Steady State and Free Vibration Analysis of a 3D Rotating Euler Beam with Arbitrary Setting Angle

2016 ◽  
Vol 2016.8 (0) ◽  
pp. 15_1288834
Author(s):  
C. C. Huang ◽  
W. Y. Lin ◽  
K. M. Hsiao
Keyword(s):  
Steady State ◽  
Free Vibration ◽  
Vibration Analysis ◽  
Free Vibration Analysis ◽  
Euler Beam ◽  
Setting Angle

An Analytical Solution for Free Vibration of Piezoelectric Nanobeams Based on a Nonlocal Elasticity Theory

2015 ◽  
Vol 32 (2) ◽  
pp. 143-151 ◽  
Author(s):  
A. A. Jandaghian ◽  
O. Rahmani
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Nonlocal Parameter ◽  
Free Vibration Analysis ◽  
Nonlocal Elasticity Theory ◽  
Nonlocal Theory ◽  
Beam Model ◽  
Euler Beam ◽  
Charge Condition ◽  
Thin Beam

ABSTRACTIn the present study, an exact solution for free vibration analysis of piezoelectric nanobeams based on the nonlocal theory is obtained. The Euler beam model for a long and thin beam structure is employed, together with the electric potential satisfying the surface free charge condition for free vibration analysis. The governing equations and the boundary conditions are derived using Hamilton's principle. These equations are solved analytically for the vibration frequencies of beams with various end conditions. The model has been verified with the previously published works and found a good agreement with them. A detailed parametric study is conducted to discuss the influences of the nonlocal parameter, on the vibration characteristics of piezoelectric nanobeams. The exact vibration solutions should serve as benchmark results for verifying numerically obtained solutions based on other beam models and solution techniques.

scholarly journals The Effect of Axial Force on the Free Vibration of an Euler-Bernoulli Beam Carrying a Number of Various Concentrated Elements

2013 ◽  
Vol 20 (3) ◽  
pp. 357-367 ◽  
Author(s):  
Gürkan Şcedilakar
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Axial Load ◽  
Natural Frequencies ◽  
Free Vibration Analysis ◽  
Mode Shapes ◽  
The Finite Element Method ◽  
Bernoulli Beam ◽  
Euler Beam ◽  
Euler Bernoulli Beam

In this study, free vibration analysis of beams carrying a number of various concentrated elements including point masses, rotary inertias, linear springs, rotational springs and spring-mass systems subjected to the axial load was performed. All analyses were performed using an Euler beam assumption and the Finite Element Method. The beam used in the analyses is accepted as pinned-pinned. The axial load applied to the beam from the free ends is either compressive or tensile. The effects of parameters such as the number of spring-mass systems on the beam, their locations and the axial load on the natural frequencies were investigated. The mode shapes of beams under axial load were also obtained.

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