702 MECHANICAL DESIGN AND PACKAGING 



vibrations, the principles of mechanical response, and the fatigue charac- 

 teristics of the contemplated materials. It has been shown above that the 

 most damaging structural effects from vibration occur at the various 

 resonant frequencies of the equipment. These frequencies can often be 

 calculated for simple designs; but in the later stages of equipment develop- 

 ment they are usually determined by the observation of a prototype on a 

 vibration testing machine. 



If the frequencies of environmental vibration are known to lie within 

 certain narrow bands, damage will be avoided by the obvious technique of 

 designing equipment all of whose resonant frequencies lie well outside of 

 these known bands. Unfortunately, this approach is not feasible for 

 random vibration or for wide ranges of sinusoidal frequencies. In such 

 cases, the maximum accelerations to which components and parts are 

 subjected can be limited only by the environment, the ^'s of the various 

 modes, and, for random excitation, the frequencies of the natural modes. 

 It is rarely possible for the designer to exercise much control over the ^'s 

 in electronic packages. He is thus left with the alternatives of designing 

 equipment which can operate reliably in spite of resonant vibration or of 

 protecting the equipment from its environment by means of vibration 

 isolators. 



In packaging for vibration, therefore, certain principles must govern the 

 detail design. Every attempt should be rhade to have all natural frequencies 

 as high as possible, even though the acceleration of a system may be 

 somewhat more violent at higher frequencies. This course is justified by 

 the relation between amplitude and frequency. As frequency increases, 

 the amplitude of a vibration with given acceleration decreases rapidly. The 

 corresponding stress, proportional to amplitude of vibration, will decrease 

 similarly. A second principle is design for efficient storage of energy. For 

 example, every member subject to stress should be efficiently proportioned 

 to give a uniform maximum stress level. All sources of stress concentration 

 should be eliminated, where possible. These procedures contribute to 

 efficient storage of energy under shock as well as vibration. 



An aircraft radar may experience shock, especially in its shipment and 

 handling prior to installation, during ordinary and arrested landings, during 

 catapult takeoffs, and in the form of blast when in action. Shock failures 

 may be brittle-state fractures caused by immediate impact, or they may be 

 low-cycle fatigue failures caused by the brief but severe vibration which 

 follows the first impulse of a shock. Shock can also hasten the complete 

 failure of parts in which fatigue cracks have previously formed. It is 

 believed that a shock of magnitude insufficient to cause total failure could 

 initiate unnoticed cracks which would cause stress concentration, reducing 

 the fatigue strength of the part. 



The design techniques which tend to give equipment reliability in an 



