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Original Articles

Estimates for Divergence Velocities of Axially Moving Orthotropic Thin Plates

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Pages 294-313 | Received 08 Aug 2014, Accepted 11 Nov 2014, Published online: 04 Mar 2015

REFERENCES

  • Archibald , F. R. , Emslie , A. G. ( 1958 ). The vibration of a string having a uniform motion along its length . ASME Journal of Applied Mechanics 25 : 347 – 348 .
  • Banichuk , N. , Jeronen , J. , Kurki , M. , Neittaanmäki , P. , Saksa , T. , Tuovinen , T. ( 2011 ). On the limit velocity and buckling phenomena of axially moving orthotropic membranes and plates . International Journal of Solids and Structures 48 ( 13 ): 2015 – 2025 .
  • Banichuk , N. , Jeronen , J. , Neittaanmäki , P. , Saksa , T. , Tuovinen , T. ( 2013a ). Theoretical study on travelling web dynamics and instability under non-homogeneous tension . International Journal of Mechanical Sciences 66C : 132 – 140 .
  • Banichuk , N. , Jeronen , J. , Neittaanmäki , P. , Tuovinen , T. ( 2010 ). On the instability of an axially moving elastic plate . International Journal of Solids and Structures 47 ( 1 ): 91 – 99 .
  • Banichuk , N. , Kurki , M. , Neittaanmäki , P. , Saksa , T. , Tirronen , M. , Tuovinen , T. ( 2013b ). Optimization and analysis of processes with moving materials subjected to fatigue fracture and instability . Mechanics Based Design of Structures and Machines: An International Journal 41 ( 2 ): 146 – 167 .
  • Biancolini , M. E. , Brutti , C. , Reccia , L. ( 2005 ). Approximate solution for free vibrations of thin orthotropic rectangular plates . Journal of Sound and Vibration 288 ( 1–2 ): 321 – 344 .
  • Chen , G. , Coleman , M. P. , Ding , Z. ( 1998 ). Some corner effects on the loss of selfadjointness and the non-excitation of vibration for thin plates and shells . The Quarterly Journal of Mechanics and Applied Mathematics 51 ( 2 ): 213 – 240 .
  • Gorman , D. J. ( 1982 ). Free Vibration Analysis of Rectangular Plates . New York : Elsevier North Holland, Inc .
  • Gorman , D. J. , Singhal , R. K. ( 1993 ). A superposition–Rayeigh–Ritz method for free vibration analysis of non-uniformly tensioned membranes . Journal of Sound and Vibration 162 ( 3 ): 489 – 501 .
  • Hatami , S. , Azhari , M. , Saadatpour , M. M. , Memarzadeh , P. ( 2009 ). Exact free vibration of webs moving axially at high speed. In: AMATH’09: Proceedings of the 15th American Conference on Applied Mathematics, Stevens Point, Wisconsin, USA. Houston, USA: World Scientific and Engineering Academy and Society (WSEAS), pp. 134–139 .
  • Huber , M. T. ( 1923 ). Die Theorie des kreuzweise bewehrten Eisenbetonplatten . Der Bauingenieur 4 : 354 – 392 .
  • Kong , L. , Parker , R. G. ( 2004 ). Approximate eigensolutions of axially moving beams with small flexural stiffness . Journal of Sound and Vibration 276 : 459 – 469 .
  • Kshirsagar , S. , Bhaskar , K. ( 2008 ). Accurate and elegant free vibration and buckling studies of orthotropic rectangular plates using untruncated infinite series . Journal of Sound and Vibration 314 ( 3–5 ): 837 – 850 .
  • Lin , C. C. ( 1997 ). Stability and vibration characteristics of axially moving plates . International Journal of Solids and Structures 34 ( 24 ): 3179 – 3190 .
  • Lin , C. C. , Mote , C. D. (1995). Equilibrium displacement and stress distribution in a two-dimensional, axially moving web under transverse loading. ASME Journal of Applied Mechanics 62:772–779.
  • Lin , C. C. , Mote , C. D. ( 1996 ). Eigenvalue solutions predicting the wrinkling of rectangular webs under non-linearly distributed edge loading . Journal of Sound and Vibration 197 ( 2 ): 179 – 189 .
  • Marynowski , K. ( 2008 ). Dynamics of the Axially Moving Orthotropic Web, Lecture Notes in Applied and Computational Mechanics, Vol. 38. Germany: Springer–Verlag .
  • Marynowski , K. ( 2010 ). Free vibration analysis of the axially moving Levy-type viscoelastic plate . European Journal of Mechanics—A/Solids 29 ( 5 ): 879 – 886 .
  • Miranker , W. L. ( 1960 ). The wave equation in a medium in motion . IBM Journal of Research and Development 4 : 36 – 42 .
  • Mote , C. D. ( 1968 ). Divergence buckling of an edge-loaded axially moving band . International Journal of Mechanical Sciences 10 : 281 – 195 .
  • Mote , C. D. ( 1972 ). Dynamic stability of axially moving materials . Shock and Vibration Digest 4 ( 4 ): 2 – 11 .
  • Mote , C. D. ( 1975 ). Stability of systems transporting accelerating axially moving materials . ASME Journal of Dynamic Systems, Measurement, and Control 97 : 96 – 98 .
  • Sack , R. A. ( 1954 ). Transverse oscillations in traveling strings . British Journal of Applied Physics 5 : 224 – 226 .
  • Seo , Y. B. ( 1999 ). Determination of in-plane shear properties by an off-axis tension method and laser speckle photography . Journal of Pulp and Paper Sciences 25 ( 9 ): 321 – 325 .
  • Shin , C. , Chung , J. , Kim , W. ( 2005 ). Dynamic characteristics of the out-of-plane vibration for an axially moving membrane . Journal of Sound and Vibration 286 ( 4–5 ): 1019 – 1031 .
  • Simpson , A. ( 1973 ). Transverse modes and frequencies of beams translating between fixed end supports . Journal of Mechanical Engineering Science 15 : 159 – 164 .
  • Skutch , R. ( 1897 ). Uber die Bewegung eines gespannten Fadens, weicher gezwungen ist durch zwei feste Punkte, mit einer constanten Geschwindigkeit zu gehen, und zwischen denselben in Transversal-schwingungen von gerlinger Amplitude versetzt wird . Annalen der Physik und Chemie 61 : 190 – 195 .
  • Swope , R. D. , Ames , W. F. ( 1963 ). Vibrations of a moving threadline . Journal of the Franklin Institute 275 : 36 – 55 .
  • Timoshenko , S. P. , Woinowsky-Krieger , S. ( 1959 ). Theory of Plates and Shells. , 2nd ed. New York , Tokyo : McGraw-Hill .
  • Ulsoy , A. G. , Mote , C. D. ( 1982 ). Vibration of wide band saw blades . ASME Journal of Engineering for Industry 104 : 71 – 78 .
  • Wang , Y. , Huang , L. , Liu , X. ( 2005 ). Eigenvalue and stability analysis for transverse vibrations of axially moving strings based on Hamiltonian dynamics . Acta Mechanica Sinica 21 : 485 – 494 .
  • Wickert , J. A. , Mote , C. D. (1990). Classical vibration analysis of axially moving continua. ASME Journal of Applied Mechanics 57:738–744.
  • Xing , Y. , Liu , B. ( 2009 ). New exact solutions for free vibrations of rectangular thin plates by symplectic dual method . Acta Mechanica Sinica 25 : 265 – 270 .
  • Yokoyama , T. , Nakai , K. ( 2007 ). Evaluation of in-plane orthotropic elastic constants of paper and paperboard. In: 2007 SEM Annual Conference & Exposition on Experimental and Applied Mechanics. Springfield, MA, June 3–6, 2007. Bethel, CT: Society for Experimental Mechanics, Inc .

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