stiffness analysis for beams delaminated

free stiff analysis

1. STIFFNESS ANALYSIS OF COMPOSITE BEAMS USING ROLLER CLAMPS 1

2. Demand for innovative materials with desired properties and cost effectiveness is of growing concern- Monolithic materials have limitations in achieving combination of mechanical properties. Composites to be a viable solution- Higher strength to weight ratio, Light weight, anticorrosion properties, design flexibilities & durability. Type of composites used varies depending upon the type of applications- Particle reinforced,fibre reinforced and structural composites. Challenges in study of composites- Owing to its distinct mechanical properties and failure conditions INTRODUCTION 2

3. UNDERSTANDINGS FROM STUDY Metal-matrix beams widely find applications because of induced damping properties of adhesives. Composite beams provide enough stiffness in longitudinal direction compared to transverse directions. The natural frequencies is minimum for clamped-free boundary condition of laminate composite beams on comparison with other boundary conditions. Composite materials often tends to fail by delamination pattern For instance in 1999,America’s cup boat “Young America“ broke in to two due to delamination of its composite sandwich structure. 3

4. STATEMENT AND OBJECTIVE Mechanical phenomenon may cause noise, instabilities may develop resonance, which improve deflections and failure Therefore studies have to be made and the possibilities to prevent these effects of vibration have to be found out, in an economical way. Introduction of roller clamps - Investigate its effect on the stiffness and natural frequencies of composite beam under free vibration. Location of roller clamps- Study on the effect of location of the roller clamps along the length of composite beam 4

5. METHODOLOGY 5 The free vibration study is simulated on metal matrix stacked composite beam owing to its experimental easiness and wide applications. Numerical simulation is done under classical cantilever boundary condition Material properties are taken from published literatures. The equivalent forces and moments created due to bolt preloads of clamping are evaluated and applied on the model. The dimensions of roller clamps and bolts are chosen in such a way that their masses are considered negligible in this study. ANSYS APDL is used for numerical modelling and simulation of free vibration. Eigen values obtained is analysed to understand its dynamic behavior.

6. METHODOLOGY 6 The free vibration of Graphite-epoxy composite cantilever beam was studied analytically by Y.Teboub and P.Hajela using Shear deformation theory [5] . The design model comprising of 30/50/30/50 fibre oriented stacked composite beam is validated using ANSYS APDL solver for obtaining natural frequencies. The maximum deviation between calculations is 11 percent. Fig 1: Graphical comparison on validation

7. DESIGN OF COMPOSITE BEAM WITH ROLLER CLAMP 7 Roller Clamps Free end Fixed end The effectiveness of clamping is studied on five layered Aluminium-Epoxy laminate composite beam stacked together as sandwich Fig 2: Side view of composite cantilever beam with roller clamps

8. 8 DESIGN OF COMPOSITE BEAM WITH ROLLER CLAMP Fig 3: a) Isometric view of composite cantilever beam with roller clamps b) Top view of composite cantilever beam with roller clamps a) b )

9. 9 MATERIAL PROPERTIES Materials Properties Source Dimensions Aluminium E=70GPa Poisson ratio:0.3 Density:2700 kg/m 3 Standard Metal mechanical properties 50*3*0.23cm each 3 layered Araldite Epoxy Adhesive K=3.792GPa Poisson ratio:0.398 Density:1000 kg/m 3 Araldite Standard Epoxy Technical data sheet, Mechanics of composite materials,Autar.K.Kaw 50*3*0.05cm Roller clamps Aluminium E=70GPa Poisson ratio:0.3 Standard Metal mechanical properties Outer diameter:1.7cm Thickness:1mm Length:7 cm

10. NUMERICAL ANALYSIS 10 F Z M x M x h l In plane displacements ux,uy Transverse displacement uz Fig 4: 2D finite element model of composite beam with clamps

11. 11 NUMERICAL ANALYSIS Parameters Conditions/Values Element quality 2D FEA model, 600 SHELL 181 4 node (for composites) Solver Mechanical APDL Element edge length(Mesh size) 5 mm Boundary condition Cantilever beam with roller clamps Condition prevailing at the plane of clamping In-plane d isplacements u x ,u y equals zero, while transverse displacement u z is set free Pretension load for each bolt (Standard M3 bolt) ( F z ) 733 N Load applicable at the line of contact of clamps Uniformly Distributed Load of 488 N/cm Moments created due to the pretension load (Mx) Moment about X-axis = 7.33 Nm Clamping length to total length ratio (h/l) Varied for clamping lengths 10,20,30 and 40 cms

12. Modes Frequencies of composite cantilever beam without roller clamps(Hz) Frequencies of composite cantilever beam with roller clamps(Hz) h/l = 0.2 h/l = 0.4 h/l = 0.598 h/l = 0.8 1 94.376 147.36 164.44 164.44 164.44 2 162.70 164.44 261.11 457.72 457.1 3 443.85 457.72 457.72 582.66 670.57 4 500.82 670.52 670.57 670.57 889.49 5 594.4 889.49 889.49 889.9 909.80 RESULTS 12

13. RESULTS 13

14. RESULTS Enhancement of stiffness and natural frequencies -The inclusion of clamps over the composite beam has minimized the transverse nodal displacement in z direction 14 Fig 6 : Transverse nodal displacement uz at plane of clamping

15. 15 Fig 6: Mode shapes a) Unclamped condition, 162.7Hz b) h/l = 0.2, 164.44 Hz RESULTS

16.   Fig 7: Mode shapes c) h/l = 0.4 , 261.11 Hz d) h/l = 0.598 , 457.7 Hz 16 RESULTS

17. KEY FINDINGS Relevance- Clamping has brought significant effect over the dynamic behavior of a composite beam Range of increment- The frequency increment varies for different modes, for instance in fundamental mode and first harmonics the range is from 35-40 % and 2-64% depending on h/l ratio between 0 and 1 Behavioral characteristic- The percent increase of natural frequencies showed steep rise for fundamental modes of h/l ratio between 0-0.4 Variation along the length- The natural frequencies tends to increase with increased clamping length and tends to have lesser effect when h/l ratio tends to 1,showing that the influence of roller clamps is less dominant. 17

18. CONCLUSION AND FUTURE SCOPE The numerical simulation results conclude that the comprisal of clamps in composite beam has invoked changes in its natural frequencies. The current study is limited to free vibration under clamped free boundary conditions, which may be analysed for other boundary conditions also. Multiple clampings may bring out better results. This study also allows to further investigate on the stiffness analysis of composite beams with roller clamps subjected to delaminations. The study on delaminations with roller clamps may bring out a simple way to sort out the problems of gradually decreasing stiffness with time 18

19. REFERENCES 19 Autar K Kaw, Mechanics of Composite Materials (Taylor and Francis Group, London, 2006), pp.4-28. Hassan Callioglu and Gokmen Atlihan ,”Vibration analysis of delaminated composite beams using analytical and FEM models”, International Journal of Engineering & Material Sciences,Vol-18,February 2011,pp 7-14 V.Vita , J.de Carvalho and J. Lirani ,”Theoretical and Experimental Dynamic Analysis of Fiber Reinforced Composite Beams”, 15th Brazilian Congress of Mechanical Engineering, Vol XXV, No 3, 2003 Y.Teboub & P.Hajela, “Free vibration of generally layered composite beams using symbolic computations”,Composite structures 33(1995) 123-134,Elsevier Hardeep Singh,Er.Sanpreet Singh,Dr.Gurpreet Singh, “Evaluation Of Free Vibration Characteristics Of Cantilever Beams Made From Different Materials, National Conference on Advances in Engineering, Technology & Management(AETM 2015),IOSR-Journal Of Mechanical And Civil Engineering,pp 32-42

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