Forming a mesh over a wire frame

I am looking for an easy method to form a mesh over a frame.
I have 2 objects and I have not been able to come up with a usable method.
In the pictures you see the frame and the mesh. Difficult part are the multiple curves at the top and bottom end of the frame.
Hope someone can help by showing me a usable method

And the middle part in place


Could you explain the reason to model the mesh?
There are mesh looking materials in Visualization, so instead of creating the complex geometry of a mesh, you could use a full flat surface, and apply a mesh material.
For example, this speaker has a flat surface, but a mesh looking fabric applied to it:

@Laci_K I assumed that materials do not lead to a printable surface. This item needs to be 3D printed.
Is my assumption correct?

In that case, yes, if you want to 3D print it, you will need to model it. I assumed you would use something ready made for it.

I was always thinking that it would be nice to have some predefined objects. Like Bolts and fabric meshes for example. That can be applied to a model without having to reinvent the wheel.