Longitudinal free vibration of inhomogeneous elastic straight strut with a variable cross section

1980 ◽  
Vol 1 (2) ◽  
pp. 149-157 ◽  
Author(s):  
Liu Shien-chih
Keyword(s):  
Free Vibration ◽  
Cross Section ◽  
Variable Cross Section ◽  
Variable Cross

scholarly journals Flexural Free Vibrations of Multistep Nonuniform Beams

2016 ◽  
Vol 2016 ◽  
pp. 1-12
Author(s):  
Guojin Tan ◽  
Wensheng Wang ◽  
Yubo Jiao
Keyword(s):  
Differential Equation ◽  
Free Vibration ◽  
Cross Section ◽  
Order Differential Equation ◽  
Variable Cross Section ◽  
Free Vibrations ◽  
Variable Cross ◽  
Exact Approach ◽  
Constant Coefficients ◽  
One Step

This paper presents an exact approach to investigate the flexural free vibrations of multistep nonuniform beams. Firstly, one-step beam with moment of inertia and mass per unit length varying as I(x)=α11+βxr+4 and m(x)=α21+βxr was studied. By using appropriate transformations, the differential equation for flexural free vibration of one-step beam with variable cross section is reduced to a four-order differential equation with constant coefficients. According to different types of roots for the characteristic equation of four-order differential equation with constant coefficients, two kinds of modal shape functions are obtained, and the general solutions for flexural free vibration of one-step beam with variable cross section are presented. An exact approach to solve the natural frequencies and modal shapes of multistep beam with variable cross section is presented by using transfer matrix method, the exact general solutions of one-step beam, and iterative method. Numerical examples reveal that the calculated frequencies and modal shapes are in good agreement with the finite element method (FEM), which demonstrates the solutions of present method are exact ones.

Free vibration analysis of a variable cross-section column partially immersed in a liquid

2013 ◽  
Vol 72 ◽  
pp. 160-166 ◽  
Author(s):  
M.A. De Rosa ◽  
M. Lippiello ◽  
F. Vairo ◽  
M.J. Maurizi
Keyword(s):  
Free Vibration ◽  
Cross Section ◽  
Vibration Analysis ◽  
Free Vibration Analysis ◽  
Variable Cross Section ◽  
Variable Cross
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