A study on lateral impact of Timoshenko beam

Yamamoto, Sumio; Sato, Keijin; Koseki, Hiroji

doi:10.1007/bf00350516

Cited by 6 publications

(1 citation statement)

References 5 publications

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“…On this basis, it is clear that a useful estimate of the initial strain can be obtained if wave propagation effects in the beam are included. Many studies have been done to calculate the response of the beam using a normal mode approach (Yamamoto, Sato, and Koseki, 1990) or infinite beam theory (Doyle, 1984a;McGhie, 1990;Stadler and Shreeves, 1970) using Hertz's contact theory (Willis, 1966), which is elastic contact law for a static case. The impact force, which is applied suddenly, causes plastic deformation at the center of the contact zone even for a small load (Cawley and Clayton, 1987) pacted medium.…”

Section: Introductionmentioning

confidence: 99%

Transient Response of an Impacted Beam and Indirect Impact Force Identification Using Strain Measurements

Park

1994

Shock and Vibration

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The impulse response functions (force-strain relations) for Euler–Bernoulli and Timoshenko beams are considered. The response of a beam to a transverse impact force, including reflection at the boundary, is obtained with the convolution approach using the impulse response function obtained by a Laplace transform and a numerical scheme. Using this relation, the impact force history is determined in the time domain and results are compared with those of Hertz's contact law. In the case of an arbitrary impact, the location of the impact force and the time history of the impact force can be found. In order to verify the proposed algorithm, measurements were taken using an impact hammer and a drop test of a steel ball. These results are compared with simulated ones.

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Section: Introductionmentioning

confidence: 99%

Transient Response of an Impacted Beam and Indirect Impact Force Identification Using Strain Measurements

Park

1994

Shock and Vibration

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Elastic impact on finite Timoshenko beam

et al. 2002

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In this paper the analytical solutions of the impact of a particle on Timoshenko beams with four kinds of different boundary conditions are obtained according to Navier's idea, which is further developed. The initial values of the impact forces are exactly determined by the momentum conservation law.. The propagation of the longitudinal and transverse waves along the beam, especially, the effects of boundary conditions on the characteristics of the reflected waves, are investigated in detail. Some results are compared with those by MSC/NASTRAN.Recently the strategy by Navier was realized and developed in Refs. [7,8], and this paper will developed the strategy further, where the impactor and the target are treated as an integrated vibration system, and only the impactor has a distributive velocity. Therefore, the problems of elastic impact between structures are transformed into traditional vibration problems with initial values, and the impact loads are the internal forces on the contact area, not the external forces acting on the integrated system. The analysis method of impact problems based on this strategy might as well be called as Direct Mode Superposition Method (DMSM).Among the methods mentioned above, the direct solution of differential equations is greatly limited because of the difficulty of getting the closed form solutions. IMSM is not suitable for the analysis of locking problems of mechanisms, and the time step size and the number of modes used influence seriously the obtained results. In comparison with IMSM, DMSM is a general method of solving the elastic problems of linear impact between structures and the locking problems of mechanisms. According to DMSM, the software systems such as NASTRAN can be directly applied to the analysis of elastic impact problems.About the applications of Timoshenko theory, much research work [3~5,9~12] has been done, where Anderson [9] gave the responses of finite Timoshenko beam with known loads by mode superposition method; Boley et alfl0] obtained the dynamical responses of semiinfinite Timoshenko beam by Laplace transform, but the loads applied to the beam are assumed to be given as simple pulses; Yamamoto[ 11] carried out a numerical analysis of impact problems with contact deformation of a ball on Timoshenko beam by IMSM; Shueei et al. [ 12] obtained analytical solutions of loaded Timoshenko beam with general elastic boundary conditions, the loads are known and no additional mass is attached to the beam, and the method is not suitable for the analysis of impact problems of structures in which the force boundary condition is defined directly by the acceleration of the impactor and there are initial conditions, and the analysis of impacts between structures such as a rod impacting against a beam and so on, But the complicated impact problems mentioned above can be easily solved by DMSM.

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Elastic impact of a spherical particle with a long, stationary, fixed Timoshenko beam

Zhang

Müftü

2021

Journal of Sound and Vibration

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A study on lateral impact of Timoshenko beam

Cited by 6 publications

References 5 publications

Transient Response of an Impacted Beam and Indirect Impact Force Identification Using Strain Measurements

Transient Response of an Impacted Beam and Indirect Impact Force Identification Using Strain Measurements

Elastic impact on finite Timoshenko beam

Elastic impact of a spherical particle with a long, stationary, fixed Timoshenko beam

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