DAMPED VIBRATION ANALYSIS OF COMPOSITE SIMPLY SUPPORTED BEAM

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http://www.iaeme.com/IJMET/issues.asp?JType=IJMET&VType=6&IType=11 ISSN Print: 0976-6340 and ISSN Online: 0976-6359

DAMPED VIBRATION ANALYSIS OF

COMPOSITE SIMPLY SUPPORTED BEAM

Vikas Mukhariyia and Raj Kumar Yadav

Asst. Prof. Department of Mechanical Engineering AIST Sagar M.P Ashish Tiwari and Pankaj Singh

M. Tech Scholar Department of Mechanical Engineering AIST Sagar M.P ABSTRACT

In this research the natural frequency of composite simply supported beam (steel +cast iron),with and without cracks at three different locations namely at 22cm ,44cm,and 66cm is investigated experimentally using universal vibration apparatus. The beam is made up of composite material of steel and cast iron with dimension (L*W*H= 1.095m*0.023m*0.012m) and E=157 GPA. A comparison is made by using damper with two different oils namely SAEJ1703F and 20W40, for both situations with and without crack. Oil SAEJ1703F gives better damping capacity than 20W40.

Key words: Universal Vibration Apparatus, Composite Beam, Damper Cracked Beam, SAEJ1703F, 20W40.

Cite this Article: Vikas Mukhariyia, Raj Kumar Yadav, Ashish Tiwari and Pankaj Singh. Damped Vibration Analysis of Composite Simply Supported Beam, International Journal of Mechanical Engineering and Technology, 6(11), 2015, pp. 106-113.

http://www.iaeme.com/currentissue.asp?JType=IJMET&VType=6&IType=11

1. INTRODUCTION

The importance of the beam and its engineering applications is obvious, and it undergoes many different of loading. Many types of loading may cause cracks in the beam. These cracks and their locations effect on the shapes and values of the beam frequency. Recently these topics are so prevailing in the industry of spacecraft, airplanes, wind turbines, turbines, robot arm and many other applications. Many engineering components used in the aeronautical, aerospace and naval construction industries are considered by designers as vibrating structures, operating under a large number of random cyclic stresses. Cracks found in structural elements like beams and columns have different causes. They may be fatigue cracks that take place under service conditions as a result of the limited fatigue strength. They may be also due to mechanical defects, as in the turbine blades of jet engines. In these engines the cracks are caused by sand and small stones sucked from the surface of runway. Another

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group involves cracks which are inside the material. They are created as a result of manufacturing processes. The presence of vibrations on structures and machine components leads to cyclic stresses resulting in material fatigue and failure. A crack on a structural member introduces a local flexibility which is a function of the crack depth. Major characteristics of structures, which undergo change due to presence of crack, are a) The natural frequency b) The amplitude response due to vibration c) Mode shape. Hence it is important to use natural frequency measurements to detect crack and its effects on the structure.

2. OBJECTIVE OF THE WORK

The objective of the study is to analyse the behaviour of the simply supported beam subjected to three rectangular cracks at different locations under free and damped vibration. A comparison is made by using two different oils under both situations with and without cracks. Cracks in vibrating components can initiate catastrophic failures. Therefore, there is a need to understand the dynamics of cracked structures. When a structure suffers from damage, its dynamic properties can change. Specifically, crack damage can cause a stiffness reduction, with an inherent reduction in natural frequencies, an increase in modal damping, and a change in the mode shapes. Since the reduction in natural frequencies can be easily observed, most researchers use this feature. Natural frequencies and mode shapes of the beam are also been determined.

Figure 1 Universal Vibration Apparatus

The rectangular crack was created on the composite beam of same dimension of 0.2 mm.

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3. METHODOLOGY

The dimension of composite beam are (L*W*H= 1.095m*0.023m*0.012m) .The material of beam was stainless steel welded with cast iron of Young’s modulus 157 GPA.

The (TM06) Universal vibration apparatus is employed in this study as shown in fig.

Figure 3 DAMPER

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Figure 4 Lubricating Oils

4. OBSERVATION TABLES

Table I without Crack S. No. Distance Of Rotor(cm) Voltage (volts) RP

M Damping Oil Type

Deflection (cm) Natural Frequency (Hz) 1 22 20 40 60 274 475 875 NIL NIL 1.31 0.86 0.80 2.89 2 44 20 40 60 274 475 875 NIL NIL 2.23 1.00 0.82 2.59 3 66 20 40 60 274 475 875 NIL NIL 1.03 0.85 0.78 3.05 4 22 20 40 60 262 369 632 Consider SAEJ1703F 0.20 0.53 0.68 4.19 5 44 20 40 60 262 369 632 Consider SAEJ1703F 0.34 0.68 0.63 3.88 6 66 20 40 60 262 369 632 Consider SAEJ1703F 0.10 0.49 0.53 4.71 7 22 20 40 60 262 369 632 Consider 20W40 0.90 0.60 0.70 3.36 8 44 20 40 60 262 369 632 Consider 20W40 0.48 0.71 0.65 3.677 9 66 20 40 60 262 369 632 Consider 20W40 0.35 0.51 0.60 4.129

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Table II with Crack (Crack Distance = 22cm from Left) S. No. Distance Of Rotor(cm) Crack depth (mm) Voltage

(volts) RPM Damping Oil Type

Deflection (cm) Natural Frequency (Hz) 1 22 0.2 20 40 60 274 475 875 NIL NIL 1.7 1.1 0.9 3.71 2 44 0.2 20 40 60 274 475 875 NIL NIL 2.42 1.5 0.98 2.25 3 66 0.2 20 40 60 274 475 875 NIL NIL 1.125 0.88 0.80 2.97 4 22 0.2 20 40 60 262 369 632 Consider SAEJ1703F 1.01 0.75 0.52 3.30 5 44 0.2 20 40 60 262 369 632 Consider SAEJ1703F 1.3 0.82 0.63 3.00 6 66 0.2 20 40 60 262 369 632 Consider SAEJ1703F 0.7 0.61 0.5 3.70 7 22 0.2 20 40 60 262 369 632 Consider 20W40 1.2 0.8 0.6 3.09 8 44 0.2 20 40 60 262 369 632 Consider 20W40 1.5 0.88 0.70 2.84 9 66 0.2 20 40 60 262 369 632 Consider 20W40 0.80 0.66 0.53 3.53

Table III with Crack (Crack Location = 44cm from Left) S. No. Distance Of Rotor(cm) Crack depth (mm) Voltage

Deflection (cm) Natural Frequency (Hz) 1 22 0.2 20 40 60 274 475 875 NIL NIL 1.8 1.3 1.1 2.43 2 44 0.2 20 40 60 274 475 875 NIL NIL 2.6 1.6 1.1 2.84 3 66 0.2 20 40 60 274 475 875 NIL NIL 1.3 0.89 0.85 2.85 4 22 0.2 20 40 60 262 369 632 Consider SAEJ1703F 1.06 0.80 0.58 3.19 5 44 0.2 20 40 60 262 369 632 Consider SAEJ1703F 1.41 0.85 0.68 2.90

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S. No. Distance Of Rotor(cm) Crack depth (mm) Voltage

Deflection (cm) Natural Frequency (Hz) 6 66 0.2 20 40 60 262 369 632 Consider SAEJ1703F 0.72 0.68 0.52 3.6 7 22 0.2 20 40 60 262 369 632 Consider 20W40 1.21 0.83 0.62 3.12 8 44 0.2 20 40 60 262 369 632 Consider 20W40 1.53 0.90 0.82 3.12 9 66 0.2 20 40 60 262 369 632 Consider 20W40 0.83 0.75 0.61 3.37

Table IV with Crack (Crack Location = 66cm from Left) S. No. Distance Of Rotor(cm) Crack depth (mm) Voltage

Deflection (cm) Natural Frequency (Hz) 1 22 0.2 20 40 60 274 475 875 NIL NIL 1.32 0.90 0.80 2.86 2 44 0.2 20 40 60 274 475 875 NIL NIL 2.40 1.20 0.90 2.34 3 66 0.2 20 40 60 274 475 875 NIL NIL 1.10 0.86 0.78 3.01 4 22 0.2 20 40 60 262 369 632 Consider SAEJ1703F 0.70 0.63 0.50 3.68 5 44 0.2 20 40 60 262 369 632 Consider SAEJ1703F 1.10 0.70 0.63 3.20 6 66 0.2 20 40 60 262 369 632 Consider SAEJ1703F 0.40 0.33 0.20 5.01 7 22 0.2 20 40 60 262 369 632 Consider 20W40 1.00 0.70 0.60 3.00 8 44 0.2 20 40 60 262 369 632 Consider 20W40 1.20 0.80 0.75 3.00 9 66 0.2 20 40 60 262 369 632 Consider 20W40 0.53 0.43 0.30 4.45

5. RESULT AND DICUSSION

A comparison is made between two different oils of different lubrication properties at different locations of composite beam along with crack and without crack. Dunkerley method is used to find the natural frequency of composite beam.

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Without Crack

As seen from TABLE I, deflection of composite beam increases as we move the rotor from 22cm to 44cm and afterwards it decreases from 44cm to 66cm. Consequently natural frequency also increases with decrease in the deflection. Minimum deflection occur in case of SAEJ1703F Oil at 66cm location, which gives the highest frequency of 4.71 Hz.

Maximum deflection occur in case of composite beam without damper at 44cm location, which gives the lowest frequency of 2.59 Hz.

As seen from TABLE I, oil SAEJ1703F reduces the deflection better than 20W40.

With Crack

Crack location at 22cm from left

As seen from TABLE II, deflection increases again as we move rotor from 22cm to 44cm and afterwards it decreases. The highest deflection occurs at 44 cm, consequently the lowest frequency of 2.25Hz also occur at same location

As seen from TABLE III, maximum deflection occurs at crack location itself i.e. 44cm, consequently gives the lowest frequency.

As seen From TABLE IV, the maximum deflection occurs at mid location i.e. 44cm. The highest frequency of 5.01Hz occurs at 66cm i.e. at the crack location using damping effect with oil SAEJ1703F.

6. CONCLUSION

From the above observation tables, we conclude that oil SAEJ1703F provides better damping effect than oil 20W40. Hence, it reduces the vibration of the composite beam to the greater extent, and enhances the natural frequency of the composite beam. We also seen that the frequency of composite beam increases as we move the rotor from 22cm to 44cm.

Crack location also effect the frequency of the composite beam, as seen from the observation table, it increases the deflection of the beam slightly, therefore the frequency decreases.

ACKNOWLEDGMENT

The authors would like to thank to Principal and Management of Adina institute of science and technology sagar for academic and valued computational support.

REFRENCES

[1] Shen, M. -H. H and Pierre C. "Modes of free vibrations of cracked beams", paper (of 46 pages) presented to UM-MEAM, (1986).

[2] Chondros T. G., Dimarogonas A. D. and Yao J "Longitudinal vibration of a bar with a breathing crack", Engineering fracture mechanics, pp.503-518, 1998.

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[3] Adams, R.D., Cawley, P., Pye, C.J. and stone, B.J., A vibration technique for non-destructively assessing the integrity of structures. Journal of Mechanical Engineering Science., 1978

[4] Fernández-Sáez, J., and Navarro, C., "Fundamental Frequency of Cracked Beams: An Analytical Approach", Journal of Sound and Vibration, 256, 2002, pp.17–31.

[5] Vidula S. Sohoni, Dr.M.R.Shiyekar. Concrete–Steel Composite Beams of A Framed Structure For Enhancement In Earthquake Resistance, International

Journal of Civil Engineering and Technology, 3(1), 2012, pp. 99-110

[6] Pankaj Charan Jena, Dayal R. Parhi, and Goutam Pohit, Faults detection of a single cracked beam by theoretical and experimental analysis using vibration signatures, IOSR Journal of Mechanical and Civil Engineering, Volume 4, Issue 3 (Nov-Dec. 2012), pp.01-18.

[7] Muhannad Al-Waily, Theoretical and Numerical Vibration Study of Continuous Beam with Crack Size and Location Effect.

[8] Sharad V. Kshirsagar and Dr. Lalit B. Bhuyar. Signature Analysis of Cracked Cantilever Beam, International Journal of Advanced Research Engineering and