Bought new early July this year. Now less than 4 hours of use since new. It has always done it.
Th 1-cylinder fires once per 720 degrees of crankshaft rotation. 525 cc of displacement, 18.5 hp. The 24 hp 2-cylinder on the previous mower is 725 cc of displacement and fires once per every 360 degrees of crankshaft rotation. So the one big cylinder firing makes much more "shaking" than do the 2 smaller cylinders firing essentially twice as often.
Being new, the mowing deck belts are stiffer than belts with more use.
And perhaps my perception of the vibration differs from that of others.
I am trying to repair my older mower as I like it much better.
It's true that a single cylinder motor will tend to have more vibration, this is not just small motors but observed in 3 cyl, 5 cyl too. The auto manufacturers tend to add more motor mount absorbing bushings and sub frame to monocoque chassis isolation, to control vibration inherent in these motors, it's not bad just a way of dealing with it (I've built a Volvo "white Block" 5 cyl turbo motor, interesting project).
The small engines will have their idles set higher to counter some of this vibration.
I do think there can be expectation differences too, but if the motor is vibrating seriously, it could be a sign of something internal, and of course new doesn't necessarily rule out a "Friday" late in the shift assembly.
My 17.5 hp motor has servived teenagers and weather, and such with extra yard trailer use, prior to my GT. I'm not going to say it's perfect, but it has been reasonably reliable and sufficient in power. I would encourage you to at least take it back to Lowes and get it checked.
Also, before giving up, I would try and find a Dealer that will let you try one as a comparison, and see if it vibrates too in the same way.
Just a thought.