Simulation of a time-depending plate-vibration

Hi everyone,

I would like to simulate a time-depending (transient) plate-vibration using the pde-Toolbox.

Therefore, I start creating the pde-equation with respect to the simulation time as a 2d-problem. Thus, I am using planestress.

tmodel = createpde('structural', transient-planestress);

The geometry is created by using decsg-command:

gdm = [3; 4; 0; 10; 10; 0; 0; 0; 10; 10];
g = decsg(gdm, 'S1', ('S1')');
geometryFromEdges(tmodel, g);

The BC are no problem, since I simply add some edges and vertices.

E = 200E9;
nu = 0.3;
rho = 8000;
structuralProperties(tmodel, 'YoungsModulus', E, ...
                           'PoissonsRatio', nu, ...
                           'MassDensity', rho);
mesh = generateMesh(tmodel);
structuralBC(tmodel, "Edge", 4, "Constraint", "fixed");

How do I apply a sinoidal force/load with a frequency of 10 Hz and an amplitude of 10, which is perpendicular to the surface? I only found force direction that is in the X-Y-Plane, but not right-angled to the surface.

structuralBoundaryLoad(tmodel, 'Vertex', 2, 'Force', [0, 10], 'Frequency', 10);

Followed by the IC

structuralIC(tmodel,'Displacement',[0;0],'Velocity',[0;0])

and the solution steps

ncycle = 50;
samplingFrequency = 60/T;
tlist = linspace(0, ncycle*T, ncycle*T*samplingFrequency);

I finally start and solve the calculation

R = solve(tmodel,tlist);

Therefore, I got two questions:

1. How can one apply a perpendicular force to the surface?
2. Is it possible to calculate the displacement of the plate in Z-direction, by using "planestress" or do I have to use "transient-solid" with a third dimension (and additional calculation time)?

Answer 1

[Vidip]

In the context of the PDE Toolbox and structural mechanics problems, the "plane stress" assumption implies that the problem is essentially two-dimensional with no stresses in the third dimension (perpendicular to the plane). Therefore, the displacements are also considered only in the plane of the structure (X and Y directions), and out-of-plane forces are not directly applied in a "plane stress" simulation.

To simulate a plate vibration with out-of-plane (Z-direction) displacements and forces, you would need to use a 3D model. In MATLAB's PDE Toolbox, this would typically be a "transient-solid" model rather than "transient-planestress".

Also, if you have a face where you want to apply a pressure load normal to the surface, you would use the ‘structuralBoundaryLoad’ function and if the pressure load varies with time, you can define a function that describes this variation and pass it to ‘structuralBoundaryLoad’ function. For more detailed explanation you can follow the below documentation -

• https://in.mathworks.com/help/pde/ug/pde.structuralmodel.structuralboundaryload.html#responsive_offcanvas