Free vibration analysis of a rotating beam with nonlinear spring and mass system

2007 ◽  
Vol 301 (1-2) ◽  
pp. 165-188 ◽  
Author(s):  
S.K. Das ◽  
P.C. Ray ◽  
G. Pohit
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Free Vibration Analysis ◽  
Rotating Beam ◽  
Mass System ◽  
Nonlinear Spring

scholarly journals Free Vibrations of a Reddy-Bickford Multi-Span Beam Carrying Multiple Spring-Mass Systems

2011 ◽  
Vol 18 (5) ◽  
pp. 709-726 ◽  
Author(s):  
Yusuf Yesilce
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Free Vibration Analysis ◽  
Beam Theory ◽  
Free Vibrations ◽  
Mode Shapes ◽  
Structural Elements ◽  
Mass System ◽  
Assembly Technique

The structural elements supporting motors or engines are frequently seen in technological applications. The operation of machine may introduce additional dynamic stresses on the beam. It is important, then, to know the natural frequencies of the coupled beam-mass system, in order to obtain a proper design of the structural elements. The literature regarding the free vibration analysis of Bernoulli-Euler and Timoshenko single-span beams carrying a number of spring-mass system and multi-span beams carrying multiple spring-mass systems are plenty, but the free vibration analysis of Reddy-Bickford multi-span beams carrying multiple spring-mass systems has not been investigated by any of the studies in open literature so far. This paper aims at determining the exact solutions for the natural frequencies and mode shapes of Reddy-Bickford beams. The model allows analyzing the influence of the shear effect and spring-mass systems on the dynamic behavior of the beams by using Reddy-Bickford Beam Theory (RBT). The effects of attached spring-mass systems on the free vibration characteristics of the 1–4 span beams are studied. The natural frequencies of Reddy-Bickford single-span and multi-span beams calculated by using the numerical assembly technique and the secant method are compared with the natural frequencies of single-span and multi-span beams calculated by using Timoshenko Beam Theory (TBT); the mode shapes are presented in graphs.

An Exact Solution to the Free Vibration Analysis of a Uniform Timoshenko Beam Using an Analytical Approach

2021 ◽  
Author(s):  
Valentin Fogang
Keyword(s):  
Exact Solution ◽  
Free Vibration ◽  
Closed Form ◽  
Timoshenko Beam ◽  
Vibration Analysis ◽  
Analytical Approach ◽  
Dynamic Stiffness ◽  
Free Vibration Analysis ◽  
Winkler Foundation ◽  
Mass System

This study presents an exact solution to the free vibration analysis of a uniform Timoshenko beam using an analytical approach, a harmonic vibration being assumed. The Timoshenko beam theory covers cases associated with small deflections based on shear deformation and rotary inertia considerations. In this paper, a moment-shear force-circular frequency-curvature relationship was presented. The complete study was based on this relationship and closed-form expressions of efforts and deformations were derived. The free vibration response of single-span systems, as well as that of spring-mass systems, was analyzed; closed-form formulations of matrices expressing the boundary conditions were presented and the natural frequencies were determined by solving the eigenvalue problem. Systems with intermediate mass, spring, or spring-mass system were also analyzed. Furthermore, first-order dynamic stiffness matrices in local coordinates were derived. Finally, second-order analysis of beams resting on an elastic Winkler foundation was conducted. The results obtained in this paper were in good agreement with those of other studies.

Free Vibration Analysis of a Beam Under Axial Load Carrying a Mass-Spring-Mass

2012 ◽  
Author(s):  
O. R. Barry ◽  
Y. Zhu ◽  
J. W. Zu ◽  
D. C. D. Oguamanam
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Axial Load ◽  
Equations Of Motion ◽  
Tensile Load ◽  
Free Vibration Analysis ◽  
Frequency Equation ◽  
Mode Shapes ◽  
Mass System ◽  
Mass Spring

This paper deals with the free vibration analysis of a beam subjected to an axial tensile load with an attached in-span mass-spring-mass system. The equations of motion are derived by means of the Hamilton principle and an explicit expression of the frequency equation is presented. The formulation is validated with results in the literature and the finite element method. Parametric studies are done to investigate the effect of the axial load, the magnitude and location of the mass-spring-mass system on the lowest five natural frequencies and mode shapes. The results indicate that the fundamental mode is independent of the tension and the in-span mass. However, a significant change in all modes is observed when the position of the mass-spring-mass is varied.

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