Vibration therapy studies have been conducted for over 10 years. In this kind of therapy a person stand on a platform that vibrates rapidly so that their body does also. Proponents of this therapy claim that the rapid vibration induces stress on the bones and the osteoblast cells (bone building cells) respond with greater activity - this increasing bone density.
On the other side, critics state the whole body vibration is a health risk for many persons with chronic conditions such as cardiovascular and that used too often or too long, it can cause damage to the spine.
There are several commercial models of machines that will vibrate your body. Some are used for physiotherapy; others for training.
The physiotherapy whole body vibration includes stretches and/or massages while you are in light contact with the machine. The most frequent position is to stand upright, lock-legged on a pivotal or low energy lineal machine.
Those who use body vibration machines for work out training, assume various positions while on the machine - thus exercising specific muscles.
It is the first of these, standing on a vibrating machine that has been advocated by some for increasing bone density.
In 2013, three researchers from Stonybrook University (M. Ete Chan, Gunes Uzer, and Clinton T. Rubin) published a study documenting both positive and negatives effects of vibration therapy. Among the positive outcomes for potential bone building was that "Exceedingly low magnitude mechanical signals, delivered using low intensity vibration (less than 1 g) may ultimately represent a safe and effective non-drug-based strategy for the treatment of osteoporosis"
At the same time these researchers state that " high intensity vibration (greater than 1g) can cause permanent damage to a range of physiologic systems, and must be avoided, particularly in the elderly, injured or infirm."
At last we may have an understanding of why for so long, researchers disagreed so strongly about the potential effectiveness and/or dangers of whole body vibration therapy for persons hoping to increase bone density.
An excellent article has been published by some Stonybrook University researchers about this form of therapy (The article is in pdf format) and you can read it here: Potential Dangers of Vibration therapy
Given the mixed reviews by researchers, I hope that you will consult with your health care provider before trying this from of exercise to improve your bone density.