If a structure is subjected to a vibration under the operation, one will be damaged by the fatigue which may make the life of the structure short. Thus, in order to predict the life time, it is essential to obtain the strains of the weak parts of the structure. However, when the strains of the operational structure can not be directly measured due to the problem of attachment, those must be obtained indirectly.
Since the displacement (deformation) and the strain in a structure are interrelated, the strain can be predicted from the measured displacement and displacement-strain transformation matrix, which may be obtained by modal analysis of a structure. The transformation matrix is dependent on the boundary condition, unfortunately, and it is also difficult to know exactly that of the operational system.
In this study, at first, the characteristics of the transformation matrix are investigated. And then, for the structure with arbitary boundary condition under the operation, the approximate method is proposed in order to predict the operational strains using the transformation matrix obtained by using free boundary conditons. Finally, the method is applied to predict the strains of leads of surface mount component under the vibration of the printed circuit board.
