5048 © JVE INTERNATIONAL LTD. JOURNAL OF VIBROENGINEERING. DEC 2016, VOL. 18, ISSUE 8. ISSN 1392-8716 2253. A Unified method for vibration analysis of moderately thick annular, circular plates and their sector counterparts subjected to arbitrary boundary conditions Fazl e Ahad 1 , Dongyan Shi 2 , Anees Ur Rehman 3 , Hafiz M. Waqas 4 College of Mechanical and Electrical Engineering, Harbin Engineering University, Harbin, China 1 Corresponding author E-mail: 1 ahad_khattak@hotmail.com, 2 shidongyan@hrbeu.edu.cn, 3 engranees@gmail.com, 4 hafizwaqas90@hotmail.com Received 14 January 2016; received in revised form 14 July 2016; accepted 17 August 2016 DOI https://doi.org/10.21595/jve.2016.16834 Abstract. The vibrations of circular, annular and sector plates are different boundary value problems due to different edge conditions and thus have been treated separately using different solution algorithms and procedures. In this paper, a unified method is proposed for vibration analysis of moderately thick annular, circular plates and their sector counterparts with arbitrary boundary conditions. The unification of these plates is physically achieved by applying the coupling spring’s technique at the radial edges to ensure appropriate continuity conditions. Irrespective of the shape of the plate and the type of boundary conditions, each of the displacement function is expressed as a new form of trigonometric expansion with high convergence rate. Unlike most of the previous studies the current method can be universally applied to a wide range of vibration problems involving different shapes, boundary conditions, varying materials and geometric properties without modifying the solution algorithms and procedure. Furthermore, the current method can easily be applied to sector plates with an arbitrary inclusion angle of 2ߨ. The accuracy, reliability and versatility of the proposed method are fully demonstrated with several numerical examples for different shapes of plates and under different boundary conditions. Keywords: vibrations, circular plates, annular plates, sector plates, natural frequency, mode shapes, arbitrary boundary conditions. 1. Introduction Circular, annular and their sectorial counterparts are important structural components widely used in many engineering fields like civil, mechanical and marine engineering. As far as previous literature is concerned different solution algorithms and procedures have been adopted to study their vibration characteristics. The main reason behind these different solution algorithms and procedures was difference in their geometries resulting in different edge conditions. A lot of research work has been done to study their dynamic characteristics under different boundary conditions. The important and comprehensive review on this subject can be found in Leissa’s 1973 book. The initial study on vibrations of circular plates or disks was done by Deresiewicz and Mindlin [1]. Employing the classical thin plate theory and Mindlin plate theory, these two researchers studied the vibration characteristics of axially symmetric circular disks. This work was further extended by Soni et al. [2] to axisymmetric orthotropic non uniform circular discs. They carried out their research using the same Mindlin plate theory and Chebyshev collocation technique. This technique was later employed by Gupta et al. to polar orthotropic annular Mindlin plates with non-uniform thickness [3]. Using Finite Element Method and three-dimensional finite strip model, Cheung et.al studied the vibration characteristics of thick and thin sector plates subjected to different types of classical boundary conditions [4, 5]. Investigation on vibration characteristics of annular sector plates having internal radial line and circumferential arc supports was carried out by Xiang et al. [6-7]. In another study Xiang et al. used first order shear deformation theory and studied the vibration response of thick circular and annular plates