency response testing or mathematically using finite element analysis.

- Mechanical
- Hammer or impacting device
- Easy to use
- Control of force pulse difficult

- Electrohydraulic
- High forces
- Low frequency only
- Very high harmonic distortion
- Equipment is heavy

- Electrodynamic
- Wide range of forces
- Wide frequency range
- Low harmonic distortion
- Equipment is portable

**Excitation techniques**

### Parameter Estimation

The process of evaluating and curve fitting frequency response functions in order to estimate modal parameters.

### Residual Terms

Terms added to a curve fit algorithm to take into account the effects of modes outside the range being fitted. These terms consist of a mass term on the low frequency end and a stiffness term on the high.

### Roots

The roots of the characteristic equation are complex and have a real and imaginary part. The real part describes the damping (decay rate) of the system and the imaginary part describes the oscillations or damped natural frequency of the system.

**See also: **Circle Fitting, Complex Modes, Driving Point Measurement, Exponential Window, Force Window, Forced Response Analysis, Frequency Response Function, Frequency Response Matrix, Impact Testing, Mode Shape, Natural Frequency, Real Modes, Vibration.

**Subjects: ** Noise & Vibration