I will come with my input.
I do not own and did not owned any commercial antenna !
According to my - our (+OK1RF) experience the problem of vibrations of the
tips of elements is a MAJOR and MAGICAL problem.
We do maintain over last 30 years an antenna farm. Right now we do have
there 87 only full size elements on 40 - 10m.
To begin with I am always ready accept my-our design is bad - as would Jan -
SM2EKM say. Please give us smart advice.
We have never ever had a problem of vibration of the tips with 15m. We have
some thin and thick elements there never ever have had a problem. We have
lost probably 6-10 times tips on 20m - low antenna - in 24m. We have never
ever lost tip on our high 20m antenna which was in the period of time in 42,
48 now 52m. Both elements vere more-less same design.
We have never lost tips on 40m full size elements.
(I do not count here losses due to heavy icing - only twice in history)
WE HAVE LOST during last 20 years more than 40 tips on 10m. We have had
various designs, stepping, material... We have used plain elements, closed
tips, end of tips with some weight- screw... open tips, ropes inside, even
Copper stranded conductor in PVC (better experience compared to rope inside
since it is less susceptible to ice and is heavier than the ROPE).
We have found that the vibration is biggest during a small breeze. It is
usually not so bad during big winds which we do get.
We have found that the mechanical resonance or with other words vibration is
HIGHLY influenced by the behavior of the tower. If the tower is "soft" -
i.e. it tends to vibrate in the wind - the winds vibrates the antenna - the
antenna moves the tower and the tower drives back the antenna - those
effects get usually worse but can be also BETTER ?!.
We have found that if the tip is made of very hard ALUMINUM it gets usually
worse - it is better to have the tips from softer material
We have found that if the tip is "too" short the probability it will fail is
bigger - I am not sure but I guess it is the frequency of mechanical self
resonance of the tip - the longer it is the slower it vibrates.
I have bought "smart" book of Jim Leeson about mechanical design of Yagi
antennas in plain hope that this - according to our experience biggest
construction problem - will be somehow scientifically cleared out. After 150
pages full of mathematical equations he finally writes something like: There
is often observed a problem of vibration on the tips. Do something with it -
experiment - use rope, wire, weight in the tips etc.
I doubt there is a possibility of analytical always valid solution to this
major and very unpleasant problem since too many things are involved.