Dynamic response of thick plates under excitation of a moving mass utilizing BCOPs

Authors

1 Head of Civil Engineering Department- University of Science and Culture

2 University of Science and Culture

Abstract

In this study, dynamic behavior of thick rectangular plates under a moving mass with constant velocity traversing the plate on a rectilinear path is investigated. A semi-analytical method with the aim of BCOPs (Boundary Characteristic Orthogonal Polynomials) is utilized to tackle with the solution of motion equations for different boundary conditions of the plate while accounting for shear deformations. The effects of thickness and boundary conditions of plate and weight and velocity of the moving mass on the dynamic response of plate are scrutinized. The obtained results revealed the accuracy of the proposed method in comparison with the other researchers’ results. The results also demonstrated the importance of the moving load inertia as well as the shear deformations of the host structures on its dynamic behavior. The importance of this study lies on the vibration of bridge-type structures with plate decks, where, the shear deformation of the base structure could be no more ignored, especially for heavy vehicles moving with high speeds.

Keywords

Main Subjects


[1] Mindlin RD (1951) Influence of rotary inertia and shear on flexural motions of isotropic, elastic plates. J Appl Mech 18(1): 31-38.
[2] Reissner E (1945) The effect of transverse shear deformation on the bending of elastic plate. J Appl Mech-T ASME 12: A69-A77.
[3] Donnell LH(1976) Beams, plates and shells. McGraw-Hill, NY.
[4] Levinson M (1980) An accurate, simple theory of the statics and dynamics of elastic plates. Mech Res Commun 7: 343-350.
[5] Ghugal YM,Shimpi RP (2002) A review of refined shear deformation  theories for isotropic and anisotropic  laminated plates. J Reinf Plast Comp 21: 775-813.
[6] Srinivas S, Joga Rao AK, Rao CV (1969) Flexure of simply supported thick homogeneous and laminated rectangular plates. ZAMM: Zeitschrift fur Angewandte Mathematic und Mchanik 49(8): 449-458.
[7] Srinivas S,Joga Rao CV, Rao AK (1970) An exact analysis for vibration of simply supported homogeneous and laminated thick rectangular plates. J Sound Vib 12(2): 187-199.
[8] Levy M (1877) Memoire sur la theorie des plaques elastique planes. J Math Pure Appl 30: 219-306.
[9] Stein  M, Jegly DC (1987) Effect of transverse shearing on cyclindrical bending, vibration and buckling of laminated plates. AIAA J 25:123-129.
[10] Senjanovic I, Vladimir N, Tomic M) 2013) An advanced theory of  moderately plate vibrations. J Sound Vib 332(7): 1868-1880.
[11] Fryba L (1999) Vibration of solids and structures under moving loads. London: Thomas Telford.
[12] Billelo C, Bergman LA, Kuchma D (2004) Experimental investigation of a small-scale bridge model under a moving mass. J Struct Eng-ASCE 130: 799-804.
[13] Esmailzadeh E, Ghorashi M (1995) Vibration analysis of beams traversed by uniform partially distributed moving masses. J Sound Vib 184(1): 9-17
[14] Kiani K, Nikkhoo A, Mehri B (2010) Assessing dynamic response of multispan viscoelastic thin beams under a moving mass via generalized moving least square method. ACTA Mech Sinica 26: 721-733
[15] Kiani K, Nikkhoo A, Mehri B (2009) Parametric analyses of multispan viscoelastic shear deformable beams under excitation of a moving mass. J Vib Acoust 131(5).
[16] Kiani K, Nikkhoo A, Mehri B (2009) Prediction capabilities of classical and shear deformable beam models excited by a moving mass. J Sound Vib 320(3):632-648
[17] Shadnam MR, Mofid M, Akin JE  (2001) On the dynamic response of rectangular plate, with moving mass. Thin Wall Struct 39(9): 797-806.
[18] Nikkhoo A, Rofooei FR (2010) Parametric study of the vibration of thin rectangular plates traversed by a moving mass. ACTA Mech Sinica 223: 15-27.
[19] Motahareh N, Nikkhoo A (2015) Inspection of a rectangular plate dynamics under a moving mass with varying velocity utilizing BCOPs. Lat Am J Solids Stru 12(2): 317-332
[20] Vaseghi Amiri J, Nikkhoo A, Davoodi MR, Ebrahimzadeh M (2013) Vibration analysis of a Mindlin elastic plate under a moving mass excitation by expansion method. Thin Wall Struct 62: 53-64.
[21] Chakraverty S (2009) Vibration of plates. CRCPress, NY.
[22] Reddy JN (2006) An introduction to the finite element method. Vol. 2. McGraw-Hill, NY.
[23] Liew KM, Lam KY, Chow ST (1990) Free vibration analysis of rectangular plates using orthogonal plate function. Comput Struct 34(1): 79-85.
[24] Shimpi RP, Patel HG, Arya H (2007) New first–order shear deformation plate theories. J Appl Mech 74: 523-533.
[25] Hosseini Hashemi S, Arsanjani M (2005) Exact characteristic equations for some of classical boundary conditions of vibrating moderately thick rectangular plates. Int J Solids Struct 42(3-4).
[26] Timoshenko S, Woinowsky-Krieger S (1959) Theory of plates and shells, Engineering societies monographs. McGraw-Hill, New York.‏