DOI QR코드

DOI QR Code

Vibration analysis of laminated plates with various boundary conditions using extended Kantorovich method

  • Singhatanadgid, Pairod (Department of Mechanical Engineering, Faculty of Engineering, Chulalongkorn University) ;
  • Wetchayanon, Thanawut (Department of Mechanical Engineering, Faculty of Engineering, Chulalongkorn University)
  • 투고 : 2012.12.12
  • 심사 : 2014.06.29
  • 발행 : 2014.10.10

초록

In this study, an extended Kantorovich method, employing multi-term displacement functions, is applied to analyze the vibration problem of symmetrically laminated plates with arbitrary boundary conditions. The vibration behaviors of laminated plates are determined based on the variational principle of total energy minimization and the iterative Kantorovich method. The out-of-plane displacement is represented in the form of a series of a sum of products of functions in x and y directions. With a known function in the x or y directions, the formulation for the variation of total potential energy is transformed to a set of governing equations and a set of boundary conditions. The equations and boundary conditions are then numerically solved for the natural frequency and vibration mode shape. The solutions are verified with available solutions from the literature and solutions from the Ritz and finite element analysis. In most cases, the natural frequencies compare very well with the reference solutions. The vibration mode shapes are also very well modeled using the multi-term assumed displacement function in the terms of a power series. With the method used in this study, it is possible to solve the angle-ply plate problem, where the Kantorovich method with single-term displacement function is ineffective.

키워드

과제정보

연구 과제 주관 기관 : Chulalongkorn University, Commission on Higher Education

참고문헌

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피인용 문헌

  1. Three-dimensional free vibration analysis of levy-type laminated plates using multi-term extended Kantorovich method vol.116, 2017, https://doi.org/10.1016/j.compositesb.2017.01.057
  2. The Kantorovich method applied to bending, buckling, vibration, and 3D stress analyses of plates: A literature review 2017, https://doi.org/10.1080/15376494.2017.1365984
  3. Buckling analysis of laminated plates using the extended Kantorovich method and a system of first-order differential equations vol.30, pp.5, 2016, https://doi.org/10.1007/s12206-016-0419-8
  4. Free vibration of symmetrically laminated quasi-isotropic super-elliptical thin plates vol.29, pp.4, 2014, https://doi.org/10.12989/scs.2018.29.4.493
  5. Review of the Methods of Transition from Partial to Ordinary Differential Equations: From Macro- to Nano-structural Dynamics vol.28, pp.7, 2014, https://doi.org/10.1007/s11831-021-09550-5