Semi-analytical modeling of cutouts in rectangular plates with variable thickness – Free vibration analysis

Rezaeepazhand, 2010, Stress concentration in metallic plates with special shaped cutout, Int. J. Mech. Sci., 52, 96, 10.1016/j.ijmecsci.2009.10.013 Barut, 2011, Stress and buckling analyses of laminates with a cutout using a {3,0}-plate theory, J. Mech. Mater. Struct., 6, 827, 10.2140/jomms.2011.6.827 Malekzadeh, 2013, Three-dimensional free vibration analysis of functionally graded cylindrical panels with cut-out using Chebyshev–Ritz method, Compos. Struct., 105, 1, 10.1016/j.compstruct.2013.05.005 Pan, 2013, Stress analysis of a finite plate with a rectangular hole subjected to uniaxial tension using modified stress functions, Int. J. Mech. Sci., 75, 265, 10.1016/j.ijmecsci.2013.06.014 Paramasivam, 1973, Free vibration of square plates with square openings, J. Sound Vib., 30, 173, 10.1016/S0022-460X(73)80111-7 Aksu, 1976, Determination of dynamic characteristics of rectangular plates with cutouts using a finite difference formulation, J. Sound Vib., 44, 147, 10.1016/0022-460X(76)90713-6 Pan, 1997, A general boundary element analysis of 2-D linear elastic fracture mechanics, Int. J. Fract., 88, 41, 10.1023/A:1007462319811 Chau, 1999, A new boundary integral formulation for plane elastic bodies containing cracks and holes, Int. J. Solids Struct., 36, 2041, 10.1016/S0020-7683(98)00078-X Wang, 2004, Static and free vibration analyses of rectangular plates by the new version of the differential quadrature element method, Int. J. Numer. Methods Eng., 59, 1207, 10.1002/nme.913 Liu, 2008, Static and free vibration analysis of laminated composite plates using the conforming radial point interpolation method, Compos. Sci. Technol., 68, 354, 10.1016/j.compscitech.2007.07.014 Hota, 2007, Vibration of plates with arbitrary shapes of cutouts, J. Sound Vib., 302, 1030, 10.1016/j.jsv.2007.01.003 Singh, 2006, Eigenvalue analysis of doubly connected plates with different configurations, J. Sound Vib., 295, 76, 10.1016/j.jsv.2005.12.044 Sabir, 1997, Natural frequencies of square plates with reinforced central holes subjected to inplane loads, Thin Walled Struct., 28, 337, 10.1016/S0263-8231(97)00051-7 Sabir, 1997, Natural frequencies of plates with square holes when subjected to in-plane uniaxial, biaxial or shear loading, Thin Walled Struct., 28, 321, 10.1016/S0263-8231(97)00050-5 Srivastava, 2004, Transverse vibration of stiffened plates with cutouts subjected to in-plane uniform edge loading at the plate boundary, Shock Vib., 11, 9, 10.1155/2004/891580 Shanmugam, 2002, Finite element modelling of plate girders with web openings, Thin Walled Struct., 40, 443, 10.1016/S0263-8231(02)00008-3 Sheikh;, 2003, Vibration of thick and thin plates using a new triangular element, J. Eng. Mech., 129, 1235, 10.1061/(ASCE)0733-9399(2003)129:11(1235) Tham, 1986, Free vibration and buckling analysis of plates by the negative stiffness method, Comput. Struct., 22, 678, 10.1016/0045-7949(86)90022-2 Ali, 1987, Prediction of natural frequencies of vibration of rectangular plates with rectangular cutouts, Comput. Struct., 12, 819, 10.1016/0045-7949(80)90019-X Laura, 1997, Transverse Vibrations of Simply supported rectangular plates with rectangular cutouts, J. Sound Vib., 202, 275, 10.1006/jsvi.1996.0703 Liew, 1995, Flexural vibration of polygonal plates: treatments of sharp re-entrant corners, J. Sound Vib., 183, 221, 10.1006/jsvi.1995.0251 Liew, 2003, Analysis of the free vibration of rectangular plates with central cut-outs using the discrete Ritz method, Int. J. Mech. Sci., 45, 941, 10.1016/S0020-7403(03)00109-7 Kwak, 2007, Free vibration analysis of rectangular plate with a hole by means of independent coordinate coupling method, J. Sound Vib., 306, 12, 10.1016/j.jsv.2007.05.041 Beslin, 1996, The use of an ‘‘ectoplasm’’ to predict free vibrations of plates with cut-outs, J. Sound Vib., 191, 935, 10.1006/jsvi.1996.0164 Sakiyama, 2003, Free vibration of orthotropic square plates with a square hole, J. Sound Vib., 259, 63, 10.1006/jsvi.2002.5181 Huang, 1999, Free vibration analysis of rectangular plates with variously-shaped holes, J. Sound Vib., 226, 769, 10.1006/jsvi.1999.2313 Cheung, 1993, Linear elastic stability analysis of shear-deformable plates using a modified spline finite strip method, Comput. Struct., 47, 189, 10.1016/0045-7949(93)90366-L Ovesy, 2012, Buckling and free vibration finite strip analysis of composite plates with cutout based on two different modeling approaches, Compos. Struct., 94, 1250, 10.1016/j.compstruct.2011.11.009 Cho, 2013, Approximate natural vibration analysis of rectangular plates with openings using assumed mode method, Int. J. Nav. Archit. Ocean Eng., 5, 478, 10.2478/IJNAOE-2013-0147 Larrondo, 2001, Vibrations of simply supported rectangular plates with varying thickness and same aspect ratio cutouts, J. Sound Vib., 244, 738, 10.1006/jsvi.2000.3492 Avalos, 2003, Transverse vibrations of simply supported rectangular plates with two rectangular cutouts, J. Sound Vib., 267, 967, 10.1016/S0022-460X(03)00217-7 Mlzusawa, 1993, Vibration of rectangular Mindlin plates with tapered thickness by the spline strip method, Comput. Struct., 46, 451, 10.1016/0045-7949(93)90215-Y Gorman, 1982 Gorman, 2012, A review of the superposition method for computing free vibration eigenvalues of elastic structures, Comput. Struct., 104-105, 27, 10.1016/j.compstruc.2012.02.018 Liew, 2001, A semi-analytical solution for vibration of rectangular plates with abrupt thickness variation, Int. J. Solids Struct., 38, 4937, 10.1016/S0020-7683(00)00329-2 Cheung, 2003, Vibration of tapered Mindlin plates in terms of static Timoshenko beam functions, J. Sound Vib., 260, 693, 10.1016/S0022-460X(02)01008-8 Eftekhari, 2013, Accurate variational approach for free vibration of variable thickness thin and thick plates with edges elastically restrained against translation and rotation, Int. J. Mech. Sci., 68, 35, 10.1016/j.ijmecsci.2012.12.012 Huang, 2005, Free vibration analysis of orthotropic rectangular plates with variable thickness and general boundary conditions, J. Sound Vib., 288, 931, 10.1016/j.jsv.2005.01.052 Eisenberger, 2000, Vibration frequencies of variable thickness plates, 645 Shufrin, 2006, Vibration of shear deformable plates with variable thickness - first-order and higher-order analyses, J. Sound Vib., 290, 465, 10.1016/j.jsv.2005.04.003 Kerr, 1969, An extended Kantorovich method for the solution of eigenvalue problems, Int. J. Solids Struct., 5, 559, 10.1016/0020-7683(69)90028-6 Shufrin, 2005, Stability and vibration of shear deformable plates-first order and higher order analyses, Int. J. Solids Struct., 42, 1225, 10.1016/j.ijsolstr.2004.06.067 Rahbar Ranji, 2010, A semi-analytical solution for forced vibrations response of rectangular orthotropic plates with various boundary conditions, J. Mech. Sci. Technol., 24, 357, 10.1007/s12206-009-1010-3 Alijani, 2008, Application of the extended Kantorovich method to the bending of clamped cylindrical panels, Eur. J. Mech. A/Solids, 27, 378, 10.1016/j.euromechsol.2007.05.011 Aghdam, 2011, Bending analysis of moderately thick functionally graded conical panels, Compos. Struct., 93, 1376, 10.1016/j.compstruct.2010.10.020 Kapuria, 2011, Extended Kantorovich method for three-dimensional elasticity solution of laminated composite structures in cylindrical bending, J. Appl. Mech., 78, 10.1115/1.4003779 Shufrin, 2008, Buckling of symmetrically laminated rectangular plates with general boundary conditions – A semi analytical approach, Compos. Struct., 82, 521, 10.1016/j.compstruct.2007.02.003 Eisenberger, 2007, The extended Kantorovich method for vibration analysis of plates, Anal. Des. Pl. Struct. Dyn., 2, 192 Bespalova, 2008, Solving stationary problems for shallow shells by a generalized Kantorovich–Vlasov method, Int. Appl. Mech., 44, 1283, 10.1007/s10778-009-0138-2 Bespalova, 2011, Determining the natural frequencies of an elastic parallelepiped by the advanced Kantorovich–Vlasov method, Int. Appl. Mech., 47, 410, 10.1007/s10778-011-0467-9 Shufrin, 2008, A semi-analytical approach for the non-linear large deflection analysis of laminated rectangular plates under general out-of-plane loading, Int. J. Nonlinear Mech., 43, 328, 10.1016/j.ijnonlinmec.2007.12.018 Shufrin, 2009, Elastic nonlinear stability analysis of thin rectangular plates through a semi-analytical approach, Int. J. Solids Struct., 46, 2075, 10.1016/j.ijsolstr.2008.06.022 Shufrin, 2010, A semi-analytical approach for the geometrically nonlinear analysis of trapezoidal plates, Int. J. Mech. Sci., 52, 1588, 10.1016/j.ijmecsci.2010.07.008 Tahani, 2012, Interlaminar stresses in thick rectangular laminated plates with arbitrary laminations and boundary conditions under transverse loads, Compos. Struct., 94, 1793, 10.1016/j.compstruct.2011.12.027 Mousavi, 2012, Analytical solution for bending of moderately thick radially functionally graded sector plates with general boundary conditions using multi-term extended Kantorovich method, Compos. Part B Eng., 43, 1405, 10.1016/j.compositesb.2011.11.068 Tahani, 2013, Analytical solution for bending problem of moderately thick composite annular sector plates with general boundary conditions and loadings using multi-term extended Kantorovich method, Arch. Appl. Mech., 83, 969, 10.1007/s00419-013-0730-0 Kapuria, 2012, Multiterm extended Kantorovich method for three-dimensional elasticity solution of laminated plates, J. Appl. Mech., 79, 10.1115/1.4006495 Kumari, 2014, Three-dimensional extended Kantorovich solution for Levy-type rectangular laminated plates with edge effects, Compos. Struct., 107, 167, 10.1016/j.compstruct.2013.07.053 Reddy, 2004 Eisenberger, 1995, Dynamic stiffness matrix for variable cross-section Timoshenko beams, Commun. Numer. Methods Eng., 11, 507, 10.1002/cnm.1640110605