I'm sure many here are familiar with the following image showing the 2D representation of how the fabric of spacetime is warped by the presence of mass:-
Can this fabric be interpreted as an elasticated sheet?
If so, imagine the following...
2 massive entities (for example black holes, as these are said to cause gravitational waves when they collide) rapidly rotating about their barycentre on this 'sheet' would have a certain displacement, x, between the neutral position of the 'sheet', i.e. no mass placed on it, and the barycentre.
When these 2 entities collide, I assume that the displacement, y, of the centre of mass of this new entity on the 'sheet', would be larger than the initial displacement, x, because the 'pressure' exerted on the 'sheet' would be larger owing to the same constant system mass being concentrated on a smaller region of the 'sheet'.
Now, say this collision between the 2 initial massive entities happened 'quickly', this sudden change in displacement would cause the centre of mass, hence the sheet, to oscillate (remember I'm saying that the sheet is elasticated), thus creating ripples that travel across the fabric of spacetime? I.e. gravitational waves.
Is this complete and utter nonsense? If so, can those with wisdom please provide an explanation/analogy of how they are formed? And possibly or if indeed necessary, tell me where my analogy is wrong?
I apologise in advance for the terrible illustrations.