The influencing factors are the basics of fatigue and strength of materials. If you excite a structure's natural frequency, it can take no time at all for that structure to reach its fatigue life. It gets amplified by the fact that the alternating stresses can be quite a bit higher than one would expect at any other operating point. Take a look at a basic S-N diagram to get an idea about this.
[quote="sri.karmarkar]Material fails is it because of lone factor "excitation frequncy reaches more than the natural frequency?". [/quote]
The point to be worried about is when the excitation frequency matches the natural frequency. If you are above or below it, you shouldn't need to worry about it. Even if you do reach the natural frequency, sometimes it's not a big deal due to the design or the system's ability to dmpen vibrations. Still if you are close to the natural frequency, you need to know what the result will be. You can't ignore it. This is why we do things like shaker and modal testing.