Vibration Analysis Of Stepped Laminated Composite Beam In .
International Journal of Applied Engineering Research ISSN 0973-4562 Volume 14, Number 9, 2019 (Special Issue) Research India Publications. http://www.ripublication.comVibration Analysis of Stepped Laminated Composite Beam in ANSYSAshutosh Kumar PandeyResearch Scholar,Govind Ballabh Pant University of Agriculture & Technology, PantnagarUttarakhand, India.Nitish Kumar SainiAssistant professor, Department of Mechanical EngineeringDev Bhoomi Institute of Technology, DehradunUttarakhand, India.Faraz AhmadAssistant professor, Department of Mechanical EngineeringDev Bhoomi Institute of Technology, DehradunUttarakhand, India.Anadi MisraProfessor, Department of Mechanical EngineeringGovind Ballabh Pant University of Agriculture & Technology, PantnagarUttarakhand, India.AbstractComposite beams and beam like elements are majorconstituents of various structures and are being used widelynow a day. A numerical study using finite element wasperformed to analyze the free transverse vibration response ofcomposite stepped cantilever beam due to transverse crack.Crack is a damage that often occurs in members of structuresand may cause sudden catastrophic failure of the structures.The finite element software ANSYS was used to stimulate thefree transverse vibrations. The parameters studied were theeffects of ply angle of the fibers, the location of cracksrelative to the restricted end, depth of cracks, fiber volumefraction and support conditions. By this research work it wasanalyzed that an increase in the depth of the cracks leads to adecrease in the values of natural frequencies, also cracklocation and support have great effect over natural frequenciesin case of free transverse vibration. The value of naturalfrequency was found to be higher in case of clamped-clampedconfiguration compared to clamped free configuration.Keywords: Composite beam, transverse vibration, compositestepped beam, cantilever beam, catastrophic failure, ply angle,ANSYS, clamped-clamped, clamped-free configuration.1.IntroductionMaterials are too much essential for each and everyindustry. Accessibility of desirable properties such as,improved specific strength, high fatigue strength, flexibility indesign, high impact strength, light weight, dimensionalstability, non-corrosiveness and a wide scope of propertiesmake composites beneficial and crucial in application. Justbecause of attracting properties of the composite materials,these are going to be utilized adequately in infrastructure,marine boats, aerospace industry and avionics industry.Basically, composite materials are characterized asthe materials comprised of at least two materials which mustnot be dissoluble themselves i. e. having considerablydifferent chemical and physical properties. When united, theyshould provide a resultant material with differentcharacteristics from the individual ones. These days almost allalloys and metal products are being replaced with compositematerials because of their high strength to weight proportionand also good forming capabilities. Use of compositematerials in 3D printing as crude materials makes them moredesirable and depicts great extent of composite materials forfuture. After the mechanical insurgency, new materials werecreated depending upon applications like enterprises initiallybegan to use metals and then alloys and these days industriesare concentrating on composite materials because of thedifferent inadequacy of alloys. However, alloys give excellentproperties but because of confinements like Hume-Rotheryrule and other properties composites are considered superiorto them.Generally, composite materials have reinforcementphase and matrix phase. Matrix phase is continuous and usedfor bonding while, reinforcement phase provides strength tocomposites. Plywood, reinforced concrete, fiberglass are someof the perfect examples of composite materials.Vibration analysis is required for practicalapplication of every structure for its better performance. Also,every system has its own permissible limit of naturalfrequency. When the permissible limit is reached or crossesby frequency caused due to external force then sudden failure(catastrophic failure) occurs. To avoid these conditions it isPage 38 of 45
International Journal of Applied Engineering Research ISSN 0973-4562 Volume 14, Number 9, 2019 (Special Issue) Research India Publications. http://www.ripublication.comvery essential to know about the natural frequency of anystructure which has mass and elasticity properties.To prevent failure of any structure which occurs dueto undesired vibrations, it is important to determine;1. Natural frequencies, for avoiding the resonancecondition.2. Damping factors.3. Mode shapes for establishing the most versatileindicators or to choose the right position so thatweight can be decreased or to increase damping.2.Reviews on vibrations of cracked compositebeamsNikpur et al. obtained the local compliance matrix for thecomposite materials which were unidirectional. It wasconcluded that the interlocking deflection modes wereimproved as a purpose of degrees of anisotropy of compositesOstachowicz et al. offered a technique to examine the impactof two surface cracks which were open upon the frequenciesfor the flexural vibrations on a cantilever beam. Here twocategory of cracks (double sided and single sided) wereanalyzed. Double-sided cracks occur when there is cyclicloading and occurrence of single-sided cracks is an outcomeof fluctuating loading. The assumption of occurrence ofcracks in the primary modes of fracture which is also calledopening mode was also taken.Krawczuk et al. originated a new beam finite element alongwith a solitary non- propagating one-edge open crackpositioned at its mid-length for the static and dynamicobservations of the structures like cracked composite beams.This component had 2 degrees of freedom at each of the threenodes: deflection in transverse direction and an autonomousrotation individually. The ideal numerical examinationsexplaining variations in the static alterations and a basicnatural frequency of composite cantilever bars caused by asingle crack were presented.Zak et al. formulated the work models of a finite elementdelaminated beam and delaminated plate component. A broadpractical investigation was conceded out to record variationsin the 1st three bending natural frequencies because ofdelamination. The outcomes of the mathematical calculationswere almost same as the outcomes of the experimentalobservations.Banerjee (2001) obtained exact terms for the frequencyequations and mode shape of Timoshenko composite beamhaving cantilever end conditions in open analytical form usingfigurative calculations. Influence of material coupling inbetween torsional and bending modes of buckling,accompanied by the impact of shear deformation and rotatinginertia was taken into consideration while formulation of thetheory. The expressions analyzed for the mode shapes werealso resulting in explicit form using figurative computation.Wang et al. examined the vibrations of a circular shapedplate surface reinforced by two piezoelectric layers,considering the Kirchhoff plate model. The nature of theelectric potential field in the piezoelectric layer was expectedto be like that of the Maxwell electricity produced via frictioncondition. The theoretical model was approved by contrastingthe frequencies of resonance of the piezoelectric coupledround plate acquired by the hypothetical model and thoseacquired by limited component examination. The modeshapes of the electrical potential acquired from free vibrationexamination was appeared to be non-uniform for most of thepart. The piezoelectric layer was appeared to affect thefrequencies of the structure. The proposed display for theexamination of a coupled piezoelectric plate gave a way toacquire the conveyance of electric potential in thepiezoelectric layer. The model gave a plan reference forapplying piezoelectric material, for example, an ultrasonicengine.Gaith et al. executed vibration theory of a continuouslycracked beam for lateral vibration of cracked Euler –Bernoulli beam having one-edge open cracks. Crack detectionfor simply supported graphite/epoxy fiber-reinforcedcomposite beam was taken into account. The impact of crackdepth, crack position, faction of fiber volume and its directionon the elasticity and therefore on natural frequency and modeshapes for cracked fiber- reinforced composite beam wasexamined.Lu and Law et al. analyzed the impact of multiple cracks inthe finite beam element by the help of dynamic analysis andlocal crack detection. The beam element was originated by thecomposite element technique with a one-member – oneelement relationship with cracks where the interactive effectamong cracks in the same component was included itself. Theaccuracy and convergence speed of the planned model inaddition were validated with the use of existing models andexperimental outcomes. The need of adjustment was find outby the crack parameters when this planned model was used.3. Material and Methods3.1. Governing EquationUnder the situation of mid-plane symmetry bending abeam ( 𝑗 0) means there is no displacement undertransverse shear and no combine effect of stretchingbending (𝜀𝑥𝑧 0 ), the differential governing equation isgiven by,IS11 q(X)(1)In general composite material is assumed as orthotropicin nature the above expression is for orthotropic material.For an isotropic beam having rectangular cross-section: 𝐼𝑆11 𝐸I.In the present analysis under the above governing equationconditions the effect of Poisson’s ratio is ignored in beamtheory as taken by Vinson & Sierakowski (1991). Staticforce is assumed in force per unit length in the equation (1).By applying D’Alembert’s Principle, product of mass andacceleration per unit length term is added in the aboveexpression then the expression becomes,IS11 q(x,t)- 𝜌𝐴(2)Both 𝜔 and q in the above expression are depends on timePage 39 of 45
International Journal of Applied Engineering Research ISSN 0973-4562 Volume 14, Number 9, 2019 (Special Issue) Research India Publications. http://www.ripublication.comand space means both are function of time and space, thusused derivatives are partial derivatives, ρ is density of beamA is cross-sectional area of the beam. The term q(x, t) usedin the above expression is varying time space dependentforcing function which is as a result of dynamic response.The response is possibly the result of intense-one timeimpact or harmonic oscillation.The formula for moment of inertia in case of steppedbeam is given as follows, which is used to calculate momentof inertia in classical method.Leq (3)It is required to know about the natural frequencies of beamin different boundary conditions to make sure that there mustnot be any cyclic forcing function nearer to the naturalfrequencies value. The cyclic forcing function possiblybecause of sudden failure (catastrophic failure) of thestructure. For finding the natural frequency the expression inradian/unit time is given by,𝜔𝑛 𝛼2 𝐼𝑆11/𝜌𝐴𝐿4Steps of Simulation in ANSYS APDLIn General procedure of simulation inANSYS is independent to the analysis. It followssame steps in all type of analysis which are givenbelow:1. Pre-processing2. Solution stage3. Post-processing3.3. Description of used elementsSolid shell type of element is used in the present analysiswhich shows two merge properties of shell element andsolid element. Solid shell 190 (SOLSH 190) element isused in the present analysis(4)In the above expression 𝛼2 is co-efficient which is specifiedby Warburton et al. For finding the natural frequencyexpression in cycles per unit time (Hertz) is given byfn (5)For free vibration condition Governing equation whichgoverns of the beam is given by[𝐾] 𝜔2[𝑀]{𝑞} 0In above above expression,K Stiffness Matrixq Degree of FreedomM Mass Matrix3.2. Model of BeamIn the present, analysis a prismatic cantilevercomposite stepped beam of rectangular cross-section is usedwhich have a transverse crack at a distance 𝐿1 from the fixedend, and a depth of crack ‘a’. In the present model of beamcrack is transverse crack having V-shape. Length (L) andheight (H) and width (B) towards the right side of the beamis shown in fig. 3.1. All the fibers are assumed to be orientedat an angle ө.Fig. 3.1 Labelled layout of composite stepped beam withtransverse crack in clamped-free configuration.Fig. 3.2. Geometry of SOLSH 190 elementTable 3.1. Properties of Boron EpoxyYoung’s Modulus(GPa)Modulus of Rigidity(GPa)Poisson's RatioMass 3.750.30.212502700Where m & f represents the properties of matrix and fiberrespectively.4. Results and DiscussionsFirst of all validation is done for Graphite polyamide andresults are compared with Krawczuck & Ostachowicz forperfect cantilever unidirectional composite beam.Fig.4.1. Ply Orientation Angle (θ) as a factor for first threedimensionless natural frequencies of perfect cantilevercomposite beam for Fiber Volume Ratio (V) 0.1Page 40 of 45
International Journal of Applied Engineering Research ISSN 0973-4562 Volume 14, Number 9, 2019 (Special Issue) Research India Publications. http://www.ripublication.comEffect of various factors on natural frequenciesEffects of various factors like beam length (L), supportboundary conditions, Fiber Volume Ratio (V) and influence ofPly Orientation Angle on first three lowest Nat. Freq. areinvestigated.4.1. Analysis for vibration behavior of unidirectionalcomposite stepped perfect beamFig. 4.4. Fiber Volume Ratio (V) as a factor for seconddimensionless Nat. Freq. of a single crackedunidirectional composite stepped cantilever beamof boron epoxy4.3. Influence of Ply Orientation Angle on naturalfrequencies for Crack Position 0.3Fig. 4.2 Analysis for vibration behavior of unidirectionalcomposite stepped cantilever beam with singletransverse crack4.2. Analysis for vibration behaviour of unidirectionalcomposite stepped cantilever beam with singletransverse crack4.2.1. Influence of Fiber Volume Ratio on naturalfrequencies for different relative crack depth0.3, 0.6 and 0.9 (Crack PositionL1/L 0.2)Fig. 4.5. Ply Orientation Angle as a function of Nat. Freq.for boron epoxy beam for Fiber Volume Ratio(V 0.1)4.3. Influence of support condition on naturalfrequencies for different Ply Orientation Angle offibers (Fiber Volume Ratio V 0.5)(a) Influence on perfect stepped beamFig. 4.3. Fiber Volume Ratio (V) as a factor for firstdimensionless natural frequency of a single crackedunidirectional composite stepped cantilever beam ofboron epoxyFig. 4.6. Different boundary conditions as a factor for firstdimensionless natural frequencies of perfectstepped beam of boron epoxyPage 41 of 45
International Journal of Applied Engineering Research ISSN 0973-4562 Volume 14, Number 9, 2019 (Special Issue) Research India Publications. http://www.ripublication.comFig. 4.7. Different boundary conditions as a factor for seconddimensionless natural frequencies of perfect steppedbeam of boron epoxyFig. 4.8. Different boundary conditions as a factor for thirddimensionless natural frequencies of perfectstepped beam of boron epoxy(b) Influence on beam with relative crack depth .2Fig. 4.10. Different boundary conditions as a factor forsecond dimensionless natural frequencies ofcomposite stepped beam with crack of boron epoxyFig. 4.11. Different boundary conditions as a factor for thirddimensionless natural frequencies of compositestepped beam with crack of boron epoxy4.4. Influence of Crack Position on Nat. Freq.(a) For clamped-free configuration in stepped beamFig. 4.9. Different boundary conditions as a parameter forfirst dimensionlessnatural frequencies ofcomposite stepped beam with crack of boron epoxyFig. 4.12. Crack Positions a factor for first dimensionlessNat. Freq. of stepped beam for different relativecrack depth ratios for boron epoxyPage 42 of 45
International Journal of Applied Engineering Research ISSN 0973-4562 Volume 14, Number 9, 2019 (Special Issue) Research India Publications. http://www.ripublication.com5. SUMMARY AND CONCLUSIONFig. 4.13. Crack Positions a factor for second dimensionlessNat. Freq. of stepped beam for different relativecrack depth ratios for boron epoxy1.Generally, with increase in the ply orientation angleof fibers under the bending condition the values ofnatural frequency decreases at 0 orientation angleof fibers t the natural frequency has maximumvalue and then with the increase of ply angle offibers it starts decreasing progressively, then at 90 natural frequency has minimum value.2.For composite stepped beam with crack ofunidirectional fibers, the value of natural frequencyincreases with the increase in the value of the angleof orientation at 90 natural frequency hasmaximum value and minimum value of naturalfrequency is at 0 .3.The beam with crack becomes more flexible for thevalue of fiber volume fraction was in between 0.2to 0.8 and maximum values of flexibility has seenat the value of fiber volume fraction V 0.5.4.The value of natural frequencies is highest for thecrack locations L1/L 0.1 and L1/L 0.9, the valueof first natural frequency is lowest at L1/L 0.15and second natural value is lowest at L1/L 0.55.5.It is clear by the present investigation for clampedclamped configuration first natural frequency haslowest value for crack location of 0.5 and highest atthe end points of beam. For second naturalfrequency lowest value is obtained at 0.3 and 0.7which are approximately same.(b) For clamped-clamped configuration in stepped beamFig. 4.14. Crack Positions a factor for first dimensionless Nat.Freq. of stepped beam for different relative crackdepth ratios for boron epoxyFig. 4.15. Crack Positions a factor for second dimensionlessNat. Freq. of stepped beam for different relative crack depthratios for boron epoxyReferences[1] Abedi, M., 2016. Viscoelastic Characterization ofOut-of-AutoclaveCompositeLaminates:Experimental and Finite Element Studies (Doctoraldissertation, Concordia University).[2] Banerjee, J.R., 2001. Frequency equation and modeshape formulae for composite Timoshenkobeams. Composite Structures, 51(4), pp.381-388.[3] Bao, G., Ho, S., Suo, Z. and Fan, B. 1992. The roleof material orthotropy in fracture specimens forcomposites. International Journal of Solids andStructures, 29(9):1105-1116.[4] Chondros, T.G., Dimarogonas, A.D. and Yao, J.1998. Longitudinal vibration of a continuous crackedbar. Engineering Fracture Mechanics, 61(5):593606.[5] Chondros, T.G., Dimarogonas, A.D. and Yao, J.1998. Longitudinal vibration of a bar with abreathing crack. Engineering Fracture Mechanics,61(5):503-518.Page 43 of 45
International Journal of Applied Engineering Research ISSN 0973-4562 Volume 14, Number 9, 2019 (Special Issue) Research India Publications. http://www.ripublication.com[6] Das, H.C. and Parhi, D.R. 2009. Detection of thecrack in cantilever structures using fuzzy gaussianinference technique. AIAA J, 47(1):105-125.[7] Gaith, M.S. 2011. Nondestructive health monitoringof cracked simply supported fiber-reinforcedcomposite structures. Journal of Intelligent MaterialSystems and Structures, 22(18):2207-2214.[8]Gaith, M.S., Zaben, A., Bawayah, N., Israwi, Y. andFarraj, M.A. 2010. On Line Health Monitoring forCracked Simply Supported Fiber ReinforcedComposite Structures. In ASME 2010 Conference onSmart Materials, Adaptive Structures and IntelligentSystems (pp. 649-655). American Society ofMechanical Engineers.[9] Ganesan, R. and Zabihollah, A. 2007. Vibrationanalysis of tapered composite beams using a higherorder finite element. Part II: parametric study.Composite Structures, 77(3):319-330.[10] Ghoneam, S.M. 1995. Dynamic analysis of opencracked laminated composite beams. CompositeStructures, 32(1-4):3-11.[11] Hamada, A.A.E.H. 1997. An investigation into theeigen-nature of cracked composite beams. CompositeStructures, 38(1-4):45-55.[12] Karaagac, C., Ozturk, H. and Sabuncu, M. 2013.Effects of
Generally, composite materials have reinforcement phase and matrix phase. Matrix phase is continuous and used for bonding while, reinforcement phase provides strength to composites. Plywood, reinforced concrete, fiberglass are some of the perfect examples of composite materials. Vibration analysis is required for practical
in case of free transverse vibration. The value of natural frequency was found to be higher in case of clamped-clamped configuration compared to clamped free configuration. Keywords: Composite beam, transverse vibration, composite stepped beam, cantilever beam, catastrophic failure, ply angle, ANSYS, clamped-clamped, clamped-free configuration. 1.
effects of shear deformation on the free vibration of an orthotropic cantilever beam, studying the free vibration analysis of orthotropic clamped free beams, using the Euler-Bernoulli beam theory without including the effect of shear deformation. Free vibration analysis of a cross-ply laminated co
on different levels of analysis of laminated composite plates. The previous work has been concerned with the linear analysis (Cetkovic et al. 2009), and the linear laminated plate element of GLPT has been formulated, while in the present paper the GLPT nonlinear laminated plate element with von Karman geometrical nonlinearity is presented.
The vibration analysis in Section 5 provides the FE-based vibration analysis procedure based on first principles direct calculations. The FE-based vibration analysis is recommended to evaluate the design during the detail design stage. If found necessary, the local vibration is tobe addressed in the detail vibration analysis. The
superstructures that use timber structural components. The lon-gitudinal deck systems included in all codes are spike-laminated, glued–laminated (glulam), and stress-laminated superstructures. The transverse deck systems on beam girders included in both codes are planks, nail-laminated, glulam panels, and concrete slabs. Specific
For the design of steel-concrete composite sections, the effective flange width . panels and stress-laminated timber bridges. The research on the former is a case study on stress-laminated timber bridges consisting of laminated deck sections combined with glued-laminated timber . Euro-Code (2000) be is the smallest of: (1) Beam span/4 (2 .
Structural Glued Laminated Timber in Religious Structures showcases several outstanding structures with laminated timber framing. Glued laminated timber trusses, beams and arches are used to provide efficient enclosures for expansive areas such as gymnasiums, educational and recreational facili-ties, indoor pools, auditoriums and shopping centers.
Walters & Sons STP. This research led to the subsequent design of the STP-laminated girder (figure 5c) as a potential replacement for the nail-laminated design being used by Jack Walters & Sons (figure 5b) The advantage of the STP-laminated girder design is that STPS not only replace th
