Spline-based investigation of natural vibrations of orthotropic rectangular plates of variable thickness within classical and refined theories

Abstract

A spline-collocation approach is proposed for studying the natural vibrations of orthotropic rectangular plates of variable thickness. The approach is based on the spline-approximation method and the method of discrete orthogonalization coupled with the step-by-step search method. The study is carried out within the framework of the classical and refined theories of plates. The dynamic response of the plates is studied depending on the variation of the plate thickness, the mechanical parameters, and the type of boundary conditions.

Discovering a pattern in the free vibrations of gently sloping shells of different geometry in the classic and refined statements

“…Paper [1] reports the results of studying the rectangular plates of different thicknesses using a spline-approximation method. A given method was subsequently used by the authors of article [2] to investigate the natural oscillation frequencies of orthotropic rectangular plates of different thicknesses. In this case, the calculations were carried out both in the classical statement and in the refined statement.…”

“…In this case, the authors examined the orthotropic shells of variable thickness and the calculations were carried out using a spline-approximation method. All the above works, except [2], report studies based only on the classic statement or only in the refined statement, without comparing the results of calculations of the same objects in both theories. Article [10] proposed an approach to determine the natural oscillation frequencies of shells of different geometry and relative thickness.…”

Natural Frequencies Calculation of Composite Annular Circular Plates with Variable Thickness Using the Spline Method

“…Ref. [22] used spline approximation to analyze rectangular orthotropic plates of variable thickness using classical and refined theories, whereas this research uses first-order shear deformation theory to examine the vibration of antisymmetric angle-ply annular circular plates of varying thickness using first order shear deformation theory.…”

Free vibration analysis of orthtropic thin cylindrical shells with variable thickness by using spline functions

“…Vibration response of flat plates with variable thickness has also been addressed by Huang et al (2005Huang et al ( , 2007, Ashour (2001), Sakiyama and Huang (1998), Grigorenko et al (2008). On the other hand, Sivadas and Ganesan (1991), Zhang and Xiang (2006), Duan and Koh (2008) investigated vibration response of the closed shells having circular profiles and variable thickness.…”