Master formula for evaluating vibration frequencies of structural members under compressive loads.

In this article, the prediction of free vibration characteristics of various initially compressively loaded structural members is given in the form of a master formula. These structural members are optimised for the strength criteria and are subjected to high initial compressive loads (or stresses). These initial compressive loads have to be considered when the free vibration characteristics are evaluated. The standard method is to solve the differential equation considering the term corresponding to these loads. Though this is possible for simple structural members, it is often difficult while dealing with complex structural members with complicated effects. Under these circumstances, the popular approximate continuum and numerical methods like the Rayleigh-Ritz and finite element methods are used to obtain reliable and accurate solutions to the initially loaded free vibration characteristics of these structural members. However, these approximate methods are also having their inherent difficulties. To avoid this, a simple but accurate formula is developed, which is very useful for the design engineers while dealing with structural members used in missiles and rockets. The use of master formula for the first mode and also higher modes of vibration has been shown for typical structural members. [ABSTRACT FROM AUTHOR]