Development of noncontact measurement methods using multiple laser displacement sensors for bending and torsional vibration stresses in piping systems

•Methods to measure vibration stress of piping conveniently and quickly were presented.•The methods include the modeling approach and noncontact measurement techniques.•The measuring technique for bending vibration stress using laser sensors was proposed.•The measuring technique for torsional vibration stress using laser sensors was proposed.•The method applicability to piping vibration was discussed based on an experiment.

In this study, two methods to measure bending and torsional vibration stresses of piping systems conveniently and quickly are proposed. The proposed methods are composed of a modeling approach of piping vibration and noncontact measurement techniques. The methods assume the vibration modes as a primary mode within the measuring range without the mode-identification and then estimate the vibration stress by approximating the vibration displacements measured in a noncontact manner as a primary mode. This paper presents the principles and calculation formulas of both methods and shows the measurement techniques for the bending and torsional vibration stresses using laser displacement sensors. Finally the applicability of one method is discussed based on the results of a vibration experiment.