Mathematical model analysis for the dynamic design of machinery

Mathematical models are developed for making a dynamic shock and vibration analysis of a turbine generator on a typical shipboard foundation. The motion response is limited to “one direction at a time” at each mass point, which still allows for two shipboard rotational motions that can be superimposed on each translatory input motion. The usual normal-mode analysis without damping is supplemented by an equivalent transient analysis, wherein the identical peak accelerations are produced corresponding to a common “frequency-spectrum” definition of shock effects. The advantage of the latter analysis is that damping, phasing effects with time and nonlinear elements can be included. The net results is a more realistic summation of dynamic stresses than is found by max-on-max normal-mode summations. The principal consideration has been to keep the model analysis simple enough so that design changes and decisions can be checked out prior to ordering materials or machining parts. Hence, the digital-computer program is used as a new tool in experimental mechanics; a tool which is compatible with the “cut-and-try” philosophy for designing machinery.