This thread seems to be for pre-'72 340s, as opposed to another similar one that is '72 up.

I removed my '69 340 vibration dampener recently and found the rubber inlay to be in bad shape. The 273, 318, and 340 all got the same dampener made with a cast iron hub and an outer cast iron circle with a rubber layer between. According to this link,

http://www.hbrepair.com/harmonic_balancer_001.htm

the purpose of a harmonic balancer or vibration dampener is to limit the amount of crankshaft twisting caused by power strokes.

I found 2 vendors that will renew the rubber inlay:

www.damperdoctor.com

www.hbrepair.com