I have a customer wanting to put their tumble dryer on top of their washing machine. Rather than plonk it straight on top of the washing machine they want it on it's own shelf, and whilst there is a shelf to make it bigger and useable to one side of it as well in their double width airing cupboard.

What's the best way to make it. I'm thinking along the lines of 2"x2" for the frame with some 18mm ply for the shelf to ensure it's sturdy enough to cope with the vibrations from the tumble dryer and it's weight. I'm planning on using six legs because of the width of the shelf. What kind of joints are best, tenon or half-lap or something else. Would some extra bracing be a good idea?

You'd possibly need to be careful with regard to the span of the worktop/ply. Too wide and it'll most likely sag.

That's why I'm planning on 6 legs for the frame to cope with the wide span. Four legs just for the dryer and an extra two at the other end of the shelf.

i personaly would go along the route andrew suggests trying to picture the exact  scenario

i would use 18mm ply sides if the sides are hidden stop the sides 2 inches away from the wall for access of pipes hosses ect with a batton of 2 by 2 at the top [internal] for the top to sit on between sides and the top
the top 18mm ply  the the full depth to the wall and the same size as the sides outer edge to outer edge
i would also suggest you finnish the top with 2 by 1 on all edges[ except batton underneath  the back to fix to wall] screw the 2x1 on with about 18mm abovethe top to give you a lip to stop the machine vibrating off  also to strenthen the edge and stop the ply edge showing
you could also finnish the font edge of the sides with 1 by 1 or a bit off 2by 1 ripped down the middle

A tumble drier in an airing cupboard?
I hope there is an outside wall to put the vent through.
Otherwise the clothes in there will be soaked most of the time.

With regards to getting the single piece of ply into the cupboard I would do this first.  Measure and cut so it will fit exactly at the height required then put inside the cupboard and temporarily support above the height desired.  This will leave you free to build your frame and just lower the top when completed otherwise it may be impossible to get it in (oo er! )  I learnt this the hard way when building some larder storage.

big-e