Krtpiloff, E., "Calculation of Normal Modes and Natural 

 KrcqiKMUMcs of Ship Hulls by Moans of the Electrical 

 Analog," DTMB Report 742,' July 1954. 



The electrical analog for the transverse vibration of a nonuniform 

 beam with botti shear and bending flexibility is reviewed to illustrate 

 the general method of development of such a network. Inasmuch as the 

 dynamics of transverse vibration of a nonuniform beam with shear and 

 bending flexibility are those for the flexural vibration of a ship hull 

 considered as a free continuous, nonuniform beam, the practical applica- 

 tion of the analog is shown by presenting the normal modes of vibratiori 

 of a naval vessel. 



Kennard, E,H., "Forced Vibrations of Beams and the 

 Effecl of Sprung Masses," DTMB Report 955, July 1955. 



Certain aspects of beam vibrations are discussed which throw 

 light upon particular features of ship vibrations. These aspects are: 

 antiresonances and effects of damping in forced vibrations, explicit 

 formulas being given for uniform beams; internal versus external damp- 

 ing; effects of sprung masses on natural frequencies; and forcing 

 functions resulting from sprung masses. 



Leibowitz, Ralph C. and Kennard, E.H., "Theory of 

 Freely Vibrating Nonuniform Beams, Including Methods of 

 Solution and Application to Ships," DTMB Report 1,317, 

 May 1961, 



A comprehensive study; which reviews and extends previous 

 work, was made of the derivation of equations for digital and electrical- 

 analog solutions of the natural frequencies and mode shapes of a ship's 

 hull idealized as an elastic beam. 



Effects of bending, shear, rotary inertia, coupled torsion and 

 bending, initial curvature of the elastic axis, applied forces and torques, 

 sprung masses, and other inertias are included. The calculation of the 

 physical parameters from ship plans is described and the accuracy of 

 results discussed. 



Lewis, F.M,, "Propeller Vibration," SNAME, Vol. 43, 

 p.252, 193.5, 



In 1931 the Council of the SNAME appointed a committee to study 

 the problem of propeller vibration. This paper covers the status of the 

 problem and the work of the committee to date. 



Lewis, F.M., "Propeller Vibration," SNAME, Vol. 44, 

 p.50, 1936. 



This paper is a report of work carried out by the vibration 

 Research Committee of SNAME during 1936. 



Lewis, F.M. and Tachmindji, A.J., "Propeller Forces 

 Exciting Hull Vibration," SNAME, Vol. 62, P.397, 1954. 



This paper deals with the work accomplished under the sponser- 

 ship of Panel «-8 of SNAME. It presents experimental results obtained 

 from models, which include such effects as rpm, axial and tip propeller 

 clearances. Experimental results obtained on full-scale vessels are 

 compared with those obtained from model experiments and the laws of 

 comparison are discussed. 



MathewHon, Alice W., "Calculation of the Normal Verti- 

 cal Flexural Modes of Hull Vibration by the Digital Process, 

 DTMB Report 706, February 1960. 



A method for the calculations of flexural frequencies and normal 

 modes of ship hulls is presented. A comparison of experimental and 

 computed natural frequencies are given for the USS NIAGARA (APA 87). 



McGoldrick, R.T., "Buoyancy Effects on Natural 

 Frequency of Vertical Modes of Hull Vibration," Journal 

 of Ship Research, Vol. 1, No. 2, p. 47, July 1957. 



This paper discusses the inertia and buoyancy effects on the 

 vertical flexural modes of hull vibration. The inertia effects of the 

 surrounding water is known to be very large and are always taken into 

 account in calculating the natural frequencies of hulls; whereas, the 



buoyancy effects are invariably neglected. It is shown that buoyancy 

 effect is negligible for vertical flexural modes except for ships with 

 extremely low fundamental vertical frequencies. 



McGoldrick, R.T. and Kane, J.R., "Longitudinal Vibra- 

 tions of Marine Propulsion Shafting Systems," SNAME, 

 Vol. 57, November 1949. Also DTMB Report 1088, Novem- 

 ber 1956. 



This paper is intended to give methods to facilitate preliminary 

 estimates of the longitudinal critical speeds based upon estimates of 

 some of the system constants, and to indicate the process by which 

 these estimated values may be calculated in more detail as detail draw- 

 ings of foundations, thrust bearing mountings, propeller installations, 

 etc., are made available. 



McGoldrick, R.T., et al., "Recent Developments in the 

 Theory of Ship Vibration," DTMB Report 739, October 

 1953. 



It is shown in this report that by considering the ship hull as a 

 floating beam having shearing and bending flexibility with a distributed 

 viscous damping proportional to mass, it is possible to derive equations 

 of motion under external forces by the general Rayleigh method which 

 yields a solution in terms of normal modes of motion. 



McGoldrick, R.T., "Ship Vibration," DTMB Report 

 1451, December 1960. 



This report presents a general treatment of the subject of ship 

 vibration, including both the structural and hydrodynamic phases, with 

 suggested procedures for dealing with vibration problems in the ship's 

 early design stage. 



Noonan, E.F., *'Mechanical Vibrations of Shipboard 

 Equipment," MIL-STD-167 (SHIPS) December 1954. 



This is the Bureau of Ships approved standard for vibration 

 testing of shipboard equipment and machinery. 



Noonan, E.F., "Tailshaft Bending Stresses on SS ESSO 

 JAMESTOWN," American Society of Naval Engineers, 

 Vol. 73, p.603, August 1961. 



This paper presents part of the results obtained under the 

 research program "Tailshaft Failures" by SNAME. The paper is com- 

 prised of the following sections: 



Section I, Background and Purpose 



Section II, Instrumentation and Calibration 



Section III, Test Results 



Section IV, Harmonic Analysis 



Section V. Phase Relationship 



Section VI, Comparison with Previous Tests 



Section VII, Comparison with Recommended Formulae 



Section VIII, Conclusions and Recommendations 



55 



