Normal Impact of an Infinite Elastic Beam by a Semi-Infinite Elastic Rod

1971 ◽  
Vol 38 (2) ◽  
pp. 455-460 ◽  
Author(s):  
S. Ranganath
Keyword(s):  
Timoshenko Beam ◽  
Laplace Transformation ◽  
Elastic Beam ◽  
Beam Theory ◽  
Bending Moment ◽  
Timoshenko Beam Theory ◽  
Elastic Rod ◽  
Normal Impact ◽  
One Dimensional ◽  
The Waves

Solutions are obtained by the method of Laplace transformation for the problem of normal impact of an infinite elastic beam by a semi-infinite elastic rod. The Timoshenko beam theory is used to describe the waves in the beam and elementary one-dimensional bar theory is used to describe the waves in the rod. Numerical results are presented for the velocity and the bending moment. These results are shown to agree well with experimental observations, except at early times.

Vibration Analysis of Axially Loaded Bridges Traversed by Accelerating Vehicles With Passenger Dynamics

Volume 2 ◽  
2004 ◽  
Author(s):  
P. Hassanpour Asl ◽  
H. Mehdigholi ◽  
E. Esmailzadeh
Keyword(s):  
Timoshenko Beam ◽  
Degrees Of Freedom ◽  
Beam Theory ◽  
Bending Moment ◽  
Timoshenko Beam Theory ◽  
The Body ◽  
Suspension Bridges ◽  
Vehicle Speed ◽  
Damping Force ◽  
Shock Absorbers

An investigation into the dynamics of vehicle-passenger-structure-induced vibration of suspension bridges traversed by accelerating vehicles is carried out. The vehicle including the driver and passengers is modeled as a half-car planer model with six degrees-of-freedom. In addition, the stiffness of compliant bushings at the connecting points of the shock absorbers to the body is considered. The bridge is assumed to obey the Timoshenko beam theory with axial load and arbitrary conventional boundary conditions. The roughness of the bridge is assumed as a differentiable function of location. Due to continuously moving the location of the variable loads on the bridge, and in the presence of damping force, the governing differential equations become complicated. The numerical simulations presented here are for the case of a vehicle traveling at a constant acceleration on a uniform bridge with rough surface and simply supported end conditions. The relationship between the bridge vibration characteristics, bridge roughness, and the vehicle speed and acceleration is rendered, which yields into search for a particular acceleration and speed that determines the maximum value of the dynamic deflection and the bending moment of the bridge. Results obtained from the Timoshenko beam theory are compared with those from the Euler-Bernoulli beam for which full agreements are found. Finally, the maximum deflection of the beam under moving loads is compared with that of the case with static loading.

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

Optimal design of high-g MEMS piezoresistive accelerometer based on Timoshenko beam theory

2017 ◽  
Vol 24 (2) ◽  
pp. 855-867 ◽  
Author(s):  
Feng Liu ◽  
Shiqiao Gao ◽  
Shaohua Niu ◽  
Yan Zhang ◽  
Yanwei Guan ◽  
...  
Keyword(s):  
Optimal Design ◽  
Timoshenko Beam ◽  
Beam Theory ◽  
Timoshenko Beam Theory

Flexural Vibration Band Gap in a Periodic Fluid-Conveying Pipe System Based on the Timoshenko Beam Theory

2011 ◽  
Vol 133 (1) ◽  
Author(s):  
Dianlong Yu ◽  
Jihong Wen ◽  
Honggang Zhao ◽  
Yaozong Liu ◽  
Xisen Wen
Keyword(s):  
Finite Element Method ◽  
Band Gap ◽  
Timoshenko Beam ◽  
Beam Theory ◽  
Flexural Vibration ◽  
Timoshenko Beam Theory ◽  
Flexural Wave ◽  
Vibration Band ◽  
Frequency Range ◽  
Pipe System

The flexural vibration band gap in a periodic fluid-conveying pipe system is studied based on the Timoshenko beam theory. The band structure of the flexural wave is calculated with a transfer matrix method to investigate the gap frequency range. The effects of the rotary inertia and shear deformation on the gap frequency range are considered. The frequency response of finite periodic pipe is calculated with a finite element method to validate the gap frequency ranges.

scholarly journals Comparison of 1D and 2D solutions for a beam under transverse impact

2018 ◽  
Vol 148 ◽  
pp. 05005 ◽  
Author(s):  
Vítězslav Adámek
Keyword(s):  
Analytical Solution ◽  
Timoshenko Beam ◽  
Elastic Beam ◽  
Beam Theory ◽  
Two Dimensional ◽  
Transverse Impact ◽  
Dimensional Theory ◽  
Beam Geometry ◽  
Stationary Vibration ◽  
Main Factors

The problem of non-stationary vibration of an elastic beam caused by a transverse impact loading is studied in this work. In particular, two different approaches to the derivation of analytical solution of the problem are compared. The first one is based on the Timoshenko beam theory, the latter one follows the exact two-dimensional theory. Both mentioned methods are used for finding the response of an infinite homogeneous isotropic beam. The obtained analytical results are then compared and their agreement is discussed in relation to main factors, i.e. the beam geometry, the character of loading and times and points at which the beams responses are studied.

Medium Frequency Vibration Analysis of Beam Structures Modeled by the Timoshenko Beam Theory

2020 ◽  
Author(s):  
Yichi Zhang ◽  
Bingen Yang
Keyword(s):  
Shear Deformation ◽  
Timoshenko Beam ◽  
Vibration Analysis ◽  
Beam Theory ◽  
Timoshenko Beam Theory ◽  
Bernoulli Beam ◽  
Beam Structure ◽  
Medium Frequency ◽  
Beam Structures ◽  
Euler Bernoulli Beam

Abstract Vibration analysis of complex structures at medium frequencies plays an important role in automotive engineering. Flexible beam structures modeled by the classical Euler-Bernoulli beam theory have been widely used in many engineering problems. A kinematic hypothesis in the Euler-Bernoulli beam theory is that plane sections of a beam normal to its neutral axis remain normal when the beam experiences bending deformation, which neglects the shear deformation of the beam. However, as observed by researchers, the shear deformation of a beam component becomes noticeable in high-frequency vibrations. In this sense, the Timoshenko beam theory, which describes both bending deformation and shear deformation, may be more suitable for medium-frequency vibration analysis of beam structures. This paper presents an analytical method for medium-frequency vibration analysis of beam structures, with components modeled by the Timoshenko beam theory. The proposed method is developed based on the augmented Distributed Transfer Function Method (DTFM), which has been shown to be useful in various vibration problems. The proposed method models a Timoshenko beam structure by a spatial state-space formulation in the s-domain, without any discretization. With the state-space formulation, the frequency response of a beam structure, in any frequency region (from low to very high frequencies), can be obtained in an exact and analytical form. One advantage of the proposed method is that the local information of a beam structure, such as displacements, bending moment and shear force at any location, can be directly obtained from the space-state formulation, which otherwise would be very difficult with energy-based methods. The medium-frequency analysis by the augmented DTFM is validated with the FEA in numerical examples, where the efficiency and accuracy of the proposed method is present. Also, the effects of shear deformation on the dynamic behaviors of a beam structure at medium frequencies are illustrated through comparison of the Timoshenko beam theory and the Euler-Bernoulli beam theory.

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