Akhavan, H., Hosseini Hashemi, Sh., Rokni Damavandi Taher, H., Alibeigloo, A., Vahabi, Sh. (2009). Exact solutions for rectangular Mindlin plates under in-plane loads resting on Pasternak elastic foundation. Part II: Frequency analysis. Computational Material Science, 44, 951-961. Amabili, M. (2006). Theory and experiments for large-amplitude vibrations of rectangular plates with geometric imperfections. Journal of Sound and Vibration, Volume 291, pp. 539-565. Amabili, M. (2008). Nonlinear vibrations and stability of shells and plates. Cambridge university press, Cambridge. ANSYS, I. (2013-a). ANSYS mechanical APDL theory reference. (P. Kohnke, Ed.) Canonsburg, PA: SAS IP, Inc. P. 586-587 ANSYS, I. (2013-b). ANSYS mechanical APDL element reference. Canonsburg, PA: SAS IP, Inc. P. 805-820 AISC. (2003). Manual of steel construction, load and resistance factor design. Third edition, American Institute of Steel Construction, Inc. ASCE. (1995). The structural design of air and gas ducts for power stations and industrial boiler applications. Air and gas duct structural committee of the energy division of the American Society of Civil Engineers (ASCE) Reston, VI. Badran, S. F., Saddek, A. B. & Leheta, H. W., 2013. Ultimate strength of Y and T stiffeners subjected to lateral loads with three different levels of initial imperfection. Elsevier Ocean Engineering, Volume 61, pp. 12-25. Bakker, M. C., Rosmanit, M., and Hofmeyer, H. (2008). Approximate large-deflection analysis of simply supported rectangular plates under transverse loading using plate post-buckling solutions. Thin-Walled Structures, 46, 1224-1235. Bassily, S. F. and Dickinson, S. M., (1973). Vibration of plates subject to arbitrary inplane loads. Applied Mechanics, Summer Conference, Georgia Institute of Technology, Atlanta, Georgia. Bedair, O., 2009. Analysis and Limit State Design of Stiffened Plates and Shells: A World View. ASME Applied Mechanics Reviews, 62(2), pp. 20801.1-20801.16. Bezier, P. (1972). Numerical control: mathematics and applications. New York: Wiley. Bletzinger, K., Bischoff, M., Ramm, E. (2000). A unified approach for shear-locking-free triangular and rectangular shell finite elements. Computers and Structures, 75, 321-334 Blodgett, O. W., 1966. Design of Welded Structures. James F. Lincoln arc welding Foundation. Brubak, L., Andersen, H. and Hellesland, J., 2013. Ultimate strength prediction by semi-analytical analysis of stiffened plates with various boundary conditions. Elsevier Thin-Walled Structures, Volume 62, pp. 28-36. Brubak L, and Hellesland J., (2007-a). Semi-analytical buckling strength analysis of plates with arbitrary stiffener arrangements. Journal of Constructional Steel Research, Volume 63, pp. 532-543. Brubak L, and Hellesland J., (2007-b). Semi-analytical postbuckling and strength analysis of arbitrarily stiffened plates in local and global bending. Thin-Walled Structures, Volume 45, pp.. 6210-633. Brubak L, and Hellesland J., (2007-c). Computational postbuckling and strength analysis of arbitrarily stiffened plates in local and global bending. Thin-Walled Structures, Volume 45(6), pp. 620–33. Brubak, L. and Hellesland, J., (2008). Strength criteria in semi-analytical, large deflection analysis of stiffened plates in local and global bending. Elsevier Thin-Walled Structures, Volume 46, pp. 1382-1390. Canadian Standards Association, (2016). CSA Standard S16-10 Design of Steel Structures. Mississauga, ON: Canadian Standard Association. Chakraverty, S. (2009). Vibration of Plates. Boca Raton: CRC Press. Chan, H.C., Foo, O., (1979). Vibration of rectangular plates subjected to in-plane forces by the finite strip method, journal of sound and vibration, 64 (4), 583-588. Cho, D.S., Kim, B.H., Vladimir, N., Choi, T.M. (2015). Natural vibration analysis of rectangular bottom plate structures in contact with fluid. Ocean Engineering, 103, 171-179. Ciarlet, P., G., (1980). A Justification of the von Kármán Equations. Archive for Rational Mechanics and Analysis, Volume 73, pp. 349-389. David, A., Hugues, F., Dauchez, N., (2018). Vibrational response of a rectangular duct of finite length excited by a turbulent internal flow. Journal of Sound and Vibration, 422, pp. 146-160. Dawe, D. J. (1969). Discrete analysis of the lateral vibration of rectangular plates in the presence of membrane stresses. Aeronautical Research Council (London), Paper No. 1062. Dickinson, S. M., (1973). Lateral vibration of rectangular plates subject to inplane forces. Journal of sound and Vibration, 29, 505 Dvorkin, E. N., and Bathe, K.-J. (1984). A continuum mechanics based four-node shell elements for general non-linear analysis. Engineering Computations, Vol. 1, 77-89. Echter, R., Oesterle, B., Bischoff, M. (2013). A hierarchic family of isogeometric shell finite elements. Computational Methods in Applied Mechanical Engineering. 254, 170-180. El Aghoury, I. M., and Galal, K. (2014). Design of rectangular industrial duct plates subjected to out-of-plane pressure considering nonlinear large deformations. Thin-Walled Structures, Vol. 77, 1-7. Gorman, D. J. (1982). Free Vibration Analysis of Rectangular Plates. New York: Elsevier North Holland Inc. Huang, C. S., Lin, Y. J. (2016). Fourier series solutions for vibrations of a rectangular plate with a straight through crack. Applied Mathematical Modelling, 40(23–24), 10389-10403. Hughes, T. J. R., Cohen, M., Haroun, M. (1978). Reduced and selective integration techniques in the finite element analysis of plates. Nuclear engineering and design, 46, 203-222. Hughes, T. J. R., Cotrell, J. A., Bazilevs, Y., (2005). Isogeometric analysis: CAD, finite elements, NURBS, exact geometry, and mesh refinement. Comput. Methods Appl. Mech. Engrg., 194, 4135-4195. Ibearugbulem, O. M., Ettu, L. O., and Ezeh, J. C. (2013). Direct integration and work principle as new approach in bending analyses of isotropic rectangular plates. The International Journal of Engineering and Science (IJES), 2(3), 28-36. Imrak, C. E., and Gerdemeli, I. (2007). The problem of isotropic rectangular plate with four clamped edges. Sadhand, 32(3), 181-186. Kaldas, M., M., and Dickinson, S., M., (1981-a). The flexural vibration of welded rectangular plates. Journal of Sound and Vibration, Volume 75(2), pp. 163-178. Kaldas, M., M., and Dickinson, S., M., (1981-b). Vibration and buckling calculations for rectangular plates subject to complicated in-plane stress distributions by using numerical integration in a Rayleigh-Rits analysis. Journal of Sound and Vibration, Volume 75(2), pp. 151-162. Katsikadelis, J. T., Nerantzaki, M., S., (1994). Non-Linear Analysis of Plates by the Analog Equation Method. Journal of Computational Mechanics, 14, pp. 154-164. Leheta, H., W., Badran, S., F., Elhanafi, A., S., (2015). Ship structural integrity using new stiffened plates. Thin-Walled Structures, Volume 94, pp. 545-561. Leissa, A. W., Kang, J. H., (2002). Exact solutions for vibration and buckling of an SS-C-SS-C rectangular plate loaded by linearly varying in-plane stresses. International Journal of Mechanical Sciences, 44, 1925-1945. Levy, S. (1941a). Bending of rectangular plates with large deformations. Report No. 737-National Advisory Committee for Aeronautics. Levy, S. (1941b). Square plate with clamped edges under normal pressure producing large deformations. Report No. 740, National Committee for Aeronautics. Levy, S. (1942). Square plates with clamped edges under normal pressure. Report No.847, National Committe for Aeronotics. Liew, K. M., Xiang, Y., and Kitipornchai, S. (1993). Transverse vibration of thick rectangular plates - IV: Influence of Isotropic In-plane Pressure. Computers and Structures, 49(1), pp. 69-78. Little, G. H. (1999). Efficient large deflection analysis of rectangular plates with general transverse form of displacement. Computers and Structures, 71, 333-352. Liu, Z., J. (2014). Nonlinear analysis of flue gas ductwork for power plant. Structures Congress, Structural Engineering Institute of ASCE, Boston, MA, April 3-5, 2014. Love, A. E. H. On the small free vibrations and deformations of elastic shells, Philosophical trans. of the Royal Society (London), 1888, Vol. série A, N° 17 p. 491–549. Manzanares-Martínez, B., Flores, J., Gutiérrez, L., Méndez-Sánchez, R.A., Monsivais, G., Morales, A., Ramos-Mendieta, F. (2010). Flexural vibrations of a recrangular plate for the lower normal modes. Journal of Sound and Vibration, 329, 5105-5115. Mei, C. and Yang, T. Y., (1972). Free vibration of finite element plates subject to complex middle-plate force systems. Journal of Sound and Vibration, 23, 145. Mindlin, R. D. (1951). Influence of rotatory inertia and shear on flexural motions of isotropic, elastic plates. ASME Journal of Applied Mechanics, 18, 31-38. Minghini, F., Tullini, N., Laudiero, F. (2007). Locking-free finite elements for shear deformable orthotropic thin-walled beams. Int. J. Numer. Meth. Engng. 72, 808-834. Ojeda, R. B., Prutsy, G., Lawrence, N. and Thomas, G., 2007. A new approach for the large deflection finite element analysis of isotropic and composite plates with arbitrary orientated stiffeners. Elsevier Finite Elements in Analysis and Design, Volume 43, pp. 989-1002. Paik, J. K., 2008. Some recent advances in the concepts of plate-effectiveness evaluation. Elsevier Thin-Walled Structures, Volume 46, pp. 1035-1046. Paik, J. K. and Seo, J. K., (2009-a). Nonlinear finite element method models for ultimate strength analysis of steel stiffened-plate structures under combined biaxial compression and lateral pressure actions-Part I: Plate elements. Elsevier Thin-Walled Structures, Volume 47, pp. 1008-1017. Paik, J. K. and Seo, J. K., (2009-b). Nonlinear finite element method models for ultimate strength analysis of steel stiffened-plate structures under combined biaxial compression and lateral pressure actions-Part II: Stiffened panels. Elsevier Thin-Walled Structures, Volume 47, pp. 998-1007. Paik, J. K. & Thayamballi, A. K., 2003. Ultimate limit states design of steel-plated structures. Chichester: Wiley. Petyt, M. (2010). Introduction to finite element vibration analysis / Second edition. Cambridge University Press, ISBN 978-0-521-19160-9. Phillips, I. G., and Jubb, J. E. M. (1974). The effect of distortion on the lowest natural frequency of a rectangular steel plate. Journal of sound and vibration, 33(1), 41-48. Powell, G. H. (2010). Modelling for Structural Analysis: Behaviour and Basics (1st ed.). Berkeley, CA: Computers and Structures, Inc. Ramberg, W., McPherson, A. E., and Levy, S. (1942). Normal-pressure tests of rectangular plates. Washington: Technical Note No.849, National Advisory Committee for Aeronautics. Reissner, E. (1945). The effect of transverse shear deformation on the bending of elastic plates. ASME Journal of Applied Mechanics, 12, 68-77. Reissner, E. (1955). On transverse vibration of thin, shallow, elastic shells. Quarterly of applied mathematics. 13, 169-176. Rezaiefar, A., Galal, K., (2016). Structural design of stiffened plates of industrial duct walls with relatively long panels undergoing large deformations. Thin-Walled Structures, 108, 406-415. Sapountzakis, E., J., and Dikaros, I., C., (2012). Large deflection analysis of plates stiffened by parallel beams. Engineering Structures, Elsevier. 35, pp. 1021-1041. Senjanović, I., Vladimir, N., Hadžić, N. (2014). Modified Mindlin plate theory and shear locking-free finite element formulation. Mechanics Research Communications, 55, 95-104. Singh, j. P., Dey, S. S., (1990). Transverse vibration of rectangular plates subjected to inplane forces by a difference based variational approach. International Journal of Mechanical Science, 32(7), 591-599. Shanmugam, N. E., Dongqi, Z., Choo, Y. S. and Arockiaswamy, M., (2014). Experimental studies on stiffened plates under in-plane load and lateral pressure. Elsevier Thin-Walled Structures, Volume 80, pp. 22-31. Soedel, W. (1993). Vibrations of Shells and Plates. New York: Marcel Dekker Inc. Timoshenko, S., and Woinowsky-Kreiger, S. (1959). Theory of plates and shells (2nd ed.). New-York: McGraw-Hill. Thanga, T., Halabieh, B., and Sivakumaran, K. S. (2011). Strength of plates of rectangular industrial ducts. Procedia Engineering, Elsevier, 14, 622-629. Timoshenko, S., and Woinowsky-Kreiger, S. (1959). Theory of plates and shells (2nd ed.). New-York: McGraw-Hill. Triotsky, D., (1976). Stiffened plates: Bending, stability and vibrations. Elsevier Scientific Publishing Co. Amsterdam, The Netherlands. Ugural, A. C. (1981). Stresses in plates and shells (1st Edition ed.). Mc Graw-Hill. Von-Kármán, T. (1910). Festigkeitsprobleme im Maschinenbau. Encyklopadie der Mathematischen Wissenschaften. 4(4), 311–385. Wang, C. T. (1948). Bending of rectangular plates with large deflections. Technical Note No.1462, National Advisory Committee for Aeronotics. Wang, D., and El-Sheikh, I. (2005). Large-deflection mathematical analysis of rectangular plates. Journal of Engineering Mechanics, ASCE, 131(8), 809-821. Wang, X., Gan, L., Wang, Y. (2006). A differential quadrature analysis of vibration and buckling of an SS-C-SS-C rectangular plate loaded by linearly varying in-plane stresses. Journal of Sound and Vibration. 298, 420-431. Wang, M., Li, K., Qiu, Y., Li, T., Zhu, X. (2017). Free vibration characteristics analysis of rectangular plate with rectangular opening based on Fourier series method. Chinese Journal of Ship Research, 12(4) 102-109. Wilson, E. L. (2016). CSi analysis reference manual for SAP2000, ETABS, SAFE and CSIBridge. Computers and Structures Inc. Berkeley, CA Xiang, Y., Zhao, Y. B., Wei, G. H., (2002). Levy solutions for vibration of multi-span rectangular plates. International journal of Mechanical Sciences, 44, 1195-1218. Xu MC, Guedes Soares C., (2011-a). Experimental study on the collapse strength of narrow stiffened panels. Proceedings of 30th international conference on offshore mechanics and arctic engineering (OMAE2011), ASME paper OMAE 2011-50293. Xu MC., Guedes Soares C., (2011-b). Numerical study of the effect of geometry and boundary conditions on the collapse behaviour of short stiffened panels. Advances in marine structures. London, UK, Taylor & Francis Group, p. 229–37. Xu MC, Guedes Soares C., (2013). Experimental study on the collapse strength of wide stiffened panels. Marine Structures, (30), 33-62. Yamaki, N., Chiba, M., (1983). Nonlinear vibrations of a clamped rectangular plate with initial deflection and initial edge displacement – Part I: Theory. Thin-Walled Structures, Volume 1, pp. 3-29. Yamaki, N., Otomo, K., Chiba, M., (1983). Nonlinear vibrations of a clamped rectangular plate with initial deflection and initial edge displacement – Part II: Experiment. Thin-Walled Structures, Volume 1, pp. 101-119. Young, W. C., and Budynas, R. G. (2002). Roark's formulas for stress and strain, vol. 6. New York: McGraw-Hill. Zeng, H.C., Huang, C.S., Leissa, A.W., Chang, M.J. (2016). Vibrations and stability of a loaded side-cracked rectangular plate via the MLS-Ritz method. Thin-Walled Structures, 106, 459-470.