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

Abstract

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.

Computational and experimental analysis of the impact of a sphere on a beam and the resulting modal energy distribution

“…Many studies address the transverse impact of a sphere on a beam experimentally and confront the results with simulation [17,18,19,20,21,22,23,24,25]. Good agreement was obtained e. g. in [19,26,22,25] in terms of displacement response and contact duration.…”

“…Good agreement was obtained e. g. in [19,26,22,25] in terms of displacement response and contact duration. Modeling approaches range from three-dimensional FEA (e. g. [22,25]) to modal superposition (e. g. [18]). Seifried et al [19] were one of the first to propose to combine modal superposition with local FE modeling of the contact region for impact simulations.…”

Impact of a ball with a flexible beam

“…The equation of motion for bending waves on a uniform, flexible beam of density ρ, crosssectional area A and Young's modulus E is given in its simplest form by [3][4][5][6][7][8][9][10][11][12] ρA…”

“…A third approach is to solve the beam equation for a given impact, to calculate the energy loss due to beam bending or vibrations. The latter approach has been adopted by several authors [3][4][5], and it provides additional insights not generally available from a rigid beam model. Nevertheless, the two models can be compared to show that a flexible beam shares some of the same properties as a rigid beam.…”

Dynamic Force Identification for Beamlike Structures Using an Improved Dynamic Stiffness Method

“…Among others, let us cite the sum of weighted acceleration technique (Gregory et aI., 1986;Wang et al, 1987), the deconvolution technique (Hillary and Ewins, 1984), and their engineering applications (Bateman et al, 1991;Carne et al, 1994). Using the wave propagation theory, Park and Park (1994) studied the identification of an arbitrary impact force, including its location and time his-tory. Almost all the force identification algorithms require the measurement of the responses to the unknown forces (displacements, velocities, accelerations, or strains) at several locations on the structure and a model of the structure.…”