Experimental modal analysis of curved composite beam with transverse open crack
Graphical abstract
Introduction
Curved beams are widely used in many structures such as gears, pumps and turbines. Due to their widespread use in real-world applications, many researchers have investigated the natural frequencies and modal structures of beams. Early studies on the field mostly investigated the effects of vibration on straight metal beams such as aluminum, carbon steel and cast iron. Following these works, studies mainly followed two research streams; (1) studies on straight and curved beams and (2) studies exploring the effects of cracks on the beams under free or forced vibrations. In Table 1, these studies are classified with respect to the material type, shape and the availability of the crack on the beam. Solution approaches, either numerical or experimental, are also included in Table 1.
In the literature, Kamble et al. [1] studied two different materials for a straight beam with a fixed stationary load on the opposite end. Natural frequencies in different modes obtained from experimental and analytical results are presented. Chogule et al. [2] experimentally obtained the natural frequency, mode structure, damping and mode shapes of a beam with a fixed rectangular shape. Mia et al. [3] studied the modal structure and natural frequencies for un-cracked and cracked beams using the finite element method (FEM). Simulations were performed in Ref. [4] to find the total deformation on the beam surface from the vibration modes. Raj et al. [5] studied numerical simulations for multi-degree-of-freedom beams. Ansys and Matlab programs have been used for modeling, simulation and analyses of steel and carbon fiber materials. Natural frequencies were obtained at different lengths and thicknesses. Imran et al. [6] conducted theoretical modal analysis and finite element analysis for cantilever beam using Euler Bernoulli beam theory.
Experimental and theoretical investigations on a cracked cantilever beam have been performed by Douka et al. [7]. They used the time-frequency method to obtain non-linear behavior of the system. Kumar et al. [8] compare the natural frequencies for I and T cantilever beams using different materials such as structural steel, stainless steel and cast iron. Orhan [9] performed free and forced vibration analysis of a cantilever beam with multiple cracks using the FEM. Vaziri et al. [10] studied different cantilever beams made of aluminum, mild steel and isotropic polymer and analyzed mode shapes and the natural frequency of the beams numerically. Satpute et al. [11] examined the first three modes on a steel shaft beam for various crack locations and depths. Effects of cracks on aluminum beams for fixed-free and simple-simple boundary conditions have been investigated in Ref. [12]. Kisa [13] studied the effects of cracks on the dynamic characteristics of a cantilever composite beam produced from graphite fiber reinforced polyamide material. Krawczuk et al. [14] studied the graphite fiber reinforced polyamide beam. Variations in the natural frequencies of the beams were investigated with respect to crack location, crack depth, fiber volume and fiber orientation. Sutar [15] opened cracks on the cantilever beam and computed the natural frequency and mode structures by using the FEM. Öz and Daş [16] studied the FEM for in-plane vibrations of circular curved Euler Bernoulli beam. Natural frequencies were obtained for different crack positions and depths on the cracked beam.
The developments in the composite technology has led to the widespread use of curved composite beams which have higher strength, lower weight, corrosion and heat resistance. However, there are only a couple of studies in the literature on straight and curved composite beams. Nobile [21] used S theory on mixed mode crack growth in curved beams. The approximate tensile strength factors of cracked composite beams were calculated. Jena et al. [18] examined cracks on a beam made of epoxy glass fiber material. Waghulde et al. [19] used various techniques and methods to work on cracked beam models. They applied an empirical method and FEM on a cantilever beam made of aluminum. The effect on the natural frequency was examined for various crack depths locations. Ramesh et al. [17] studied the stress, deformations and frequency changes on un-cracked and cracked beams using the FEM. They worked with five different materials (Aluminum alloy 7475, Stainless Steel, Composite materials Kevlar, Carbon Fiber and High Strength Carbon Fiber Static). Recently, Baba [20] made vibration analyses of sandwich composite beams with different curvature angles under fixed-fixed boundary condition. In this paper, we focus on experimental modal analysis of curved cracked composite (CCC) beams. The main contribution of this study is to conduct a modal shape and first three mode natural frequencies of CCC beam at different crack locations and crack depths. A general-purpose composite structure is preferred. The CCC beams used in the experiments are made of fiber-glass which is one of the mostly used composite.
The rest of the paper is organized as follows. In Section 2, the mathematical model and the application of the FEM for the CCC beam are presented. In Section 3, the manufacturing process of CCC beams and the experimental study are presented. The numerical and experimental results are examined in this section. Finally, conclusion is discussed in section 4.
Section snippets
Numerical analysis
In this section, the numerical solution of vibration analysis for the CCC beams obtained using the ANSYS software is presented. The CCC beam of a constant angle was investigated. The radius of curvature and the curvature angle of the beam are represented by R and γ respectively as shown in Fig. 1.
Manufacturing of CCC beams
In this study, the die-laying technique was used to produce the tested CCC beams. Molds of width 40 mm and length 850 mm were used for manufacturing the composite material. First, fiber-glass materials are cut in required beam thickness and width. Then, epoxy resin was applied over the determined area and spread on fiber-glass was laid on the mold. Composite beams were produced by hand laying method. Each beam is made up of twenty layers of epoxy-glass material. Thickness of the beams was set
Conclusion
It is observed from the simulations and the experimental results that the variation of the natural frequency values depends on the crack depth & location. Compared with the results obtained in the literature, it is observed that natural frequency is mostly decreasing with respect to the crack depth ratio. However, for the cantilever beam, as the distance Lc of the cracks from the fixed point is increased, the values of the modes increase with the natural frequency. Furthermore, the results show
Acknowledgments
We would like to thank Caner Gencoglu for his support in conducting the experiments. We express our gratitude to Roketsan Company for for allowing us to use their facilities and equipment during the experiments.
References (24)
- et al.
Investigation on modal parameters of rectangular cantilever beam using Experimental modal analysis
Mater. Today: Proceed.
(2015) - et al.
Modal analysis of cracked cantilever beam by finite element simulation
Proced. Eng.
(2017) - et al.
FEA simulation of vibrating cantilever plate with transverse surface crack
Mater. Today: Proceed.
(2017) - et al.
Time–frequency analysis of the free vibration response of a beam with a breathing crack
NDT E Int.
(2005) Analysis of free and forced vibration of a cracked cantilever beam
NDT E Int.
(2007)- et al.
Crack detection in cantilever shaft beam using natural frequency
Mater. Today: Proceed.
(2017) - et al.
Crack detection in beams using changes in frequencies and amplitudes of frequency response functions
J. Sound Vib.
(2003) Free vibration analysis of a cantilever composite beam with multiple cracks
Compos. Sci. Technol.
(2004)- et al.
Modelling and vibration analysis of a cantilever composite beam with a transverse open crack
J. Sound Vib.
(1995) Mixed mode crack growth in curved beams with radial edge crack
Theor. Appl. Fract. Mech.
(2001)
Crack identification in vibrating beams using the energy method
J. Sound Vib.
Free vibration analysis of horizontally curved steel I-girder bridges
Thin-Walled Struct.
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