# Modulus, Shape Factor, and Reading a Nomogram

When designing a vibration isolation solution, modulus and shape factor are among the first variables described by shock and vibration engineers. In Part 1 of a 3-part video series, E-A-R™ Application Engineer Chirag Patel walks us through how to determine these attributes.

Inputs

The first step in the process requires knowledge of two inputs: frequency and operating temperature. These inputs represent the vibration issue that needs solved - what is the problem frequency or frequencies being produced, and at what temperature(s) will the device or component be operating. With these numbers in-hand, they can then be applied to a material nomogram to derive shear modulus and loss factor.

Material Nomogram (example here)

When examining a nomogram you will first want to notice the axis on the right, Frequency, and top, Temperature. These correlate with the two inputs described above. The two curved lines on the chart represent the shear modulus (the "S"-shaped curve, shear stress to shear strain) and the loss factor (the bell-shaped curve, energy dissipated to energy stored). Using the inputs, find:

1)      The point of intersection of the diagonal temperature line and horizontal frequency line

2)      At that point, draw a vertical line

3)      Where the drawn vertical line intersects the "S"-shaped curve is the material modulus. The scale for this is on the left (note: compressive modulus is approximated 3x shear modulus)

4)      Where the drawn vertical line intersects the bell-shaped curve is the loss factor. The scale on the left is generally 10x loss factor (values to scale are sometimes annotated in parenthesis)

In general, a higher loss factor is more desirable in most applications. Many ISODAMP™ materials contain peak damping above 1, which is considered highly damped, and some ISOLOSS™ SL materials even reach 2! Material nomograms are available for all E-A-R™ Precision Electronics materials.

Shape Factor

While the modulus of the material displays its rigidity, shape factor is also used in geometric design to add or remove stiffness. This is calculated by dividing the area under load by the area free to bulge. A rule of thumb is to use a shape factor of 0.5 - 1.0, depending on the application and load. Features such as ribs are often utilized to modify this value.

The next video, Part 2 of Designing a Vibration Isolation Solution, will highlight stiffness and natural frequency.

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