For detailed study please go to Free vibrations on elastic support documentation.

In this project the functionality of the elastic support boundary condition on SimScale platform is validated. The geometry used was a simple cube with partitioned top face as shown below. The dimension of the box was *1 m x 1 m x 1 m*.

Two mesh types were considered; one with equally distributed elements on each partitioned face and other with unequal distribution. Meshes used for *case A-x* and *case B-x* are shown in figures below.

Density of material was defined as *10 kg/m*^{3} which makes the weight of cube equal to *10 kg*. Furthermore the gravity was also taken in to account. The cases below based on the mesh only differs in how the elastic support was applied on the partitioned faces based on which the free vibrations of cube was measured.

## Case A - 1

In this case isotropic spring stiffness of *K=9810 N/m* with total stiffness definition was applied on both faces and static analysis was performed.

## Case A - 2

In this case isotropic spring stiffness of *K=9810 N/m* with total stiffness definition was applied on both faces and dynamic analysis was performed.

## Case B - 1

In this case isotropic spring stiffness of *K=4905 N/m* on *face 1* and orthotropic spring stiffness of *K*_{x}=K_{y}=K_{z}=4905 N/m on *face 2* with total stiffness definition was applied and static analysis was performed.

## Case B - 2

In this case isotropic spring stiffness of *K/A=9810 N/m*^{3} on *face 1* and orthotropic spring stiffness of *K*_{x}/A=K_{y}/A=K_{z}/A=9810 N/m^{3} on *face 2* with distributed stiffness definition was applied and static analysis was performed.

## Case B - 3

In this case isotropic spring stiffness of *K=1962 N/m* on *face 1*, orthotropic spring stiffness of *K*_{x}=K_{y}=K_{z}=1962 N/m on *face 2* with total stiffness definition and isotropic spring stiffness of *K/A=3924 N/m*^{3} on both faces was applied and static analysis was performed.

The table below shows the result comparison between [SCHAUM] and SimScale case A-1/B-1/B-2/B-3.

The graph below shows the result comparison between [SCHAUM] and SimScale case A-2.

Finally, the figure below shows the animation of free vibrations of the cube on elastic support.

**Reference:**

[SCHAUM] (2011) ”*McGraw-Hill Schaum’s outlines, Engineering Mechanics: Dynamics*”, *pg 271-273*, N. W. Nelson, C. L. Best, W. J. McLean, Merle C. Potter