having motion in translation, rotation, or coupled translation and rotation. Analytical, 

 electric-analog and digital computer methods have been devised to determine the natural fre- 

 quencies and mode shapes of beam-sprung-inertia systems. The results of these studies are 

 given in TMB Reports 955, 1215, 1317, 1507, and 1540. 



D. STUDY OF SIGNIFICANT PARAMETERS 



To determine the normal mode frequencies and mode shapes of a particular ship it is 

 necessary to evaluate the physical parameters of each section of the ship for use in the 

 finite difference equations. For the general case of coupled torsion-horizontal bending 

 vibrations, methods for manually computing these parameters from ship plans and other in- 

 formation have been devised and reported in TMB 1317. For steady forced vibrations, the 

 mathematical representation of hull damping is based upon experimental results and is re- 

 ported in TMB Reports 1060 and 1451. An example of its application in calculations of hull 

 response is given in TMB Report 1384. As an alternative to using a constant value of ; cor- 

 responding to the two-noded mode, a method has been developed which will allow for a dif- 

 ferent / factor for each mode and is reported in TMB Reports 1317 and 1623. The need for 

 the development of methods which will give more accurate parameter values for the bending 

 shear and torsional rigidities as well as the virtual mass still persists. A method which 

 uses a digital computer to calculate the hull parameters from basic data tabulations obtained 

 from ship plans in accordance with a preestablished systematized procedure is being devised 

 to reduce the labor, expense, etc. of making such calculations. 



II. INFLUENCE OF OTHER SHIP STRUCTURES ON HULL STRUCTURAL RESPONSE 



A. MACHINERY-INDUCED VIBRATION 



It is obvious that the propeller, as a machinery item, is probably the major contributor 

 to the steady-state vibration of a ship. The TMB program on propeller-excited vibratory 

 forces is described in Section III. This section will deal with machinery-induced vibration 

 except that introduced by the ship propellers directly. 



The major cyclic forces which may stimulate the ship hull are associated with the 

 main propulsion system and result from cyclic forces which may or may not reflect conditions 

 of resonance. These forces may be associated with excitation originating within the machin- 

 ery system or with excitation corresponding with propeller blade frequencies or harmonics of 

 it. Of course the presence of machinery resonance and the tuning of such resonance with a 

 natural frequency of the hull may result in very severe and often damaging vibration. For 

 convenience, we can classify machinery-induced vibration as longitudinal, rotational, or 

 lateral. 



