The overall assessment of closed-form solution methods for free vibrations of rectangular thin plates. (May 2018)

• Record Type: Journal Article
• Authors: Xing, Yufeng; Sun, Qiaozhen; Liu, Bo; Wang, Zekun
• Is Part Of: International journal of mechanical sciences. Volume 140(2018)
• Page Start: 455
• Page End: 470
• Publication Date: 2018-05
• Subjects: Closed-form solution -- Free vibrations -- Rectangular thin plate -- Separable variable method -- Residual; Mechanical engineering -- Periodicals; Génie mécanique -- Périodiques; Mechanical engineering; Maschinenbau; Mechanik; Zeitschrift; Periodicals; 621.05
• DOI: 10.1016/j.ijmecsci.2018.03.013
• Languages: English
• ISSNs: 0020-7403

Abstract

Highlights: The new separable variable closed-form method expands solution range. The new separable variable closed-form method is more accurate. The iterative separable variable method is easy to use and has no limitations. All closed-form solutions are presented in an explicit form. The separable variable methods are assessed comprehensively. Abstract: In this work, a new separation-of-variable (nSOV) method for the free vibration of Kirchhoff rectangular thin plates is developed based on the Rayleigh quotient variational principle. Using this nSOV method, all closed-form solutions can be obtained as long as not both directions include free edge, and the solution accuracy is improved compared with the separation-of-variable (SOV) method proposed previously by the present authors. In addition, as a natural extension of the nSOV method, an iterative SOV (iSOV) method is developed, which is suitable for rectangular thin plates with any kinds of homogeneous boundary conditions. Moreover, all closed-form solutions are presented in explicit forms, and the proposed methods and results are validated via theoretical and numerical comparisons. Graphical abstract : Image, graphical abstract