Free vibration of arbitrary thick FGM deep arches using unconstrained higher-order shear deformation theory. (March 2019)

• Record Type: Journal Article
• Authors: Javani, M.; Kiani, Y.; Eslami, M.R.
• Is Part Of: Thin-walled structures. Volume 136(2019)
• Page Start: 258
• Page End: 266
• Publication Date: 2019-03
• Subjects: Unconstrained higher-order theory -- Differential quadrature method -- Functionally graded material -- Circular arch; Thin-walled structures -- Periodicals; 690.1
• DOI: 10.1016/j.tws.2018.12.020
• Languages: English
• ISSNs: 0263-8231

Abstract

Abstract: Natural frequencies of circular deep arches made of functionally graded materials (FGMs) with general boundary conditions are obtained in this research based on the unconstrained higher-order shear deformation theory taking into account the depth change, complete effects of shear deformation, and rotary inertia. The material properties are assumed to vary continuously through the thickness direction of the arch. Displacement field within the arch is obtained through expansion up to an arbitrary order. Governing differential equations of the in-plane vibration are derived using Hamilton's principle. These equations are solved numerically utilizing the differential quadrature method (DQM) formulation. In order to illustrate the validity and accuracy of the presented results, results are compared with the available data in the open literature. Afterwards, novel numerical results are given for free vibration behaviour of the FGM deep arches with various boundary conditions. Abstract : Highlights: Displacement of the arch is estimated by means of a higher order theory up to an arbitrary order. Different types of boundary conditions are covered in this research. GDQ method is used to solve the governing equations. Properties are distributed across the depth of the arch using a power law function.