DYNAMIC ANALYSIS OF CANTILEVER BEAMused a cantilever beam contacting a stiff stop to compare cases of moderate and large stiffness ratios (the ratio between the stiffness of the first

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International Journal of Mechanical Engineering and Technology (IJMET) Volume 8, Issue 5, May 2017, pp. 1167–1173, Article ID: IJMET_08_05_122 Available online at http://www.iaeme.com/IJMET/issues.asp?JType=IJMET&VType=8&IType=5 ISSN Print: 0976-6340 and ISSN Online: 0976-6359 © IAEME Publication Scopus Indexed

DYNAMIC ANALYSIS OF CANTILEVER BEAM Sreekanth Sura

Assistant Professor, Department of Aeronautical Engineering, MLR Institute of Technology, Hyderabad, India

Alka Sawale Assistant Professor, Department of Aeronautical Engineering,

MLR Institute of Technology, Hyderabad, India

M Satyanarayana Gupta Professor, Department of Aeronautical Engineering,

MLR Institute of Technology, Hyderabad, India

ABSTRACT The free vibration analysis carried out on cantilever beam to find The natural

frequencies and their mode shapes, the harmonic analysis is done to find the maximum response at different frequencies by using ANSYS are compared with starting three modes obtained from theoretical calculations and the experimental starting three frequency values obtained by using FFT in association with Lab VIEW software (National Instruments) the accelerometer is used to find the frequency plots displacement velocity and acceleration graphs with respect to time. The test carried out on aluminum beam. It is very effective and difficult to representing the dynamic behavior of cantilever beam while it is disturbed by some external force and different scenarios where tested, the beam set up as a cantilever with theoretical, numerical and experimental. The data recorded shows that the frequency of the beam is accurately measured with some small error.

Keywords: Natural frequency, cantilever beam, accelerometer. Cite this Article: Sreekanth Sura, Alka Sawale and M Satyanarayana Gupta. Dynamic Analysis of Cantilever Beam. International Journal of Mechanical Engineering and Technology, 8(5), 2017, pp. 1167–1173. http://www.iaeme.com/IJMET/issues.asp?JType=IJMET&VType=8&IType=5

1. INTRODUCTION Systems in which impacts of matching elements occur play an important role in the theory of vibration of mechanical systems. They became an object of investigation already in the mid 1950s and since then the interest in them has been still growing. It is not surprising as vibro-impact motion characterizes a large class of physical systems. For example, printing hammers, tooling machines, gear boxes, and heat exchangers all involve motion of an object which is limited by a stop. The procedure followed for different Analysis problems to validate

Dynamic Analysis of Cantilever Beam


the results in software’s and finding the proper processor for solving complicated vibration like mechanisms. Two software’s are used Finite Element method [FEM] in ANSYS and LabVIEW. The basic testing done on cantilever beam to validate results theoretically numerically and experimentally. In FEM the modal analysis done and the first three natural frequencies are recorded for first three modes. The procedure to be applied for any complex mechanisms like switchgear mechanism.

A vibro-impact system is usually modeled as a spring-mass system with amplitude constraint. In a number of studies, one degree of freedom (1-DOF) has been used. Impact gives rise to nonlinearity and discontinuity so that vibro-impact systems can exhibit rich and complicated dynamic behavior. In recent years, dynamics of mechanical systems with impacts have been the subject of several investigations, and many new theoretical issues have been advanced in research of vibro-impact problems. From the viewpoint of application of impact oscillators, the regularity of their motion is of special importance. Therefore, regions of stable regular behaviors of such systems have become an object of extensive studies. Shaw and Holmes analytically determined the stability of periodic solutions and identified chaotic features such as period-doubling, horseshoes and strange attractors. Moon and Shaw considered a single-DOF approach to modeling a vibro-impact cantilever beam experiment, also by reducing the model to a single mode. In this case, the system was considered as piecewise linear, and the single-DOF model was obtained using the Galerkin method applied to each linear part. Further analysis and experimental studies were conducted by Shaw who used a cantilever beam contacting a stiff stop to compare cases of moderate and large stiffness ratios (the ratio between the stiffness of the first beam bending mode and the stiffness at the stop). For the system, high damping to discourage contribution to the response from higher beam modes was considered.

2. CANTILEVER BEAM

2.1. Theoretical Analysis of Cantilever A projected structure, such as a beam, that is supported at one end and carries a load at the other end or along its length is called a cantilever. The natural frequencies and mode shapes for a continuous cantilever beam can be found by using following equations (1) and (2).

(1) And the natural frequencies are given as equation 3.2

(2) The frequencies and mode shapes are shown in Fig. 3.1.

Sreekanth Sura, Alka Sawale and M Satyanarayana Gupta


Figure 1 Frequencies and Mode Shapes for Cantilever Beam

2.2. Vibration Measurement Vibration can be measured by means of time wise displacement, velocity, and acceleration. Transducers, meters, data collectors and real time analysers are some of the tools needed for measuring vibration levels. Accelerometers, velocity transducers and LVDT are some typical transducers used for this purpose. However the signals must be either differentiated or integrated in some cases. In this work accelerometers are used to measure the acceleration of the different masses.

3. CALIBRATION OF THE ACCELEROMETER For calibrating the accelerometer, the following experiment and analysis is performed by fabricating a cantilever beam.

3.1. Experimental Cantilever Analysis The experimental setup for calibration of accelerometer is shown in fig 1. The cantilever is further attached with an accelerometer at the free end (Fig.2) and connected to NI data acquisition (Fig1). The date is analysed by using LABVIEW sound and vibration tool kit.

Figure 2 Experimental setup for cantilever beam



Figure 3 Accelerometer mounted on cantilever beam Figure 4 Data Acquisition Device

Figure 5 Block diagram used for acceleration velocity and displacement data

The raw acceleration plot and further filtered acceleration, velocity and displacement plots of cantilever are shown from Fig 6 to 9.

Figure 6 Raw acceleration Figure 7 Filtered acceleration

Accelerometer



Figure 8 Velocity Figure 9 Displacement

Figure 10 Linear and Logarithmic block diagram

4. RESULTS AND DISCUSSION

4.1. Finite Element Analysis of Cantilever Beam The natural frequencies of the beam (Fig. 1) on linear scale and logarithmic scale are plotted from the finite element analysis are shown in the Fig. 11 and 12



Figure 11 Linear frequency data Figure 12 Logarithmic frequency data

Through the same experimental setup and DAQ analysis, the natural frequencies for the cantilever are plotted on the linear scale and logarithmic scale are shown in Fig. 13 and 14 and the results are plotted.

Figure 13 Linear Frequency data Figure 14 Logarithmic Frequency data

Table 1 A comparison of cantilever Natural frequencies from three different procedures are given below

Natural Frequencies

Theoretical Analysis (Hz)

Experimental Analysis (labview)

(Hz)

FEA Analysis (Hz)

Mode 1 34.102 38 33.38 Mode 1 213.71 206 209 Mode 1 598.41 562 582.41

As we can see the cantilever first three natural frequency results are in fairly good agreement with the given input.

5. CONCLUSIONS A free vibration analysis of cantilever beam is analyzed by using finite element methods in ANSYS. Comparison of theoretical, numerical and experimental results obtained with smaller



difference only less than 10%. The raw acceleration plot and further filtered acceleration, velocity and displacement plots of cantilever are captured and analyzed by using FFT in association with LabVIEW software (National Instruments) the accelerometer. An Experimental study has been presented to validate dynamic values for s cantilever. The frequency data collected from DAQ Analysis are in good agreement that is obtained by using ANSYS software.

6. FUTURE SCOPE The dynamic analyses can be further extended for mechanisms like four bar and switchgear mechanisms. The friction at revolute joints and damping effect of links may be included in the analysis.

REFERENCES [1] Alessandro Gasparetto “On the Modeling of Flexible-Link Planar Mechanisms:

Experimental Validation of an Accurate Dynamic Model” journal of dynamic systems, measurement, and control. JUNE 2004, Vol. 126 / 365.

[2] S. D. Yu and F.Xi “Free Vibration Analysis of Planar Flexible Mechanisms” Contributed by the Design Automation Committee for publication in the journal of mechanical design.rev. Vol. 125, March 2003.

[3] J.Anjaneyulu, G.Venkata Rao and G.Krishna Mohan Rao, "Multi-body dynamic analysis of spring operated mechanism of sf6 switchgear and its validation” international conference in advances in mechanical and building sciences (ICAMB-2012) at VIT University.

[4] C. B. Patel1, P. P. Gohil1 and B. Borhade2” Modelling And Vibration Analysis Of A Road Profile Measuring System” International Journal of Automotive and Mechanical Engineering (IJAME) ISSN: 1985-9325(Print); ISSN: 2180-1606 (Online); Volume 1, pp. 13-28, January-June 2010

[5] Suhas S Vokunnaya, Ravindranatha and Tanaji.Thite, Construction Stage Analysis of Segmental Cantilever Bridge. International Journal of Civil Engineering and Technology, 8(2), 2017, pp. 373–382.

[6] Vikram Anand, A Krishnamoorthy and Radha BP , Analysis on Impact of Height Criterion on the Performance of Vee-Type Folded Plate Cantilever Retaining Wall, International Journal of Civil Engineering and Technology, 8(4), 2017, pp. 422–430

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DYNAMIC ANALYSIS OF CANTILEVER BEAMused a cantilever beam contacting a stiff stop to compare cases of moderate and large stiffness ratios (the ratio between the stiffness of the first