Bending of a Viscoelastic Timoshenko Cracked Beam Based on Equivalent Viscoelastic Spring Models

Chao Fu,Xiao Yang,Piotr Smarzewski

doi:10.1155/2021/8663213

Chao Fu, Xiao Yang + Show 1 more

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https://doi.org/10.1155/2021/8663213

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Abstract

Considering the transverse crack as a massless viscoelastic rotational spring, the equivalent stiffness of the viscoelastic cracked beam is derived by Laplace transform and the generalized Dirac delta function. Using the standard linear solid constitutive equation and the inverse Laplace transform, the analytical expressions of the deflection and rotation angle of the viscoelastic Timoshenko beam with an arbitrary number of open cracks are obtained in the time domain. By numerical examples, the bending results of the analytical expressions are verified with those of the FEM program. Additionally, the effects of the time, slenderness ratio, and crack depth on the bending deformations of the different cracked beam models are revealed.

Highlights

Viscoelastic materials [1, 2] are widely used in civil, mechanical, biological, and aerospace engineering
Biondi and Caddemi [16] proposed that multiple singularities in the flexural stiffness can be used to represent the effect of the concentrated damage of the cracked beam, and the Dirac delta function is proper to represent the singular flexural stiffness corresponding to the crack position. e negative Dirac delta function is employed to present the damage of the flexural stiffness at the crack location by Buda and Caddemi [17] and Caddemi and Calio [18]; the flexural stiffness cannot be negative, so this description is physically imperfect. en, Palmeri and Cicirello [19] and Cicirello and Palmeri [20] presented a physically based “flexibility modelling” of concentrated damage to avoid physical incompleteness
For the crack effect at the crack location ξ1 0.5, there exist a cusp on the deflection curve and a jump on the rotation angle curve

Summary

Introduction

Viscoelastic materials [1, 2] are widely used in civil, mechanical, biological, and aerospace engineering. Biondi and Caddemi [16] proposed that multiple singularities in the flexural stiffness can be used to represent the effect of the concentrated damage of the cracked beam, and the Dirac delta function is proper to represent the singular flexural stiffness corresponding to the crack position. E negative Dirac delta function is employed to present the damage of the flexural stiffness at the crack location by Buda and Caddemi [17] and Caddemi and Calio [18]; the flexural stiffness cannot be negative, so this description is physically imperfect. By considering the effect of crack gap, Yang et al [21] gave the equivalent flexural rigidity using Dirac delta function and present the closed form general solutions of bending deformation of Timoshenko beams with an arbitrary number of cracks. Donaet al. [22] developed a twonode multidamaged beam element to analyze the static and dynamic behaviors of the cracked beam, which is suitable for the beam with axial spring, rotational spring, and shearing spring

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