Biomedical Engineering Reference
In-Depth Information
stiffness coefficient measured by vibration was closely associated with sensory panel
subjective evaluations of Red Delicious apples (Finney, 1970, 1971). Garrett (1970) argued
that the stiffness factor should be proportional to the frequency squared times mass to the
two-thirds power. Cooke (1972) confirmed Garrett's theory using elastic theory relating the
stiffness factor to the shear modulus of the fruit flesh. Both Finney's and Garrett's stiffness
factors have been shown to correlate well with the fruit modulus (Clark and Shackelford,
1973; Yamamoto et al., 1980; and De Bardemaeker
(1989); Abbott, 1994; Abbott and Liljedahl,
1994). Differences in shear moduli between green and ripe fruits can be detected non-
destructively, and relatively easily, by vibration testing.
Through a few decades of development, a vibration-based characterization method called
Experimental Modal Analysis (EMA) has advanced to become a very efficient tool for
obtaining the dynamic properties such as natural frequency, damping and mode shapes in
aerospace and mechanical engineering. For fruits, natural frequency is related to the shear
modulus of the tissue (Cooke, 1972), which in turn determines the firmness of the fruit. For
instance, in apples, high damping prevents them from giving a nice them from giving a nice
crispy ringing sound when tapped (De Baerdemaeker and Wouters, 1987). Mode shapes are
an important indicator of the whole fruit's conditions such as ripeness, bruises, or defects
(Cherng, 2000). It is obvious that there is abundant information on the texture and quality of
fruits that could be associated with their acoustic parameters. This section of the chapter is
meant to give an idea of the direction that researchers have taken in the last decade or so. To
give specific examples, a few details are given on the measurement of Young's modulus,
finite element modeling, and experimental modal analysis.
2.2.2.1 Measuring modulus of elasticity
An instrument that measures force as a function of displacement, such as a UTM, can be
used to obtain force-displacement curves of the samples. For a melon, the flesh and the
rind should be tested differently. Melons have a rind that is significantly stiffer than the
flesh. The cylindrical samples of the flesh can be tested with a compression test. The rind
samples can be tested using a three point jig, and treated as a simply supported beam for
analysis.
For modeling vibrations, where only small displacements are of interest, the tests should
be limited to small displacements and changes in the cross-section and in the length can
be ignored in the data processing. Also, the mechanical properties of biological materials
in general are not constant. Because of the structures at the micro scale, the Young's
modulus is a function of strain. The following method can be used to facilitate the
computation of the Young's modulus at zero deformation. The stress-strain curve can be
fit to a cubic function
3
2
a
a
a
a
(20)
3
2
1
0
The coefficients
a
0
through
a
3
can be obtained by cubic regression analysis. The Young's
modulus is the derivative of the stress with respect to strain
d
2
(21)
E
3
a
2
a
a
3
2
1
d
