Free in-plane vibration of cracked curved beams: Experimental,analytical,and numerical analyses

Abstract

In this study, free vibration of a cracked curved beam utilizing analytical, numerical, and experimental methods is investigated. The differential quadrature element method is used to solve the equations of motion numerically. The governing equations are also solved analytically. The crack, which is considered to be open, is modeled as a rotational spring. Furthermore, the effect of curvature on mode shapes is studied. To verify the validity of the proposed methods of determining frequencies and mode shapes, an experimental modal analysis test is conducted on a sample beam having crack with some different depths. This study revealed that the behavior of curved beams toward the mode transition phenomenon depends greatly on the boundary conditions of the beam. Also, both the location and depth of crack have considerable effects on natural frequencies.

Keywords

Differential quadrature element method crack curved beam vibration mode transition phenomenon modal testing

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References

Karaagac

Ozturk

Sabuncu

. Crack effects on the in-plane static and dynamic stabilities of a curved beam with an edge crack. J Sound Vib 2011; 330: 1718–1736.

Chen

. DQEM analysis of in-plane vibration of curved beam structures. J Adv Eng Softw 2005; 36: 412–424.

Toygar

Sayman

Kemiklioğlu

et al.

Vibration and buckling analysis of a curved sandwich composite beam with FEM. Res Eng Struct Mater 2016; 2: 49–59.

Öz

Das

. In-plane vibrations of circular curved beams with a transverse open crack. Math Comput Appl 2006; 11: 1–10.

Lee

Jeong

. Flexural and torsional free vibrations of horizontally curved beams on Pasternak foundations. Appl Math Model 2016; 40: 2242–2256.

Viola

Artioli

Dilena

. Analytical and differential quadrature results for vibration analysis of damaged circular arches. J Sound Vib 2005; 288: 887–906.

Tarnopolskaya

Hoog

FRD

Fletcher

. Low-frequency mode transition in the free in-plane vibration of curved beams. J Sound Vib 1999; 228: 69–90.

Torabi

Afshari

Aboutalebi

. A DQEM for transverse vibration analysis of multiple cracked non-uniform Timoshenko beams with general boundary conditions. Comput Math Appl 2014; 67: 527–541.

Huynh

Luu

Lee

. Bending, buckling and free vibration analysis of functionally graded curved beams with variable curvatures using isogeometric approach. Meccanica 2017; 52: 2527–2546.

10.

Ishaquddin

Raveendranath

Reddy

. Efficient coupled polynomial interpolation scheme for out-of-plane free vibration analysis of curved beams. Finite Elem Anal Des 2016; 110: 58–66.

11.

Mochida

Ilanko

Reddy

. Condensation of independent variables in free vibration analysis of curved beams. Adv Aircraft Spacecraft Sci 2016; 3: 45–59.

12.

Dey

Talukdar

. Modal characteristics of cracked thin walled unsymmetrical cross- sectional steel beams curved in plan. Thin-Walled Struct 2016; 108: 75–92.

13.

Reinoso

Paggi

Areias

. A finite element framework for the interplay between delamination and buckling of rubber-like bi-material systems and stretchable electronics. J Eur Ceram Soc 2016; 36: 2371–2382.

14.

Paggi

Corrado

Berardone

. A global/local approach for the prediction of the electric response of cracked solar cells in photovoltaic modules under the action of mechanical loads. Eng Fract Mech 2016; 168: 40–57.

15.

Reinoso

Paggi

Rolfes

. A computational framework for the interplay between delamination and wrinkling in functionally graded thermal barrier coatings. Comput Mater Sci 2016; 116: 82–95.

16.

Carpinteri

Paggi

Zavarise

. The effect of contact on the decohesion of laminated beams with multiple microcracks. Int J Solids Struct 2016; 45: 129–143.

17.

Issa

Wang

Hsiao

. Extensional vibration of continuous circular curved beams with rotary inertia and shear deformation. J Sound Vib 1987; 114: 297–308.

18.

Cerri

Dilena

Ruta

. Vibration and damage detection in undamaged and cracked circular arches: Experimental and analytical results. J Sound Vib 2008; 314: 83–94.