The breakthroughs for the large double row radial came around 1939 for P&W and 1941 for Wright. It was all slide rule and trial and error. For the R2800, P&W broke many engines on the test stands trying to solve vibration with damper designs, rod design changes, forging techniques, bearing changes, machining changes and material changes. By the time the produced a production engine, vibration was within spec and the production changes improved longevity. The R2800's reputation for reliability speaks for itself.
In terms of vibration, the development of the R4360 was less troublesome (4 rows of 7 cylinders) than the R2800 (2 rows of nine). However, the R4360 did break crankshafts during testing due to resonance issues within the crankshaft. P&W solved the problem by strategically adding and removing metal from various locations along the crankshaft's length.
Both P&W and Wright had issues with development of their respective 18 cylinder two row radials due to vibration. But both were able to solve the vibration issues to produce two engines (P&W R2800 and Wright R3350) that would eventually demonstrate the full potential of the radial engine.
-Old Ag