Benefit-Function of Two- Identical Cold Standby System subject to Failure due to Natural Frequency Resonance causes catastrophic failures or Failure due to fatigue

Abstract

-Natural Frequency Resonance -Recipe for Failure. All objects in the universe resonate at their natural frequency when excited. This can cause catastrophic failures in structures, machines, and components. This is relevant in a power plant scenario also. "The principle cannot fail. It is as powerful when applied to the earth as it is when applied to a [violin note shattering a] wineglass, a [boy pushing a man on a] swing, or a steel link. Anyone who doubts should only bear in mind the illustration of the swing. A small boy, by each time adding a pound to the force with which a 200-pound man swings, can soon set the man swinging with the force of 500 pounds. It is necessary only to keep adding a little force at the right time." Nikola Tesla – the master of resonance.  Every object depending on its mass and stiffness when excited vibrates at its natural frequency. Watches, musical instruments, microwave ovens, mobile phones and many other devices in our day-to-day life make use of this phenomenon. However, there is an undesirable side to these vibrations that can lead to the failure of structures and components. This failure mode, resonance failures, is equally applicable to large structures and small machine parts alike. Not only bridges, towers and skyscrapers, but also blades, bearings, piping and fasteners can fail due to resonance. Air and gas vapor columns can also resonate at their natural frequencies, in the same way that percussion instruments work, and this can lead to failures.  The war cries and the pounding of foot of marauding armies in history aimed at the destruction of the enemy’s defenses by the principle of resonance. The Biblical myth of the Fall of the Walls of Jericho (Joshua 6:3-5) seems to assert this fact.  Large towers and buildings swaying during an earthquake can fail if the swaying coincides with the natural frequency of the structure. Architects consider this while designing these buildings. The Taipei 101, one the tallest building in the world, has a 660 Ton pendulum acting as mass damper to cancel any resonance. In this paper we have taken Failure due to Natural Frequency Resonance causes catastrophic failures or fatigue failure. When the main unit fails due to Failure due to Natural Frequency Resonance then cold standby system becomes operative. Failure due to Natural Frequency Resonance cannot occur simultaneously in both the units and after failure the unit undergoes very costly repair facility immediately. Applying the regenerative point technique with renewal process theory the various reliability parameters MTSF, Availability, Busy period,