Drum heads are attached to the shell using so-called hoops. They are tightened, and thus tuned, using tension rods, which have their counterparts, the lugs, along the side of the shell. The more lugs there are, the more precisely and balanced your drum head can be tuned. One very important aspect in this method of tuning is that the screws and nuts remain securely in place even after extended energetic drumming - otherwise, things will begin to rattle very quickly! And drummers certainly do not appreciate having to take their drum sets apart repeatedly just to tighten some screws. Nylon inserts in the lugs of modern sets ensure that the tension rods remain as they are supposed to, thus guaranteeing professional operation free of unwanted noises.
On their continued search for ever-better hardware, many manufacturers have begun to use just a single screw to fix the lugs to the shell, allowing for even more resonance in the drum. After all, if you look at it closely, every hole in the shell is a hole too many!
Die cast hoops are usually thicker and more stable than triple flange hoops and as such they aid in very even tightening/tuning. As a result, the drum heads respond very well over a broad tuning range and deliver balanced overtones. But the greater weight of die cast hoops can affect the resonance particularly of smaller shells.
The different materials used to manufacture the die cast hoops (e.g. nickel or aluminium) may also change the sound of the shell.
Triple flange hoops are made from a wide variety of metal alloys, which in turn affects the sound character of the shell. Many drummers prefer the lighter-weight triple flange hoops, as they make for thicker/warmer tuning than the die cast hoops. Aluminium triple flange hoops deliver a higher, more present sound than steel hoops and are very popular on snares, therefore. Brass triple flange hoops make the shell sound more musical and deliver pleasant and balanced overtones.
Depending on material thickness, wood hoops can be as rigid as die cast hoops or be reminiscent of triple flange hoops in their sound. The actual difference to metal hoops is in the rim shot sound. wood hoops basically work like an extension of the wooden shell and deliver sonorous and brilliant rim shots.
Just like the lugs, the mounting system and mounts themselves must be fastened to the shell somehow. and the rule applies here, too: every hole drilled is a hole too many, and every lump of metal attached to the drum changes its sound characteristics. In order to avoid this, manufacturers have become very creative and come up with quite a box of tricks: There's Yamaha, for example. While their inspired YESS mounting system is fastened to the shell, it uses so-called nodal points, which are areas where the shell resonates less and where the mounting fixtures have very little effect. Second point: the actual clamps are made of metal, but as small as possible. Of course, the system must still guarantee optimum stability and on-the-road usability in spite of the objective of affecting the shell vibration as little as possible.
The floor tom clamps, too, are very small with modern drum sets, and require very little contact with the shell. But they still manage to secure the legs adequately without negatively impacting the shell vibration.
But there are also some manufacturers who are working with free-floating mounting systems which do entirely without shell contact. Pearl has baptized its system the OptiMount Suspension System. The fasteners are fixed to the tuning rods, and their rubber sleeves ensure that the parts are securely connected without the vibrations being negatively affected.
As we have already mentioned: nowadays, all manufacturers offer their own hard ware mounting system. But they all share the same goal: minimising the hardware's influence on the shell vibrations and the sustain. You'd best look at the manufacturers' websites to find out what system the drum set of your choice comes with!