Free vibration of bi-directional functionally graded material circular beams using shear deformation theory employing logarithmic function of radius

Abstract

Curved beams such as arches find ubiquitous applications in civil, mechanical and aerospace engineering, e.g., stiffened floors, fuselage, railway compartments, and wind turbine blades. The analysis of free vibrations of curved structures plays a critical role in their design to avoid transient loads with dominant frequencies close to their natural frequencies. One way to increase their applications and possibly make them lighter without sacrificing strength is to comprise them of Functionally Graded Materials (FGMs) that are composites with continuously varying material properties in one or more directions. In this thesis, we study free vibrations of FGM circular beams by using a logarithmic shear deformation theory that incorporates through-the-thickness logarithmic variation of the circumferential displacement, does not require a shear correction factor, and has a parabolic through-the-thickness distribution of the shear strain. The radial displacement of a point is assumed to depend only upon its CONTENTS

Study on nonlinear vibrations of temperature- and size-dependent FG porous arches on elastic foundation using nonlocal strain gradient theory

“…Large amplitude free vibration analysis of shallow arches made of FG materials resting on nonlinear elastic foundation is investigated by Babaei et al [14]. A shear deformation theory including logarithmic function of the radius of arch is developed by Fariborz and Batra [15] to obtain the natural frequencies of bi-directional FGM circular curved beams using the GDQ method. Poit et al [16] worked on the nonlinear frequency analysis of FG graphene platelets reinforced porous composite arches by using the finite element method.…”

Nonlinear Forced Vibration of Bidirectional Functionally Graded Porous Material Beam

“…Truong and co-workers [15,16] proposed an evolution method for material optimization in the design of bending and free vibration behaviors of BDFG beam. Fariborz and Batra [17] researched free vibration of curved BDFG circular beams and explored the mode veering phenomenon. Using the DQM, Lei et al [18] analyzed the critical buckling load and static response of BDFG imperfect beam subjected to axial load.…”

Peridynamic formulation for higher order functionally graded beams

“…In another study, Fariborz and Batra (2019) performed free vibration analysis of functionally graded circular beams using a shear deformation theory by incorporating through-the-thickness logarithmic variation of the circumferential displacement and has a parabolic through-the-thickness distribution of shear strain. More recently, presented dynamic analysis of functionally graded sandwich plates rested on elastic foundation using refined shear deformation theory.…”