Abstract
The analysis of the vibration responses of a fruit is suggested to measure firmness non-destructively. A wooden ball excited the fruits and the response signals were captured using an accelerometer sensor. The method has been well studied and understood on ellipsoidal shaped fruit (watermelon). In this work, using the finite element simulations, the applicability of the method on watermelon was investigated. The firmness index is dependent on the mass, density, and natural frequency of the lowest spherical modes (under free boundary conditions). This developed index extends the firmness estimation for fruits or vegetables from a spherical to an ellipsoidal shape. The mode of Finite element analysis (FEA) of watermelon was generated based on measured geometry, and it can be served as a theoretical reference for predicting the modal characteristics as a function of design parameters such as material, geometrical, and physical properties. It was found that there were four types of mode shapes. The 1st one was first-type longitudinal mode, the 2nd one was the second-type longitudinal mode, the 3rd one was breathing mode or pure compression mode, and the fourth was flexural or torsional mode shape. As suggested in many references, the First-type spherical vibration mode or oblate-Prolate for watermelon is the lowest bending modes, it's most likely related to fruit firmness. Comparisons of finite element and experimental modal parameters show that both results were agreed in mode shape as well as natural frequencies. In order to measure the vibration signal of the mode, excitation and sensors should be placed on the watermelon surface far away from the nodal lines. The excitation and the response sensors should be in accordance with vibration directions. The correlations between the natural frequency and firmness was 0.856, natural frequency and Young's modulus was 0.800, and the natural frequency and stiffness factor (SF) was 0.862. The stiffness factor (SF) is adequate expression for the Modulus of Elastic (MOE), and adopted in the evaluation of their firmness.
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Claims 11
Claim · model-written summary
The firmness index depends on mass, density, and lowest spherical-mode frequency.
- Taxon
- watermelon
Citrullus lanatust0 - Outcome
- firmness indexe0
- Qualifier
- mass, density, and natural frequency of the lowest spherical modese0
Not reportedOrgan / stageDirection
Organisms pictured · Representative pictures of the matched species, not figures from the paper.
Verbatim
e0“The firmness index is dependent on the mass, density, and natural frequency of the lowest spherical modes”
t0“watermelon”
Claim · model-written summary
The developed index extends firmness estimation from spherical to ellipsoidal produce.
- Taxon
- watermelonCitrullus lanatust0
- Outcome
- firmness estimatione0
- Direction
- extendse0
- Comparator
- sphericale0
Organisms pictured · Representative pictures of the matched species, not figures from the paper.
Verbatim
e0“This developed index extends the firmness estimation for fruits or vegetables from a spherical to an ellipsoidal shape”
t0“watermelon”
Claim · model-written summary
Finite element analysis produced four watermelon vibration mode shapes.
- Taxon
- watermelonCitrullus lanatust0
- Outcome
- four types of mode shapese0
- Value
- four typese0
Organisms pictured · Representative pictures of the matched species, not figures from the paper.
Verbatim
e0“It was found that there were four types of mode shapes”
t0“watermelon”
Claim · model-written summary
The four mode shapes were two longitudinal modes, breathing or compression, and flexural or torsional.
- Taxon
- watermelonCitrullus lanatust0
- Outcome
- fourth was flexural or torsional mode shapee0
Organisms pictured · Representative pictures of the matched species, not figures from the paper.
Verbatim
e0“The 1st one was first-type longitudinal mode, the 2nd one was the second-type longitudinal mode, the 3rd one was breathing mode or pure compression mode, and the fourth was flexural or torsional mode shape”
t0“watermelon”
Claim · model-written summary
The first spherical or oblate-prolate mode is the lowest bending mode and likely related to firmness.
- Taxon
- watermelonCitrullus lanatuse0
- Outcome
- fruit firmnesse0
- Comparator
- First-type spherical vibration mode or oblate-Prolatee0
Not reportedDirection
Organisms pictured · Representative pictures of the matched species, not figures from the paper.
Verbatim
e0“First-type spherical vibration mode or oblate-Prolate for watermelon is the lowest bending modes, it's most likely related to fruit firmness”
Claim · model-written summary
Finite element and experimental modal results agreed in mode shape and natural frequencies.
- Taxon
- watermelonCitrullus lanatust0
- Outcome
- agreed in mode shape as well as natural frequenciese0
- Comparator
- experimental modal parameterse0
Organisms pictured · Representative pictures of the matched species, not figures from the paper.
Verbatim
e0“Comparisons of finite element and experimental modal parameters show that both results were agreed in mode shape as well as natural frequencies”
t0“watermelon”
Claim · model-written summary
The authors recommend locating excitation and sensors far from nodal lines and aligning sensors with vibration.
- Taxon
- watermelonCitrullus lanatuse0
- Outcome
- excitation and sensors should be placed on the watermelon surface far away from the nodal linese0
- Qualifier
- response sensors should be in accordance with vibration directionse0
Organisms pictured · Representative pictures of the matched species, not figures from the paper.
Verbatim
e0“excitation and sensors should be placed on the watermelon surface far away from the nodal lines. The excitation and the response sensors should be in accordance with vibration directions”
Claim · model-written summary
Natural frequency correlated with firmness at 0.856.
- Taxon
- watermelonCitrullus lanatust0
- Outcome
- firmnesse0
- Value
- 0.856e0
- Comparator
- natural frequencye0
Not reportedDirection
Organisms pictured · Representative pictures of the matched species, not figures from the paper.
Verbatim
e0“The correlations between the natural frequency and firmness was 0.856”
t0“watermelon”
Claim · model-written summary
Natural frequency correlated with Young's modulus at 0.800.
- Taxon
- watermelonCitrullus lanatust0
- Outcome
- Young's moduluse0
- Value
- 0.800e0
- Comparator
- natural frequencye0
Not reportedDirection
Organisms pictured · Representative pictures of the matched species, not figures from the paper.
Verbatim
e0“natural frequency and Young's modulus was 0.800”
t0“watermelon”
Claim · model-written summary
Natural frequency correlated with stiffness factor at 0.862.
- Taxon
- watermelonCitrullus lanatust0
- Outcome
- stiffness factor (SF)e0
- Value
- 0.862e0
- Comparator
- natural frequencye0
Not reportedDirection
Organisms pictured · Representative pictures of the matched species, not figures from the paper.
Verbatim
e0“the natural frequency and stiffness factor (SF) was 0.862”
t0“watermelon”
Claim · model-written summary
The stiffness factor was considered adequate for evaluating modulus of elasticity and fruit firmness.
- Taxon
- watermelonCitrullus lanatust0
- Outcome
- evaluation of their firmnesse0
- Comparator
- Modulus of Elastic (MOE)e0
Organisms pictured · Representative pictures of the matched species, not figures from the paper.
Verbatim
e0“The stiffness factor (SF) is adequate expression for the Modulus of Elastic (MOE), and adopted in the evaluation of their firmness”
t0“watermelon”