Vibration of Circular Plates with Mixed EdgeConditions. Part I: Review of Research
Article Sidebar
Main Article Content
บทคัดย่อ
The vibration problems of elastic plates with uniformly constrained boundary edges have been several considered many times over the past years, but there are few scientific or technical literatures on vibrating plates under discontinuous edge conditions. Therefore, this paper attempts to review and summarize the extensive published technical literature relevant to the problems involving circular plates with mixed edge conditions. Of particular attentional interest is mainly addressed to plate vibration research. The static plate bending problems, however, are also explored optionally to complete the literature survey. The review is conducted with emphasis on the numerous methods being solved successfully previously for this class of plate problems.
Article Details
กองบรรณาธิการวารสารวิชาการ มหาวิทยาลัยเทคโนโลยีราชมงคลกรุงเทพ มีความยินดีที่จะรับบทความจากอาจารย์ นักวิจัย นักวิชาการทั้งภายในและภายนอกมหาวิทยาลัย ในสาขาวิชาวิทยาศาสตร์และเทคโนโลยี ได้แก่ สาขาวิชาวิทยาศาสตร์ วิศวกรรมศาสตร์ และสาขาอื่นๆ ที่เกี่ยวข้อง รวมถึงสาขาต่างๆ ที่มีการบูรณาการข้ามศาสตร์ที่เกี่ยวข้องวิทยาศาสตร์และเทคโนโลยี ที่เขียนเป็นภาษาไทยหรือภาษาอังกฤษ ซึ่งผลงานวิชาการที่ส่งมาขอตีพิมพ์ต้องไม่เคยเผยแพร่ในสิ่งพิมพ์อื่นใดมาก่อน และต้องไม่อยู่ในระหว่างการพิจารณาของวารสารอื่น
การละเมิดลิขสิทธิ์ถือเป็นความรับผิดชอบของผู้ส่งบทความโดยตรง บทความที่ได้รับการตีพิมพ์ต้องผ่านการพิจารณากลั่นกรองคุณภาพจากผู้ทรงคุณวุฒิและได้รับความเห็นชอบจากกองบรรณาธิการ
ข้อความที่ปรากฏอยู่ในแต่ละบทความที่ตีพิมพ์ในวารสารวิชาการเล่มนี้ เป็นความคิดเห็นส่วนตัวของผู้เขียนแต่ละท่าน ไม่เกี่ยวข้องกับมหาวิทยาลัยเทคโนโลยีราชมงคลกรุงเทพแต่อย่างใด ความรับผิดชอบด้านเนื้อหาและการตรวจร่างบทความแต่ละบทความเป็นของผู้เขียนแต่ละท่าน หากมีความผิดพลาดใดๆ ผู้เขียนแต่ละท่านจะต้องรับผิดชอบบทความของตนเองแต่ผู้เดียว
กองบรรณาธิการขอสงวนสิทธิ์มิให้นำเนื้อหา หรือข้อคิดเห็นใดๆ ของบทความในวารสารวิชาการ มหาวิทยาลัยเทคโนโลยีราชมงคลกรุงเทพ ไปเผยแพร่ก่อนได้รับอนุญาตจากกองบรรณาธิการ อย่างเป็นลายลักษณ์อักษร ผลงานที่ได้รับการตีพิมพ์ถือเป็นลิขสิทธิ์ของวารสาร
References
Ventsel E, Krauthammer T. Thin Plates and Shells: Theory, Analysis, and Ap-plications. New York: Marcel Dekker, Inc.; 2001.
Szilard R. Theories and Applications of Plates Analysis: Classical, Numeri-cal and Engineering Method. New Jersey: John Wiley & Sons, Inc; 2004.
Timoshenko SP, Woinowsky-Krieger S. Theory of Plates and Shells. 2nd ed. Singapore: McGraw-Hill; 1959.
Nowacki W. Dynamics of Elastic Sys-tems. London: Chapman & Hall Ltd.; 1963.
Meirovitch L. Analytical Methods in Vibrations. New York: Macmillan Pub-lishing Co., Inc.; 1967.
Rao JS. Dynamics of Plates. New Delhi: Narosa Publishing House; 1999.
Leissa AW. Free vibrations of elastic plates. Proceedings of the AIAA 7th Aerospace Sciences Meeting, 1963 January 20-22, New York City, New York. 1963.
Leissa AW. Vibration of Plates. Re-printed ed. Washington, DC: Acousti-cal Society of America; 1993.
Leissa AW. The free vibration of rec-tangular plates. J Sound Vib. 1973; 31: 257-93.
Leissa AW, Narita Y. Natural fre-quencies of simply supported circular plates. Journal of Sound and Vibra-tion. 1980; 70: 221-9.
Malison R, Sompornjaroensuk Y. Nu-merical finite element determination on free, transverse vibrations of circu-lar plates. Engineering Transactions. 2015; 18: 61-9.
Liew KM, Xiang Y, Kitipornchai S. Research on thick plate vibration: A literature survey. J Sound Vib. 1995; 180: 163-76.
Liew KM, Wang CM, Xiang Y, Kitipornchai S. Vibration of Mindlin Plates: Programming the p-Version Ritz Method. Amsterdam: Elsevier Science Ltd.; 1998.
Nowacki W, Olesiak Z. Vibration, buckling and bending of a circular plate clamped along part of its peri-phery and simply supported on the remaining part. Bulletin de L’Acade-mie Polonaise des Sciences. 1956; 4: 247-58.
Bartlett CC. The vibration and buckl-ing of a circular plate clamped on part of its boundary and simply supported on the remainder. Quarterly Journal of Mechanics and Applied Mathematics. 1963; 16:431-40.
Noble B. The vibration and buckling of a circular plate clamped on part of its boundary and simply supported on the remainder. Proceedings of the 9th Midwestern Mechanics Conference, 1965 April 16-18, Madison, Wiscon-sin. 1965.
Ramachandran J. Large amplitude vi-brations of circular plates with mixed boundary conditions. Computers and Structures. 1974; 4: 871-7.
Hirano Y, Okazaki K. Vibrations of a circular plate having partly clamped or partly simply supported boundary. Bulletin of the JSME. 1976; 19: 610- 8.
Narita Y, Leissa AW. Transverse vi-bration of simply supported circular plates having partial elastic cons-traints. Journal of Sound and Vibra-tion. 1980; 70: 103-16.
Leissa AW, Laura PAA, Gutierrez RH. Transverse vibrations of circular plates having nonuniform edge cons-traints. J Acoust Soc Am. 1979; 66: 180-4.
Narita Y, Leissa AW. Flexural vibra-tions of free circular plates elastically constrained along parts of the edge. Int J Solid Struct. 1981; 17: 83-92.
Leissa AW, Narita Y. Vibrations of free circular plates having elastic con-straints and added mass distributed along edge segments. Journal of Ap-plied Mechanics. 1981; 48: 196-8.
Eastep FE, Hemmig FG. Natural fre-quencies of circular plates with par-tially free, partially clamped edges. J Sound Vib. 1982; 84: 359-70.
Liew KM. Frequency solutions for circular plates with internal supports and discontinuous boundaries. Int J Mech Sci. 1992; 34: 511-20.
Yuan J, Dickinson SM. On the vibra-tion of annular, circular and sectorial plates with cut-outs or on partial supports. Computers and Structures. 1996; 58: 1261-4.
Rossi RE, Laura PAA. Transverse vibrations of a thin, elastic circular plate with mixed boundary conditions. J Sound Vib. 2002; 255: 983-6.
Hassan SM, Makary M. Transverse vibrations of elliptical plate of linearly varying thickness with half of the boundary clamped and the rest simply supported. Int J Mech Sci. 2003; 45: 873-90.
Hassan SM. Numerical solution for frequencies and mode shapes of ellip-tical plate half of whose boundary is simply supported and the rest free. Int J Mech Sci. 2004; 46: 1747-61.
Hassan SM. Free transverse vibration of elliptical plates of variable thick-ness with half of the boundary clamped and the rest free. Int J Mech Sci. 2004; 46: 1861-82.
Febbo M, Vera SA, Laura PAA. Free, transverse vibrations of thin plates with discontinuous boundary condi-tions. J Sound Vib. 2005; 281: 341-56.
Bauer H, Eidel W. Determination of the lower natural frequencies of circu-lar plates with mixed boundary condi-tions. J Sound Vib. 2006; 292: 742-64.
Hassan SM. Numerical computation of BCOPs in two variables for solv-ing the vibration problem of a CF-elliptical plate. Journal of King Saud University (Science). 2010; 22: 195-204.
Conway HD, Farnham KA. Deflections of uniformly loaded circular plates with combinations of clamped, simply supported and free boundary condi-tions. Int J Mech Sci. 1967; 9: 661-71.
Leissa AW, Clausen WE. Deflection of a circular plate having mixed boun-dary conditions. AIAA Journal. 1967; 5: 2287-8.
Das Gupta SP. Deflection of a thin circular plate under mixed boundary condition with clamped and simply supported edge. J Appl Math Mech Z Angew Math Mech . 1972; 52: 369-71.
Stahl B, Keer LM. Bending of a uni-formly loaded circular plate with mixed boundary conditions. AIAA Journal. 1972; 10: 739-43.
Alexsandrov VM, Chebakov MI. The method of dual series in terms of Bes-sel functions in mixed problems of the theory of elasticity for a circular plate. J Appl Math Mech. 1977; 41: 492-9.
Hamada M, Inoue Y, Mizushima I, Mifune T, Morisawa Y. A new ap-proach to bending problems of circu-lar plates with mixed boundary condi-tions. Bulletin of JSME. 1986; 29: 4059-63.
Hamada M, Mizushima I, Mifune T. Bending of a simply supported circu-lar plate subjected to elastic constraint for inclination at its edge. Int J Mech Sci. 1987; 29: 213-8.
Kiattikomol K, Sriswasdi V. Bending of a uniformly loaded annular plate with mixed boundary conditions. AIAA Journal. 1988; 26: 487-92.
Mifune t, Masuo R, Hamada M. A new approach for bending of axisym-metrically loaded circular plates hav-ing mixed boundary conditions. Pro-ceedings of the First Pacific/Asia Off-shore Mechanics Symposium, 1990 June 24-28, Seoul, Korea. 1990.
Zheng XP, Ye TQ, Chen BP. An ana-lytical method for a mixed boundary value problem of circular plates under arbitrary lateral loads. Appl Math Mech. 1991; 12: 841-8.
Strozzi A, Vaccari P. Circular solid plate supported along an edge arc and deflected by a central transverse force. Proceedings of the Institution of Me-chanical Engineering, Part C: Journal of Mechanical Engineering Science. 2001; 215: 389-404.
Monegato G, Strozzi A. On the form of the contact reaction in a solid circu-lar plate simply supported along two antipodal edge arcs and deflected by a central transverse concentrated force. J Elasticity. 2002; 68: 13-35.
Monegato G, Strozzi A. On the con-tact reaction in a solid circular plate simply supported along an edge arc and deflected by a central transverse concentrated force. J Appl Math Mech Z Angew Math Mech. 2005; 85: 460-70.
Zheng X, Huang Q, Wang B. An adaptive boundary collocation method for plate bending problems. Tsinghua Science and Technology. 2007; 12: 567-71.
Strozzi A, Monegato G. Solid circular plate clamped along two antipolal edge arcs and deflected by a central trans-verse concentrated force. J Elasticity. 2009; 97: 155-71.
Ostryk VI, Ulitko AF. Bending of a partially supported circular plate. J Math Sci. 2017; 220: 149-61.
Williams ML. Surface stress singula-rities resulting from various bounda-ry conditions in angular corners of plates under bending. Proceedings of the 1st U.S. National Congress of Applied Mechanics, American Society of Mechanical Engineers (ASME), June 1952, Illinois Institute of Technology, Chicago. 1952.
Leissa AW, McGee OG, Huang CS. Vibrations of sectorial plates having corner stress singularities. J Appl Mech. 1993; 60: 134-40.
Huang CS, Leissa AW, McGee OG. Exact analytical solutions for the vi-brations of sectorial plates with sim-ply-supported radial edges. J Appl Mech. 1993; 60: 478-83.
McGee III OG, Kim JW, Kim YS. Influence of boundary stress singular-rities on the vibration of clamped and simply-supported sectorial plates with arbitrary radial edge conditions. J Sound Vib. 2010; 329: 5563-83.
Chen SS-H, Pickett G. Bending of plates of any shape and with any variation in boundary conditions. J Appl Mech. 1967; 34: 217-8
Leissa AW, Clausen WE, Hulbert LE, Hopper AT. A comparison of approxi-mate methods for the solution of plate bending problems. AIAA Journal. 1969; 7: 920-8.
Leissa AW. Singularity considerations in membrane, plate and shell beha-viors. Int J Solid Struct. 2001; 38: 3341-53.
Kongtong P, Sompornjaroensuk Y. On the Williams’ solution in plates hav-ing stress singularities. Proceedings of the 15th National Convention on Civil Engineering (NCCE15), 2010 May 12-14 , Ubonratchatani, Thailand, 2010.
Sompornjaroensuk Y, Kiattikomol K. Solving problems of plate with mixed boundary conditions using Hankel in-tegral transforms: Part 1 - Solution method and static bending problems. Proceedings of the 12th National Con-vention on Civil Engineering (NCCE12), 2007 May 2-4, Pisanulok, Thailand, 2007.
Sompornjaroensuk Y, Kiattikomol K. Solving problems of plate with mixed boundary conditions using Hankel in-tegral transforms: Part 2 - Free vibra-tion and buckling problems. Proceed-ings of the 12th National Convention on Civil Engineering (NCCE12), 2007 May 2-4, Pisanulok, Thailand, 2007.
Huang CS, Lee MC, Chang MJ. Vibration and buckling analysis of internally cracked square plates by the MLS-Ritz approach. International Int J Struct Stabil Dynam. 2018; 18: 1850105.
Huang CS, Lee HT, Li PY, Hu KC, Lan CW, Chang MJ. Three-dimen-sional buckling analyses of cracked functionally graded material plates via the MLS-Ritz method. Thin-Walled Structures. 2019; 134: 189-202.
Huang T, Lu H, McFarland DM, Li WL, Tan CA, Bergman LA, Gong J. Natural frequency veering and mode localization caused by straight through -cracks in rectangular plates with elas-tic boundary conditions. Acta Mech. 2018; 229: 4017-31.
Xue J, Wang Y. Free vibration analy-sis of a flat stiffened plate with side crack through the Ritz method. Arch Appl Mech. 2019; 89: 2089-102.
Xue J, Wang Y, Chen L. Buckling and free vibration of a side-cracked Mindlin plate under axial in-plane load. Arch Appl Mech. 2020; 90: 1811-27.