Vibrations of an Euler-Bernoulli beam with hysteretic damping arising from dispersed frictional microcracks

Maiti, Soumyabrata; Bandyopadhyay, Ritwik; Chatterjee, Anindya

doi:10.1016/j.jsv.2017.09.025

Cited by 11 publications

(4 citation statements)

References 36 publications

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“…Here we extend Piché's formulation to include hysteretic damping in the otherwise-linear structural dynamics. In our method the stiffness and inertia terms are integrated implicitly (without iteration, being linear) and the nonsmooth hysteresis is monitored at Gauss points [25] and treated with explicit time-integration. Thus, overall, our method is semi-implicit.…”

Section: Our Present Approachmentioning

confidence: 99%

“…Finally, in work more directly related to ours, for an Euler-Bernoulli beam with hysteretic dissipation, Maity et al [25] used the first few undamped modes to expand the solution and performed the virtual work integration using a few Gauss points chosen over the full domain. However, they used a different hysteresis model motivated by distributed microcracks.…”

Section: Our Present Approachmentioning

confidence: 99%

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Semi-implicit Integration and Data-Driven Model Order Reduction in Structural Dynamics with Hysteresis

Goswami¹,

Chatterjee²

2022

Preprint

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Structural damping is known to be approximately rate-independent in many cases. Popular models for rate-independent dissipation are hysteresis models; and a highly popular hysteresis model is the Bouc-Wen model. If such hysteretic dissipation is incorporated in a refined finite element model, then the mathematical model includes the usual structural dynamics equations along with nonlinear nonsmooth ordinary differential equations for a large number of internal hysteretic states at Gauss points, to be used within the virtual work calculation for dissipation. For such systems, numerical integration becomes difficult due to both the distributed non-analytic nonlinearity of hysteresis as well as the very high natural frequencies in the finite element model. Here we offer two contributions. First, we present a simple semi-implicit integration approach where the structural part is handled implicitly based on the work of Piché, and where the hysteretic part is handled explicitly. A cantilever beam example is solved in detail using high mesh refinement. Convergence is good for lower damping and a smoother hysteresis loop. For a less smooth hysteresis loop and/or higher damping, convergence is observed to be roughly linear on average. Encouragingly, the time step needed for stability is much larger than the time period of the highest natural frequency of the structural model. Subsequently, data from several simulations conducted using the above semi-implicit method are used to construct reduced order models of the system, where the structural dynamics is projected onto a small number of modes and the number of hysteretic states is reduced significantly as well. Convergence studies of error against the number of retained hysteretic states show very good results.

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Section: Our Present Approachmentioning

confidence: 99%

Section: Our Present Approachmentioning

confidence: 99%

Semi-implicit Integration and Data-Driven Model Order Reduction in Structural Dynamics with Hysteresis

Goswami¹,

Chatterjee²

2022

Preprint

Self Cite

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“…Meanwhile, damping capacity is also significant for structures materials where undesirable noise and vibration can be passively attenuated. Maiti et al reported vibrations of an Euler-Bernouli beam with hysteretic damping arising from dispersed friction microcracks based on a theoretical study [17]. Göken et al deemed that the presence of cracks contributed to the dissipation of energy by displacement of crack surfaces [18].…”

Section: Introductionmentioning

confidence: 99%

Effect of micro-cracks on mechanical and damping properties of double-layered Al/Al plate

Wang

Chen

Chai

et al. 2022

Materials Science and Technology

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To investigate the influence of micro-cracks (including formation and growing) on mechanical and damping capacity, the grooved (with two dimensions) and non-grooved Al plates were subjected to cold roll bonding (CRB). Microscopic morphology, tensile and damping test of the experimental materials were investigated. Due to uneven stress distribution, the edges of grooves were heavily inclined in the normal direction (ND), and the grooves were changed into micro-cracks with the sizes of a few to a dozen microns. Mechanical properties of the Al sheet with micro-cracks were decreased, which further lowered with micro-cracks growing. There were two internal friction peaks for the Al sheet with micro-cracks, which mainly attributed to the stronger local stress and local plastic deformation around the micro-cracks.

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“…However, it implies a dissipated energy per a vibration cycle depending on the frequency. Hysteretic damping, whose force is proportional to the displacement and in phase with the velocity, leads to a dissipated energy per cycle which is independent of the frequency [4,5]. Experiments on structural materials indicate that the energy dissipation is independent of the cyclic frequency [6][7][8].…”

Section: Introductionmentioning

confidence: 99%

The Direct Integration Method with Virtual Initial Conditions on the Free and Forced Vibration of a System with Hysteretic Damping

Pan

2019

Applied Sciences

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The energy dissipated in hysteretic damping is independent of cyclic frequency, which agrees with the experimental results of energy dispersion of many materials under cyclic loading. Despite these desirable properties, hysteretic damping suffers from a notable drawback; the direct integration solution of the equation of motion is divergent. In this paper, a virtual initial condition is proposed to address the instability of the solution. The new method develops virtual initial conditions associated to the real initial conditions, which make the direct integration solution eliminate the divergence term of the complementary solution and converge to the exact solution. The stability and accuracy of the proposed direct integration method are demonstrated to be effective in solving the divergence problem by the comparison of the numerical and theoretical solutions on the free and forced vibration of a system with hysteretic damping.

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Vibrations of an Euler-Bernoulli beam with hysteretic damping arising from dispersed frictional microcracks

Cited by 11 publications

References 36 publications

Semi-implicit Integration and Data-Driven Model Order Reduction in Structural Dynamics with Hysteresis

Semi-implicit Integration and Data-Driven Model Order Reduction in Structural Dynamics with Hysteresis

Effect of micro-cracks on mechanical and damping properties of double-layered Al/Al plate

The Direct Integration Method with Virtual Initial Conditions on the Free and Forced Vibration of a System with Hysteretic Damping

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