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http://dx.doi.org/10.12989/sem.2016.59.6.1139

Effects of deformation of elastic constraints on free vibration characteristics of cantilever Bernoulli-Euler beams  

Wang, Tong (College of Civil Engineering, Shanghai Normal University)
He, Tao (College of Civil Engineering, Shanghai Normal University)
Li, Hongjing (College of Civil Engineering, Nanjing Tech University)
Publication Information
Structural Engineering and Mechanics / v.59, no.6, 2016 , pp. 1139-1153 More about this Journal
Abstract
Elastic constraints are usually simplified as "spring forces" exerted on beam ends without considering the "spring deformation". The partial differential equation governing the free vibrations of a cantilever Bernoulli-Euler beam considering the deformation of elastic constraints is firstly established, and is nondimensionalized to obtain two dimensionless factors, $k_v$ and $k_r$, describing the effects of elastically vertical and rotational end constraints, respectively. Then the frequency equation for the above Bernoulli-Euler beam model is derived using the method of separation of variables. A numerical analysis method is proposed to solve the transcendental frequency equation for the continuous change of the frequency with $k_v$ and $k_r$. Then the mode shape functions are given. Finally, effects of $k_v$ and $k_r$ on free vibration characteristics of the beam with different slenderness ratios are calculated and analyzed. The results indicate that the effects of $k_v$ are larger on higher-order free vibration characteristics than on lower-order ones, and the impact strength decreases with slenderness ratio. Under a relatively larger slenderness ratio, the effects of $k_v$ can be neglected for the fundamental frequency characteristics, while cannot for higher-order ones. However, the effects of $k_r$ are large on both higher- and lower-order free vibration characteristics, and cannot be neglected no matter the slenderness ratio is large or small.
Keywords
deformation; elastic constraint; free vibration characteristic; cantilever beam; Bernoulli-Euler beam; frequency equation; mode shape function;
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Times Cited By KSCI : 3  (Citation Analysis)
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