ABSTRACT 



Equations are developed for two-dimensional harmonic trans- 

 verse forcing at any point of an undamped uniform beam having 

 bending and shearing flexibilities and for harmonic end forcing 

 of a uniform beam having also external and internal damping. 

 Variations of beam influence and inertia coefficients with fre- 

 quency are discussed for an undamped beam without shear warping. 

 Equations are also developed for the determination of the 

 flutter speed of a rigid hydrofoil flexibly attached to such a 

 beam. The flutter process is illustrated by a detailed discus- 

 sion of two simple cases of flutter. 



1 . INTRODUCTION 



Sea trials of USS FOREST SHERMAN (DD 931) indicated that during a 

 steady horizontal maneuver severe vibrations were transmitted by the 

 rudders to the hull. To anticipate the occurrence of severe vibrations 

 and possible control-surface flutter within the range of ship operating 



speeds , the authors undertook a series of studies of the flutter 



2 

 phenomenon. A theory was advanced for treating the vibration character- 

 istics of a control surface (eug. , rudder or diving plane) hull system 



3* 



subject to hydrodynamic forces on the control surfaces. This theory has 



1 References are listed on page 92. 



* This theory has been applied to USS ALBACORE (AGSS 569) and to the motor 



gunboat PGM. The results for these two cases will be reported 



separately. 



