PART ONE 

 TMB Hull Vibration Program 



I. HULL STRUCTURAL RESPONSE (PRIMARY HULL GIRDER) 



A. DEVELOPMENT OF HULL VIBRATION THEORY IN FLEXURE AND TORSION 



A comprehensive study reviewing and extending previous wori< was made of the deri- 

 vation of equations for digital and electric-analog solution of the natural frequencies and 

 mode shapes of a ship hull idealized as an elastic beam. 



Effects of bending, shear, rotary inertia, coupled torsion and bending, initial curva- 

 ture of the elastic axes, applied forces and torques, sprung masses, and other sprung iner- 

 tias are included. Methods for manually calculating the physical parameters of the hull from 

 ship plans and other sources have also been treated. The accuracy of the results obtained 

 by these methods for uniform and nonuniform beams has also been determined. The results 

 of this study were reported in TMB Report 1317. A more general three-dimensional approach 

 to ship vibration is also being studied. 



B. DEVELOPMENT OF COMPUTER AND MODEL TECHNIQUES 



Electrical analog circuitry and digital computer codes incorporating all of the preced- 

 ing effects have been devised and reported in TMB Report 1317. The analog circuitry is set 

 up on the Structural Mechanics Laboratory Analog Computing Facility, called TMB Network 

 Analyzer, which is described in TMB Report 1272. Extensive improvements recently made 

 on the analyzer increase the ease and flexibility of operation as well as the speed of analy- 

 sis. Control and analysis features include manual and automatic scanning of each of the 

 48 stations (positions) on the analyzer patch board selection so that these stations may be 

 scanned in any desired order, instantaneous visual electronic display of the selected sta- 

 tions on a 17-inch scope, automatic digitizing, and print out data together with simultaneous 

 point-by-point graphing of the data on a 17-inch scale. In addition, 10 active analog com- 

 puter amplifier channels have been installed. These may be incorporated in the analyzer 

 circuitry to simulate active systems, generate specialized forcing functions, or perform spe- 

 cial analysis of data. 



C. INFLUENCE OF SPRUNG MASS ON HULL VIBRATION THEORY 



On certain classes of ships, flexibly mounted masses such as machinery, rudders, 

 cargo, and superstructures affect hull vibrations. Therefore, to explore the possibility of a 

 more adequate representation of a ship hull as a mass-elastic system subject to vibration, 

 studies have been made to investigate the characteristics of a beam with attached inertias 



