Investigation of the effect of shape on the acoustic response of 'conference' pears by finite element modelling

The impulse response method is often used to measure firmness of spherical fruits. In this method the fruit is excited using an impact hammer and the response signal is captured using a microphone. This vibration response sig nal is subsequently analysed and related to the firmness of the fruit. In o ur work the effect of the shape of pears on their resonant frequencies is i nvestigated using finite element (FE) modal analysis. Fifty differently sha ped 3D FE meshes of 'Conference' pears were generated using a geometrical m odelling system. The FE model was validated, and found to be sufficiently a ccurate. The length/maximal diameter (L/D) ratio and the Fourier descriptor s were used as shape descriptors. A strong linear relationship (r(2) > 0.84 ) was found between the third normalised Fourier descriptor (F3) and the re sonant frequencies. A weak linear relation was detected using the L/D and t he other normalised Fourier descriptors. A simulation of firmness measureme nts based on the calculated resonant frequency values was carried out to es timate the Young's (E) modulus of the pear as a measure of its firmness. Th e estimated error with these simulations was found to be 31.44, 8.02 and 3. 82% if the bending, the compression and the oblate-prolate modes were pleas ured and the LID was used as a shape descriptor. If F3 was used, the follow ing error values were found: 6.0% for the bending, 3.39% for compression an d 3.38% for the oblate-prolate modes. The results of this study may help in the development of a non-destructive firmness sensor for non-spherical fru its. (C) 2001 Elsevier Science B.V. All rights reserved.