Orthogonal Bases for Eigenvalue Sensitivities—Torsional Vibration

1995 ◽  
Author(s):  
S. A. Nayfeh ◽  
H. Asada
Keyword(s):  
Boundary Conditions ◽  
Natural Frequency ◽  
Torsional Vibration ◽  
Natural Frequencies ◽  
General Boundary ◽  
General Boundary Conditions ◽  
Orthogonal Bases ◽  
Design Changes

Abstract The sensitivity of the natural frequencies of torsional vibration of an initially uniform shaft to nonuniform changes in its radius is studied. For the particular example of a fixed-fixed shaft, a set of design changes are found that modify a single natural frequency without modifying any of the others. The possibility of finding such a set of design changes for general boundary conditions is then investigated, and conditions for the existence of such a set are determined.

scholarly journals A Unified Approach of Free Vibration Analysis for Stiffened Cylindrical Shell with General Boundary Conditions

2019 ◽  
Vol 2019 ◽  
pp. 1-14 ◽  
Author(s):  
Xue-Qin Li ◽  
Wei Zhang ◽  
Xiao-Dong Yang ◽  
Lu-Kai Song
Keyword(s):  
Cylindrical Shell ◽  
Free Vibration ◽  
Boundary Conditions ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Free Vibration Analysis ◽  
General Boundary ◽  
General Boundary Conditions ◽  
Unified Approach ◽  
Stiffened Cylindrical Shell

A unified approach of free vibration analysis for stiffened cylindrical shell with general boundary conditions is presented in this paper. The vibration of stiffened cylindrical shell is modeled mathematically involving the first-order shear deformation shell theory. The improved Fourier series is selected as the admissible displacement function while the arbitrary boundary conditions are simulated by adjusting the equivalent spring stiffness. The natural frequencies and modal shapes of the stiffened shell are obtained by solving the dynamic model with the Rayleigh-Ritz procedure. Various numerical results of free vibration analysis for stiffened cylindrical shell are obtained, including natural frequencies and modes under simply supported, free, and clamped boundary conditions. Moreover, the effects of stiffener on natural frequencies are discussed. Compared with several state-of-the-art methods, the feasibility and validity of the proposed method are verified.

Natural Frequencies and Normal Modes for Externally Damped Spinning Timoshenko Beams With General Boundary Conditions

1998 ◽  
Vol 65 (3) ◽  
pp. 770-772 ◽  
Author(s):  
J. W. Zu ◽  
J. Melanson
Keyword(s):  
Boundary Conditions ◽  
Natural Frequencies ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Normal Modes ◽  
General Boundary ◽  
Mode Shapes ◽  
General Boundary Conditions ◽  
Timoshenko Beams ◽  
Classical Boundary

Vibration analysis of externally damped spinning Timoshenko beams with general boundary conditions is performed analytically. Exact solutions for natural frequencies and normal modes for the six classical boundary conditions are derived for the first time. In the numerical simulations, the trend between the complex frequencies and the damping coefficient is investigated, and complex mode shapes are presented in three-dimensional space.

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