Vibration of Steel–Concrete Composite Beams Using the Timoshenko Beam Model

2005 ◽  
Vol 11 (6) ◽  
pp. 829-848 ◽  
Author(s):  
Stefan Berczyński ◽  
Tomasz Wróblewski
Keyword(s):  
Dynamic Behavior ◽  
Timoshenko Beam ◽  
Beam Theory ◽  
Composite Beams ◽  
Free Vibrations ◽  
Timoshenko Beam Theory ◽  
Analytical Models ◽  
Beam Model ◽  
Euler Beam ◽  
Flexural Vibrations

In this paper we present a solution of the problem of free vibrations of steel–concrete composite beams. Three analytical models describing the dynamic behavior of this type of constructions have been formulated: two of these are based on Euler beam theory, and one on Timoshenko beam theory. All three models have been used to analyze the steel–concrete composite beam researched by others. We also give a comparison of the results obtained from the models with the results determined experimentally. The model based on Timoshenko beam theory describes in the best way the dynamic behavior of this type of construction. The results obtained on the basis of the Timoshenko beam theory model achieve the highest conformity with the experimental results, both for higher and lower modes of flexural vibrations of the beam. Because the frequencies of higher modes of flexural vibrations prove to be highly sensitive to damage occurring in the constructions, this model may be used to detect any damage taking place in such constructions.

A New Methodology for Modeling and Free Vibrations Analysis of Rotating Shaft Based on the Timoshenko Beam Theory

2016 ◽  
Vol 138 (2) ◽  
Author(s):  
S. H. Mirtalaie ◽  
M. A. Hajabasi
Keyword(s):  
Free Vibration ◽  
Cross Section ◽  
Timoshenko Beam ◽  
Variable Coefficient ◽  
Slenderness Ratio ◽  
Beam Theory ◽  
Free Vibrations ◽  
Timoshenko Beam Theory ◽  
Euler Angles ◽  
Shear Deformations

The linear lateral free vibration analysis of the rotor is performed based on a new insight on the Timoshenko beam theory. Rotary inertia, gyroscopic effects, and shear deformations are included, but the torsion is neglected and a new dynamic model is presented. It is shown that if the total rotation angle of the beam cross section is considered as one of the degrees-of-freedom of the Timoshenko rotor, as is common in the literature, some terms are missing in the modeling of the global dynamics of the system. The total deflection of the beam cross section is divided into two steps, first the Euler angles relations are employed to establish the curved geometry of the beam due to the elastic deformation of the beam centerline and then the shear deformations was superposed on it. As a result of this methodology and the mutual interaction of shear and Euler angles some variable coefficient terms appeared in the kinetic energy of the system which makes the problem be classified as the parametrically excited systems. A linear coupled variable coefficient system of differential equations is derived while the variable coefficient terms have been missing in all previous studies in the literature. The free vibration behavior of parametrically excited system is investigated by perturbation method and compared with the common Rayleigh, Timoshenko, and higher-order shear deformable spinning beam models in the rotordynamics. The effects of rotating speed and slenderness ratio are studied on the forward and backward natural frequencies and the critical speeds of the system are examined. The study demonstrates that the shear and Euler angles interaction affects the high-frequency free vibrations behavior of the spinning beam especially for higher slenderness ratio and rotating speeds of the rotor.

Estimation of damping in riveted short cantilever beams

2020 ◽  
Vol 26 (23-24) ◽  
pp. 2163-2173
Author(s):  
Yemineni Siva Sankara Rao ◽  
Kutchibotla Mallikarjuna Rao ◽  
V V Subba Rao
Keyword(s):  
Timoshenko Beam ◽  
Damping Ratio ◽  
Beam Theory ◽  
Timoshenko Beam Theory ◽  
Analytical Models ◽  
Cantilever Beams ◽  
Bernoulli Beam ◽  
Bernoulli Beam Theory ◽  
Half Power ◽  
Euler Bernoulli Beam

In layered and riveted structures, vibration damping happens because of a micro slip that occurs because of a relative motion at the common interfaces of the respective jointed layers. Other parameters that influence the damping mechanism in layered and riveted beams are the amplitude of initial excitation, overall length of the beam, rivet diameter, overall beam thickness, and many layers. In this investigation, using the analytical models such as the Euler–Bernoulli beam theory and Timoshenko beam theory and half-power bandwidth method, the free transverse vibration analysis of layered and riveted short cantilever beams is carried out for observing the damping mechanism by estimating the damping ratio, and the obtained results from the Euler–Bernoulli beam theory and Timoshenko beam theory analytical models are validated by the half-power bandwidth method. Although the Euler–Bernoulli beam model overestimates the damping ratio value by a very less fraction, both the models can be used to evaluate damping for short riveted cantilever beams along with the half-power bandwidth method.

scholarly journals Beam Theory of Thermal–Electro-Mechanical Coupling for Single-Wall Carbon Nanotubes

Nanomaterials ◽  
2021 ◽  
Vol 11 (4) ◽  
pp. 923
Author(s):  
Kun Huang ◽  
Ji Yao
Keyword(s):  
Mechanical Properties ◽  
Carbon Nanotubes ◽  
Beam Theory ◽  
Bending Stiffness ◽  
Single Wall Carbon Nanotubes ◽  
Beam Model ◽  
Euler Beam ◽  
New Model ◽  
Mechanical Coupling ◽  
Electrostatic Fields

The potential application field of single-walled carbon nanotubes (SWCNTs) is immense, due to their remarkable mechanical and electrical properties. However, their mechanical properties under combined physical fields have not attracted researchers’ attention. For the first time, the present paper proposes beam theory to model SWCNTs’ mechanical properties under combined temperature and electrostatic fields. Unlike the classical Bernoulli–Euler beam model, this new model has independent extensional stiffness and bending stiffness. Static bending, buckling, and nonlinear vibrations are investigated through the classical beam model and the new model. The results show that the classical beam model significantly underestimates the influence of temperature and electrostatic fields on the mechanical properties of SWCNTs because the model overestimates the bending stiffness. The results also suggest that it may be necessary to re-examine the accuracy of the classical beam model of SWCNTs.

Exact Dynamic Analysis of Space Structures Using Timoshenko Beam Theory

AIAA Journal ◽  
2004 ◽  
Vol 42 (4) ◽  
pp. 833-839 ◽  
Author(s):  
Jen-Fang Yu ◽  
Hsin-Chung Lien ◽  
B. P. Wang
Keyword(s):  
Dynamic Analysis ◽  
Timoshenko Beam ◽  
Beam Theory ◽  
Timoshenko Beam Theory ◽  
Space Structures
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