COMSOL 6.4 - Heat Generation in a Vibrating Structure

Heat Generation in a Vibrating Structure

When a structure is subjected to vibrations of high frequency, a significant amount of heat can be generated within the structure because of mechanical losses in the material such as, for example, viscoelastic effects.

In this example, you model the slow rise of the temperature in a vibrating beam-like structure. You use a transient heat-transfer problem with source term which represents the heat generation due to mechanical losses. The simulation is based on a structural analysis performed in the frequency domain.

Model Definition

The beam consists of two layers made of aluminum and titanium, respectively, with the corresponding loss factors 0.001 and 0.005. One end of the beam is fixed, and the other one is subjected to periodic loading in the z direction, which is represented in the frequency domain as Fy exp( j ω t), where j is the imaginary unit, and the angular frequency is

The excitation frequency f = 7760 Hz and the load magnitude Fy = 0.05 MPa are used in this example. The frequency is close to the first natural frequency of the structure.

The temperature rise is given by the heat-transfer equation

where k is the thermal conductivity, and the volumetric heat capacity ρCp is independent of the temperature in accordance with the Dulong-Petit law.

Note that T represents the temperature averaged over the time period 2π/ω. The heat source

presents the internal work of the nonelastic (for example, viscous) forces over the period. In the above expression, η is the loss factor, ε is the strain tensor, and

is the elasticity tensor. The term is computed from a structural analysis performed in the frequency domain.

The initial state at time t = 0 is stress-free, and the initial temperature is 293.15 K over the entire beam.

Use the following boundary conditions:

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At the fixed end, use the temperature condition T = 293.15 K.

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At the end subjected to periodic force, use the thermal insulation condition.

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The boundary between the layers of different materials is an interior boundary.

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At all other boundaries, use the convective cooling condition:

where h = 5 W/(m2·K) is the heat transfer coefficient and Text = 293.15 K is the external temperature.

For the simulation, apply a periodic loading in the y direction of magnitude 0.05 MPa and frequency 7760 Hz at the free end of the beam for 2 seconds, keeping the fixed end and the structure environment at a constant temperature of 300 K during the process.

Results and Discussion

The stress solution computed in frequency domain is shown in Figure 1. It appears that the maximum stresses are located at the fixed end. As consequence more energy is dissipated at this location.

Figure 1: von Mises stress from the frequency domain solution.

Figure 2 displays the temperature distribution at the end of the simulated 2-second forced vibrations. As the figure shows, the maximum temperature rise in the beam is about 27.6 K.

Figure 2: Temperature increase in the beam after 2 seconds of forced vibrations.

The maximum temperature increase is plotted in Figure 3, it shows that the maximum temperature increases in the first time steps, then starts to stabilize around the end time.