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MEASUREMENT

Figure 5. Rectangular enclosure with material type and first significant Figure 7. First significant natural frequency (Hz) for similar rectangular and
natural frequency (Hz). cylindrical shapes

Should I design a rectangular or a cylindrical enclosure? rectangle is better at withstanding deformation. However, the
Figure 6 shows both a hollow rectangular and cylindrical stainless cross-sectional area, A, of the cylinder is three times larger than
steel extrusion, with 2 mm wall thickness and 40 mm height. The the rectangle. A larger A parameter means a larger fixed constraint
outer diameter of the cylinder is 43 mm, and the rectangular piece both in simulation and reality – the cylinder is better designed for
is also 43 mm on both x and y axes. increased rigidity or higher stiffness.
For modal analysis, the entire 2 mm wall surface (or x, y cross- Using the Table 3 values and equation 5, the critical frequency
sectional area) is a fixed constraint. Figure 7 shows modal FEM is 60.74 kHz for the cylinder and 26.56 kHz for the rectangle.
analysis results. The first natural frequency with significant MPF
(greater than 0.1 for the ratio of effective mass to total mass of Table 3. Area moment of inertia (iyy), shear modulus (g), density (ρ),
the system) is plotted vs. material shape. The cylindrical shape has and cross-sectional area (a) for cylinder and rectangular pieces
the highest first significant natural frequency for x and y axes, with 2 3 2
similar performance in the z direction. Shape IYY (m4) G (N/m ) ρ (kg/m ) A (m )
Cylinder 6.24E-8 7.7E10 7850 1.03E-3
Geometry – area and inertia Rectangle 9.21E-8 7.7E10 7850 0.33E-3
Equation 4 includes both material and geometric dependencies.
As both rectangular and cylindrical pieces were simulated using
stainless steel parameters, the only reason for better performance
with the cylindrical piece is geometry. Figure 8 illustrates the
cylinder and rectangle cross section for calculation of the area
moment of inertia and cross-sectional area of the pieces.
The area moment of inertia, I YY, of the rectangle is almost
50% greater than that of the cylinder, as shown in Table 3. The

Figure 6. Similar rectangular and cylindrical shapes for modal design study. Figure 8. Area moment of inertia (IYY) and cross-sectional area.

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