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.

Excitation techniques
  • Hammer or impacting device
  • Easy to use
  • Control of force pulse difficult
  • High forces
  • Low frequency only
  • Very high harmonic distortion
  • Equipment is heavy
  • Wide range of forces
  • Wide frequency range
  • Low harmonic distortion
  • Equipment is portable

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.


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.

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Subjects: Noise & Vibration