International Journal of Mechanical Engineering and Technology (IJMET) Volume 6, Issue 11, Nov 15, pp. 106-113, Article ID: IJMET_06_11_013 Available online at http://www.iaeme.com/ijmet/issues.asp?jtype=ijmet&vtype=6&itype=11 ISSN Print: 0976-63 and ISSN Online: 0976-6359 IAEME Publication 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 cm,cm,and cm 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 and W, for both situations with and without crack. Oil gives better damping capacity than W. Key words: Universal Vibration Apparatus, Composite Beam, Damper Cracked Beam,, W. 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), 15, 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 http://www.iaeme.com/ijmet/index.asp 106 editor@iaeme.com
Damped Vibration Analysis of Composite Simply Supported Beam 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. 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 mm. Figure 2 Beam With Cracks At Different Locations http://www.iaeme.com/ijmet/index.asp 107 editor@iaeme.com
Vikas Mukhariyia, Raj Kumar Yadav, Ashish Tiwari and Pankaj Singh 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 Dunkerley s Method http://www.iaeme.com/ijmet/index.asp 108 editor@iaeme.com
Damped Vibration Analysis of Composite Simply Supported Beam 4. OBSERVATION TABLES Figure 4 Lubricating Oils Table I without Crack 1 2 3 4 5 6 7 8 9 Distance Of RP M Damping Oil Type W W W 1.31 0.86 2.23 1.00 0.82 1.03 0.85 0.78 0. 0.53 0.68 0.34 0.68 0.63 0.10 0.49 0.53 0.90 0. 0.48 0.71 0.65 0.35 0.51 0. 2.89 2.59 3.05 4.19 3.88 4.71 3.36 3.677 4.129 http://www.iaeme.com/ijmet/index.asp 109 editor@iaeme.com
Vikas Mukhariyia, Raj Kumar Yadav, Ashish Tiwari and Pankaj Singh Table II with Crack (Crack Distance = cm from Left) 1 2 3 4 5 6 7 8 9 Distance Of Crack depth (mm) RPM Damping Oil Type W W W 1.7 1.1 0.9 2.42 1.5 0.98 1.125 0.88 1.01 0.75 0.52 1.3 0.82 0.63 0.7 0.61 0.5 1.2 0.8 0.6 1.5 0.88 0. 0.53 3.71 2.25 2.97 3.30 3.00 3.70 3.09 2.84 3.53 Table III with Crack (Crack Location = cm from Left) 1 2 3 4 5 Distance Of Crack depth (mm) RPM Damping Oil Type 1.8 1.3 1.1 2.6 1.6 1.1 1.3 0.89 0.85 1.06 0.58 1.41 0.85 0.68 2.43 2.84 2.85 3.19 2.90 http://www.iaeme.com/ijmet/index.asp 110 editor@iaeme.com
Damped Vibration Analysis of Composite Simply Supported Beam 6 7 8 9 Distance Of Crack depth (mm) RPM Damping Oil Type W W W 0.72 0.68 0.52 1.21 0.83 0.62 1.53 0.90 0.82 0.83 0.75 0.61 3.6 3.12 3.12 3.37 Table IV with Crack (Crack Location = cm from Left) 1 2 3 4 5 6 7 8 9 Distance Of Crack depth (mm) RPM Damping Oil Type W W W 1.32 0.90 2. 1. 0.90 1.10 0.86 0.78 0.63 0.50 1.10 0.63 0. 0.33 0. 1.00 0. 1. 0.75 0.53 0.43 0.30 2.86 2.34 3.01 3.68 3. 5.01 3.00 3.00 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. http://www.iaeme.com/ijmet/index.asp 111 editor@iaeme.com
Vikas Mukhariyia, Raj Kumar Yadav, Ashish Tiwari and Pankaj Singh Without Crack As seen from TABLE I, deflection of composite beam increases as we move the rotor from cm to cm and afterwards it decreases from cm to cm. Consequently natural frequency also increases with decrease in the deflection. Minimum deflection occur in case of Oil at cm location, which gives the highest frequency of 4.71 Hz. Maximum deflection occur in case of composite beam without damper at cm location, which gives the lowest frequency of 2.59 Hz. As seen from TABLE I, oil reduces the deflection better than W. With Crack Crack location at cm from left As seen from TABLE II, deflection increases again as we move rotor from cm to cm and afterwards it decreases. The highest deflection occurs at cm, consequently the lowest frequency of 2.25Hz also occur at same location Crack location at cm from left As seen from TABLE III, maximum deflection occurs at crack location itself i.e. cm, consequently gives the lowest frequency. Crack location at cm from left As seen From TABLE IV, the maximum deflection occurs at mid location i.e. cm. The highest frequency of 5.01Hz occurs at cm i.e. at the crack location using damping effect with oil. 6. CONCLUSION From the above observation tables, we conclude that oil provides better damping effect than oil W. 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 cm to cm. 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. http://www.iaeme.com/ijmet/index.asp 112 editor@iaeme.com
Damped Vibration Analysis of Composite Simply Supported Beam [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 of Cracked Beams: An Analytical Approach", Journal of Sound and Vibration, 256, 02, pp.17 31. [5] Vidula 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), 12, 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. 12), 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 Technology, 1(1), 10, pp. 105 117. http://www.iaeme.com/ijmet/index.asp 113 editor@iaeme.com