Vibration modal analysis of Korla pear and establishment of stiffness evaluation index

Abstract: Stiffness is an important biomaterial property in assessing the internal quality of fruits. The vibration response technique can be used for estimating the stiffness of fruits with natural frequency measurements. Existing researches always simplified fruits as spherical structure to analyze the vibration modal and study the effects of mass and density on natural frequency of fruits. Thus, the different firmness indices were proposed. Nevertheless, some studies indicated that the natural frequency of ellipsoidal fruit was also affected by its shape. Consequently, these indices had the limitations on stiffness evaluation of Korla pear with different shapes. Therefore, a general stiffness index suitable for different fruit shapes should be established. In the study the aspect ratio was employed to describe the fruit shape of Korla pear. It was expressed as the ratio of mean value of shoulder height to equator diameter of pear. The vibration characteristics of pear were analyzed using the experimental modal method combined with the finite element (FE) method. By experimental modal analysis, 3 modals including oblate-oblate mode (Modal A), the first spherical mode (Modal B) and the second spherical mode (Modal C) were obtained. The stem end (or the calyx end) and equatorial region of pear were the suitable positions for the detection using Modal A and B, respectively. This was because the largest deformation could appear and the nodes could be avoided when the pear was impacted on these positions. The Modal C was not used in this work because its natural high-order frequency was not easy to measure. In the FE analysis, the geometric model of Korla pear was created by reserving processing and free meshing using tetrahedral structural solid element. Three mode shapes and natural frequencies extracted from the output of FE modal analysis agreed well with the experimental results assuming Korla pear as the linear elastic and isotropic material. Therefore, the FE method was used to analyze the influence of Korla pear shape on the natural frequency of Modal A and B. The results showed that fruit shape had significant effect on natural frequencies of these 2 modals. With the increasing of the aspect ratio of Korla pear, the frequency linearly decreased for Modal A while linearly increased for Modal B. Based on the linear relationship between the aspect ratio and frequencies of Modal A and B, a new stiffness index was established. The ratios of the frequency from the FE method to that from the experiment calculated by the new index were 1.0050±0.0042 and 1.0000±0.0043, respectively for Model A and B. Compared with the frequency ratios calculated by the traditional index, the results were closer to 1. Therefore, the new stiffness index can accurately evaluate the stiffness of Korla pear; moreover, it can eliminate the influence of Korla pear shape on the frequency. The results can provide a practical guidance for non-destructive measurements of Korla pear stiffness using vibration detection technology.