## Vibration measurements using continuous scanning laser Doppler vibrometry : theoretical velocity sensitivity analysis with applications

journal contribution

posted on 02.05.2008 by Ben Halkon, Steve Rothberg#### journal contribution

Any type of content formally published in an academic journal, usually following a peer-review process.

It is readily accepted that a Laser Vibrometer measures target velocity in the direction of the incident laser beam but this measured velocity must be considered in terms of the various target velocity components. This paper begins with a review of the theoretical description of the velocity sensed by a single laser beam incident in an arbitrary direction on a rotating target undergoing arbitrary vibration. The measured velocity is presented as the sum of six terms, each the product of a combination of geometric parameters, relating to the laser beam orientation, and a combination of motion parameters – the “vibration sets”. This totally general velocity sensitivity model can be applied to any measurement configuration on any target. The model is also sufficiently versatile to incorporate time dependent beam orientation and this is described in this paper, with reference to continuous scanning Laser Doppler Vibrometry. For continuous scanning applications, the velocity sensitivity model is shown formulated in two useful ways. The first is in terms of the laser beam orientation angles, developing the original model to include time dependency in the angles, whilst the second is an entirely new development in which the model is written in terms of the mirror scan angles, since it is these which the operator would seek to control in practice. In the original derivation, the illuminated section of the rotating target was assumed to be of rigid cross-section but, since continuous scanning measurements are employed on targets with flexible cross-sections, such as beams, panels and thin or bladed discs, the theory is developed in this paper for the first time to include provision for such flexibility.

### History

#### School

- Mechanical, Electrical and Manufacturing Engineering