Free vibration analysis of cracked functionally graded non-uniform beams

Abstract

This paper presents the free vibration analysis of an edge cracked non-uniform symmetric beam made of functionally graded material. The Timoshenko beam theory is used for the finite element analysis of the multi-layered sandwich beam and the cantilever beam is modeled by 50 layers of material. The material properties vary continuously along the thickness direction according to the exponential and power laws. A MATLAB code is used to find the natural frequencies of two types of non-uniform beams, having a constant height but an exponential or linear width variation along the length of the beam. The natural frequencies of the beam are verified with ANSYS software as well as with available literature and good agreement is found. In the study, the effects of different parameters such as crack location, crack depth, power-law index, geometric index and taper ratio on natural frequencies are analyzed in detail.

Modal analysis of an aluminum beam coated with damaged and porous functionally graded material

“…For this reason both the Timoshenko beam element as the bar element are incorporated into one element by the principle of superposition. The expanded Timoshenko beam element stiffness and mass matrices are given by [7]: $$…”

Porosi̇teli̇ FDM İle Kapli Alümi̇nyum Ki̇ri̇şi̇n Serbest Ti̇treşi̇mi̇ni̇n İncelenmesi̇

“…Çözümün doğruluğunu artırmak için kiriş elemanın her düğümü üç serbestlik derecesine sahiptir. Bunun için serbestlik derecesine göre rijitlik ve kütle matrisleri birleştirilirse nihai ifadeler aşağıdaki gibi olur [11]; 4 , 4 3 , 4 2 , 4 1 , 4 4 , 3 3 , 3 2 , 3 1 , 3 2 , 2 1 , 2 4 , 2 3 , 2 2 , 2 1 , 2 4 , 1 3 , 1 2 , 1 1 , 1 2 , 1 1 , 1 1…”

“…Shabani ve ark. [11] kesiti uzunluk boyunca değişken kesitli çatlaklı kirişlerin serbest titreşim analizini Timoshenko kiriş teorisiyle incelemişlerdir.…”

Free vibration analysis of a single edge cracked symmetric functionally graded stepped beams

“…There are plenty of studies on free vibration behaviour and characteristics of uniform cross-section homogeneous and composite intact structures (Erdurcan and Cunedioğlu, 2020; Jiang et al, 2018; Kim and Shin, 2008; Mohanty et al, 2013; Zahedinejad, 2016; Zhang et al, 2020) and cracked structures (Cunedioglu, 2015; Ferezqi et al, 2010; Gayen and Chakraborty, 2016; Gayen et al, 2017a, 2017b, 2018; Han et al, 2020; Kisa and Brandon, 2000; Kisa et al, 1998; Liu et al, 2017; Papadopoulos, 2004; Papadopoulos and Dimarogonas, 1987; Shabani and Cunedioglu, 2019).…”