Loud buzzing noise in iPhone 6 while vibrating

I do not know whether this is a problem or it is a kind of common issue with all iPhone 6. Whenever the device vibrate is generate a annoying loud buzzing noise. The same issue I had seen in iPhone 4S before. But in iPhone 5S this was not present. Now I am getting it back in iPhone 6. I keep the phone on vibration when I am in meeting or sleeping. I keep the phone on a desk. When it vibrate it just create a very loud buzzing noise. And it is disturbing. I do not want to keep the phone on silent because then I will not get notified about upcoming calls. Is there a way to reduce the intensity of this buzzing sound. Through settings or through some app.

I am also dealing with the same kind of problem. It gets annoying when you keep the phone the surface. I am not able to find any settings for reducing the vibration power. Most of the time I keep my handkerchief below the phone so that it does not annoy others. I found a nice plastic case of the device. After adding that the intensity is lower. But still it is sometime disturbing. I am trying to find another case that can reduce the same a lot. I think if we use something made of rubber, the vibration will get lower. Apple must have taken care of this. It looks like I am having a very old Nokia phone which buzz like this on vibration.

I had turned off vibration because of this problem. Most of the time when the phone vibrate it catch others attention. So I turned that off completely. Before switching this off I had tried almost everything but it does not work. I create a separate profile in my phone as busy. And here I had kept the phone ring volume to lowest. Whenever there is a call it rings in very low volume. So if people are talking they are not disturbed. And I can receive or reject it as per my need. The silent button of iPhone 6 is also not proper. Sometime when I use to that to silent my phone it gets stuck on that part forever. I have to restart the phone to make it normal.