EFFECTS OF INFILL WALLS ON FREE VIBRATION CHARACTERISTICS OF MULTI-STOREY FRAMES USING DYNAMIC STIFFNESS METHOD

Yıl 2019, Cilt: 37 Sayı: 3, 885 - 902, 01.09.2020

Baran Bozyigit Yusuf Yesilce

Öz

This study aims to obtain exact natural frequencies and mode shapes of infilled multi-storey frames using single variable shear deformation theory (SVSDT) which considers parabolic transverse shear stress distribution across the cross-section. The effects of infill walls on free vibration characteristics are investigated for different frame models such as one storey infilled, soft storey and fully infilled. The infill walls are modeled using equivalent diagonal strut approach. Natural frequencies are calculated via dynamic stiffness formulations for different wall thickness values. The results of SVSDT are tabulated with Euler-Bernoulli beam theory (EBT) and Timoshenko beam theory (TBT) results. Additionally, finite element solutions are presented to verify the natural frequencies that obtained from dynamic stiffness formulations. The results show that SVSDT can be used effectively for free vibration analysis of infilled frame structures by using dynamic stiffness formulations. The numerical analyses show that the effects of shear deformation and rotation inertia become observable for higher modes of infilled frame structures. It is seen from the results that ignoring effects of infill walls may cause significant errors on calculation of natural frequencies of frames.

Anahtar Kelimeler

Infilled frame, mode shape, natural frequency, single variable shear deformation theory

Kaynakça

• [1] Polyakov S.V., (1950) Investigation of the strength and of the deformational characteristics of masonry filler walls and facing on framed structures, Construction Industry Instıtute 3.
• [2] Holmes M., (1961) Steel Frames with brick work and concrete infilling, Proceedings of Institution of the Civil Engineers 19, 473-478.
• [3] Holmes M., (1963) Combined Loading on Infilled Frames, Proceeding of The Institution of Civil Engineers 25, 31-38.
• [4] Stafford S.B. and Carter C., (1969) A method of analysis for infill frames, Proceedings of the Institution of Civil Engineers 44(1), 31-48.
• [5] Mainstone R.J., (1974) Supplementary Note on the Stiffness and Strenght of Infilled Frame, Building Research Establishment, London, England.
• [6] El-Dakhakhni W.W., Elgaaly M. and Hamid A.A., (2003) Three-Strut Model for Concrete Masonary-Infilled Steel Frames, Journal of Structural Engineering 129(2), 177-185.
• [7] Eurocode 6, (1996) Design of masonry structures-Part 1-1: General rules for reinforced and unreinforced masonry structures, European Committee for Standardization, Brussels, Belgium.
• [8] FEMA-356, (2000) Prestandard and commentary for the seismic rehabilitation of buildings, Federal Emergency Management Agency, Washington, DC.
• [9] TSDC, (2007) Turkish seismic design code, Ministry of Public Works and Settlement, Ankara, Turkey.
• [10] Reflak J. and Fajfar P., (1991) Elastic analysis of infilled frames using substructures, 6th Canadian Conf. on Earthquake Engineering, University of Toronto Press, Toronto.
• [11] Mohebkhah A., Tasnimi A.A. and Moghadam H.A., (2008) Nonlinear analysis of masonry-infilled steel frames with openings using discrete element method. Journal of Constructional Steel Research 64(12), 1463-1472.
• [12] Mondal G. and Jain S.K., (2008) Lateral stiffness of masonry infilled reinforced concrete (RC) frames with central opening, Earthquake Spectra 24(3), 701-723.
• [13] Stavridis A. and Shing P.B., (2010) Finite-element modeling of nonlinear behavior of masonry-infilled RC frames, Journal of Structural Engineering 136(3), 285-296.
• [14] Moaveni B., Stavridis A., Lombaert G., Conte J.P. and Shing P.B., (2013) Finite-element model updating for assessment of progressive damage in a 3-story infilled RC frame, Journal of Structural Engineering 139(10), 1665-1674.
• [15] Ozturkoglu O., Ucar T. and Yesilce Y., (2017) Effect of masonary infill walls with openings on nonlinear response of reinforced concrete frames, Earthquakes and Structures 12(3), 333-347.
• [16] Asteris P.G., Antoniou S.T., Sophianopoulos D.S. and Chrysostomou C.Z., (2011) Mathematical macromodelling of infilled frames: State of the Art, Journal of Structural Engineering 137(12), 1508-1517.
• [17] Asteris P.G., Chrysostomou C.Z., Giannopoulos I.P. and Smyrou E., (2011) Masonry infilled reinforced concrete frames with openings, COMPDYN 2011, III ECCOMAS Thematic Conference on Computational Methods in Structural Dynamics and Earthquake Engineering, Greece.
• [18] Asteris P.G., Cotsovos D.M., Chrysostomou C.Z., Mohebkhah A. and Al-Chaar G.K., (2013) Mathematical micromodeling of infilled frames: State of the Art, Engineering Structures 56, 1905-1921.
• [19] Thiruvengadam V., (1985) On the natural frequencies of infilled frames, Earthquake Engineering and Structural Dynamics 13, 401- 419.
• [20] Chaker A.A. and Cherifati A., (1999) Influence of Masonary Infill Panels On The Vibration and Stiffness Characteristics of R/C Frame Building, Earthquake Engineering and Structural Dynamics 28, 1061-1065.
• [21] Thambiratnam D., (2009) Modelling and Analysis of Infilled Frame Structures Under Seismic Loads, The Open Construction and Building Technology Journal 3, 119-126.
• [22] Tamboli H.R. and Karadi U.N., (2012) Seismic Analysis of RC Frame Structure with and without Masonary Infill Walls, Indian Journal of Natural Sciences 3(14), 1137-1194
• [23] Manju G., (2014) Dynamic Analysis of Infills on R.C Framed Structures, International Journal of Innovative Research in Science, Engineering and Technology 3(9), 16150-16158.
• [24] Beiraghi H., (2016) Fundamental period of masonry infilled moment-resisting frame buildings, The Structural Design of Tall and Special 26(5), 1-10.
• [25] Crowley H. and Pinho R., (2004) Period-height relationship for existing European reinforced concrete buildings, Journal of Earthquake Engineering 8(1), 93-119.
• [26] Crowley H. and Pinho R., (2006) Simplified equations for estimating the period of vibration of existing buildings, Proceedings of the First European Conference on Earthquake Engineering and Seismology, Geneva.
• [27] Amanat K.M. and Hoque E., (2011) A rationale for determining the natural period of RC building frames having infill, Engineering Structures 28(4), 495-502.
• [28] Asteris P.G., Repapis C.C., Cavaleri L., Sarhosis V. and Athanasopoulou A., (2015) On the fundamental period of infilled RC frame buildings, Structural Engineering and Mechanics 54(6), 1175-1200.
• [29] Asteris P.G., Repapis C.C., Tsaris A.K., Di Trapani F. and Cavaleri L., (2015) Parameters affecting the fundamental period of infilled RC frame structures, Earthquakes and Structures 9(5), 999-1028.
• [30] Asteris P.G., Repapis C.C., Foskolos F., Fotos A. and Tsaris A.K., (2017) Fundamental period of infilled RC frame structures with vertical irregularity, Structural Engineering and Mechanics 61(5), 663-674.
• [31] Asteris P.G., Repapis C.C., Repapi E.V. and Cavaleri L., (2017) Fundamental period of infilled reinforced concrete frame structures, Structure and Infrastructure Engineering 13 (7), 929-941.
• [32] Asteris P.G., Cavaleri L., Di Trapani F. and Tsaris A.K., (2017) Numerical modelling of out-of-plane response of infilled frames: State of the art and future challenges for the equivalent strut macromodels, Engineering Structures 132, 110-122.
• [33] Nikolakopoulos P.G., Katsareas D.E. and Papadopoulost C.A., (1997) Crack identification in frame structures, Computers and Structures 64(1-4), 389-406.
• [34] Wu J.J., (2008) Transverse and longitudinal vibrations of a frame structure due to a moving trolley and the hoisted object using moving finite element, International Journal of Mechanical Sciences 50, 613-625.
• [35] Minghini F., Tullini N. and Laudiero F., (2010) Vibration analysis of pultruded FRP frames with semi-rigid connections, Engineering Structures 32, 3344-3354.
• [36] Mehmood A., (2015) Using finite element method vibration analysis of frame structure subjected to moving loads, International Journal of Mechanical Engineering and Robotics Research 4(1), 50-65.
• [37] Paola M.D. and Scimemi G.F., (2016) Finite element method on fractional visco-elastic frames, Computers and Structures 164, 15-22.
• [38] Ozel H.F., Saritas A. and Tasbahji T., (2017) Consistent matrices for steel framed structures with semi-rigid connections accounting for shear deformation and rotary inertia effects, Engineering Structures 137, 194-203.
• [39] Mei C., (2012) Free vibration analysis of classical single-storey multi-bay planar frames, Journal of Vibration and Control 19(13), 2022-2035.
• [40] Labib A., Kennedy D. and Featherstone C., (2014) Free vibration analysis of beams and frames with multiple cracks for damage detection, Journal of Sound and Vibration 333, 4991-5003.
• [41] Lien T.V. and Hao T.A., (2014) Determination of the Shape function of a Multiple Cracked Beam Eement and Its Application for the Free Vibration Analysis of a Multiple Cracked Frame Structure, American Journal of Civil Engineering and Architecture 2(1), 12-25.
• [42] Mei C. and Sha H., (2016) Analytical and experimental study of vibrations in simple spatial structures, Journal of Vibration and Control 22(17), 3711-3735.
• [43] Bozyigit B. and Yesilce Y., (2018) Investigation of natural frequencies of multi-bay and multi-storey frames using single a variable shear deformation theory, Structural Engineering and Mechanics 65(1), 9-17.
• [44] Banerjee J.R., (1997) Dynamic stiffness for structural elements: A general approach, Computers and Structures 63, 101-103.
• [45] Li J., Chen Y. and Hua H., (2008) Exact dynamic stiffness matrix of a Timoshenko three-beam system, International Journal of Mechanical Sciences 50, 1023-1034.
• [46] Bao-hui L., Hang-shan G., Hong-bo Z., Yong-shou L. and Zhou-feng Y., (2011) Free vibration analysis of multi-span pipe conveying fluid with dynamic stiffness method, Nuclear Engineering and Design. 241, 666-671.
• [47] Banerjee J.R., (2012) Free vibration of beams carrying spring-mass systems – A dynamic stiffness approach, Computers and Structures 104-105, 21-26.
• [48] Damanpack A.R. and Khalili S.M.R., (2012) High-order free vibration analysis of sandwich beams with a flexible core using dynamic stiffness method, Composite Structures 94, 1503-1514.
• [49] Banerjee J.R., Jackson D.R., (2013) Free vibration of a rotating tapered Rayleigh beam: A dynamic stiffness method of solution, Computers and Structures 124, 11-20.
• [50] Tounsi D., Casimir J.B., Abid S., Tawfik I. and Haddar M., (2014) Dynamic stiffness formulation and response analysis of stiffened shells, Computers and Structures 132, 75-83.
• [51] Su H. and Banerjee J.R., (2015) Development of dynamic stiffness method for free vibration of functionally graded Timoshenko beams, Computers and Structures 147, 107-116.
• [52] Li J., Wang S., Li X., Kong X. and Wu W., (2015) Modeling the coupled bending-torsional vibrations of symmetric laminated composite beams, Archive of Applied Mechanics 85, 991-1007.
• [53] Liu X. and Banerjee J.R., (2016) Free vibration analysis for plates with arbitrary boundary conditions using a novel spectral-dynamic stiffness method, Computers and Structures 164, 108-126.
• [54] Casimir J.B., Khadimallah M.A. and Nguyen M.C., (2016) Formulation of the dynamic stiffness of a cross-ply laminated circular cylindrical shell subjected to distributed loads, Computers and Structures 166, 42-50.
• [55] Bozyigit B. and Yesilce Y., (2016) Dynamic stiffness approach and differential transformation for free vibration analysis of a moving Reddy-Bickford beam, Structural Engineering and Mechanics 58(5), 847-868.
• [56] Li J., Xiang H. and Li X., (2016) Free vibration analyses of axially loaded laminated composite beams using a unified higher-order shear deformation theory and dynamic stiffness method, Composite Structures 158, 308-322.
• [57] Li J., Bao Y. and Hu P., (2017) A dynamic stiffness method for analysis of thermal effect on vibration and buckling of a laminated composite beam, Archive of Applied Mechanics 87(8), 1295-1315.
• [58] Náprstek J. and Fischer C., (2017) Investigation of bar system modal characteristics using Dynamic Stiffness Matrix polynomial approximations, Computers and Structures 180, 3-12.
• [59] Trong D.X. and Khiem N.T., (2017) Modal Analysis of Tower Crane with Cracks by the Dynamic Stiffness Method, Topics in Modal Analysis and Testing 10, 11-22.
• [60] Bozyigit B. and Yesilce Y., (2018) Natural frequencies and harmonic responses of multi-storey frames using single variable shear deformation theory, Mechanics Research Communications 92, 28-36.
• [61] Banerjee J.R. and Ananthapuvirajah A., (2018) Free vibration of functionally graded beams and frameworks using the dynamic stiffness method, Journal of Sound and Vibration 442, 34-47.
• [62] Han S.M., Benaroya H. and Wei T., (1999) Dynamics of transversely vibrating beams using four engineering theories, Journal of Sound and Vibration 225(5), 936-988.
• [63] Levinson M., (1981) A new rectangular beam theory, Journal of Sound and Vibration 74, 81-87.
• [64] Bickford W.B., (1982) A consistent higher order beam theory, Development in Theoretical and Applied Mechanics 11, 137-150.
• [65] Reddy J.N., (1984) A simple higher-order theory for laminated composite plates, Journal of Applied Mechanics 51,745-752.
• [66] Heyliger P.R. and Reddy J.N., (1988) A higher order beam finite element for bending and vibration problems, Journal of Sound and Vibration 126, 309-326.
• [67] Li J., Wu Z., Kong X., Li X. and Wu W., (2014) Comparison of various shear deformation theories for free vibration of laminated composite beams with general lay-ups, Composite Structures 108,767-778.
• [68] Ghugal Y.M. and Shimpi R.P., (2001) A review of refined shear deformation theories for isotropic and anisotropic laminated beams, Journal of Reinforced Plastics and Composites 20, 255-272.
• [69] Shimpi R.P., (2002) Refined plate theory and its variants, American Institute of Aeronautics and Astronautics Journal 40, 137-146.
• [70] Shimpi R.P., Patel H.G. and Arya H., (2007) New first order shear deformation plate theories, Journal of Applied Mechanics 74, 523- 533.
• [71] Shimpi R.P., Shetty R.A. and Guha A., (2017) A simple single variable shear deformation theory for a rectangular beam, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 231(24), 4576-4591.
• [72] Rao S.S., (1995) Mechanical Vibrations. Addison-Wesley Publishing Company.
• [73] Paz M. and Leigh, W., (2004) Structural Dynamics-Theory and Computation. Kluwer Academic Publishers.
• [74] Yuan S., Ye K., Xiao C., Williams F.W. and Kennedy D., (2007) Exact dynamic stiffness method for non-uniform Timoshenko beam vibrations and Bernoulli-Euler column buckling, Journal of Sound and Vibration. 303, 526-537.
• [75] Viola E., Ricci P. and Aliabadi M.H., (2007) Free vibration analysis of axially loaded cracked Timoshenko beam structures using the dynamic stiffness method, Journal of Sound and Vibration 304,124-153.
• [76] Lien T.V., Duc N.G. and Khiem, N.T., (2017) Free Vibration Analysis of Multiple Cracked Functionally Graded Timoshenko beams, Latin American Journal of Solids and Structures 14, 1752-1766.
• [77] Banerjee J.R. and Su H., (2004) Development of a dynamic stiffness matrix for free vibration analysis of spinning beams, Computers and Structures 82(23-26), 2189-2197.
• [78] Banerjee J.R. and Gunawardana, W.D., (2007) Dynamic stiffness matrix development and free vibration analysis of a moving beam, Journal of Sound and Vibration 303(1-2), 135-143.
• [79] Asteris P.G. and Nikoo, M., (2019) Artificial bee colony-based neural network for the prediction of the fundamental period of infilled frame structures. Neural Computing and Applications. 1-11.
• [80] Asteris P.G., Tsaris A.K., Cavaleri L., Repapis C.C., Papalou A., Trapani F.D. and Karypidis D.F., (2016) Prediction of the Fundamental Period of Infilled RC Frame Structures Using Artificial Neural Networks, Computational Intelligence and Neuroscience 5104907.