#SOULVER MODULUS HOW TO#
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If you make the beam thinner, this difference would be even more pronounced. For all other modes, the relative shift in frequency is significantly smaller. The first thing to note is that the bending eigenmodes for the doubly clamped beam stand out and have a strong temperature dependence. The following table shows the cantilever beam results. The doubly clamped beam results are shown below.

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A cantilever beam, where one end is fixed and the other end is free.The eigenfrequencies of the beam have been calculated for two different types of boundary conditions: Eigenfrequencies of Doubly Clamped and Cantilever Beams To compute the reference solution, you either add a separate Eigenfrequency study or run the same study sequence, but without thermal expansion. The two study steps shown in the Model Builder tree. An Eigenfrequency study step in which the previously computed solution is used.

A Stationary study step that computes the displacements and stresses caused by the thermal expansion.To analyze the effect of thermal expansion, add a Prestressed Analysis, Eigenfrequency study.Īdding the Prestressed Analysis, Eigenfrequency study. Orthotropic thermal expansion coefficients are used to highlight some properties of the solution. To better separate the various effects, Poisson’s ratio is set to zero, but this assumption does not change the results in any fundamental way.

The material parameters have values that are of the same order of magnitude as those for many other engineering materials. The beam geometry and mesh used in the example. Rectangular Beam ExampleĬonsider a rectangular beam with the following data: PropertyĬoefficient of thermal expansion, x directionĬoefficient of thermal expansion, y directionĬoefficient of thermal expansion, z direction Setting up simulations that accurately capture such small effects can be a challenging task, since several phenomena can interact. In very high precision applications, the frequency stability requirements might specify a precision at the ppb (parts-per-billion, 10 -9) level. The most common parameter is temperature, but the same type of phenomena could, for example, be caused by hygroscopic swelling due to changes in humidity. Some devices require a very high degree of frequency stability with respect to changes in the environment. Studying Temperature-Dependent Eigenfrequencies We also explore effects like stress softening, geometric changes, and the temperature dependence of material properties.

#SOULVER MODULUS HOW TO#

In this blog post, we show how to do this using COMSOL Multiphysics® version 5.3. In some applications, particularly within the MEMS field, it is important to study the sensitivity of a device’s eigenfrequencies with respect to a variation in temperature.

Soulver modulus