Vibration Characteristics of a Cracked Cantilever Beam under Free Vibration

Abstract

The objective of this paper is to perform free vibration analysis of a cracked cantilever and to analyze the relation between the modal natural frequency with crack depth, modal natural frequency with crack location. Also the relation among the crack depth, crack location and natural frequency has been analyzed. Only single cracks at different depths and at different locations are evaluated. And the analysis reveals a relationship between crack depth and modal natural frequency. As we know when a structure suffers from damage its dynamic property can change and it was observed that cracks caused a stiffness reduction with an inherent reduction in modal natural frequencies. Consequently it leads to the change in the dynamic response of the beam. The analysis was performed using ALGOR software. Modal natural frequency was found to be decreasing with increases in crack depth. And the same was found to be increasing with increases in crack location from the fixed end.

A Multi-Wave-Packets Decomposition Algorithm of Vibration Signal

“…Similarly we can acquire λ 2 , w 2 by v k . Various existing modal decomposition methods (such as Levy, orthogonal polynomials fitting, ITD, ARMA modeling [1][2][3][4][5][6][7][8][9][10][11][12], etc.) is available for the vibration mode parameters extraction of u k and v k .…”

“…With infiltration of signal processing theories, there are numerous theories and methods [1][2][3][4][5][6][7][8][9][10][11][12][13] in the field of the vibration signal analysis, including transfer function solution, traditional mode analysis, time-frequency analysis, wavelet analysis and time series. All of them acquire some identities after analyzing a vibration signal, and then use pattern recognition for characteristic set classification and fault testing [1][2][3][4][5][6][7][8][9][10][11][12][13]. From the perspective of mechanical wave propagation, we propose a new approach to develop vibration signal in this paper.…”

An Empirical Torsional Spring Model for the Inclined Crack in a 3D-Printed Acrylonitrile Butadiene Styrene (ABS) Cantilever Beam

“…Since the cracks with different depths can be easily replaced by torsional springs with corresponding stiffness, the Ostachowicz model enabled and simplified the modal analysis of the cracked structure. It was then widely used by a large amount of research [ 8 , 9 , 10 , 11 , 12 ]. Radhakrishnan used the Ostachowicz model to simplify a rectangular cantilever beam structure with cracked beams to help him study the effect of crack length on the spring stiffness, the fundamental frequency, vibration amplitude and the occurrence of resonance [ 8 ].…”

Adaptive mesh refinement for finite element analysis of elastic buckling disturbance of circularly curved beams due to multiple micro-cracks damage

“…, 2016). Others established the free vibration model of a beam with cracks and determined that the position and depth of a crack and the crack size have different effects on the free vibration frequency (Nikhil and Jeyashree, 2016; Sutar and Pattnaik, 2010). In addition, the geometric free vibration of an Euler–Bernoulli curved beam was analysed, and a theoretical analysis of its frequency accuracy was performed (Sun et al.…”

“…Some researchers simulated the inhomogeneity of the material using the equivalent intrinsic strain and used Eringen's non-local elastic model to determine that the crack size has a significant influence on the brittle fracture characteristics of a material (Afsar and Sekine, 2000;Jamia et al, 2016). Others established the free vibration model of a beam with cracks and determined that the position and depth of a crack and the crack size have different effects on the free EC 40,1 vibration frequency (Nikhil and Jeyashree, 2016;Sutar and Pattnaik, 2010). In addition, the geometric free vibration of an Euler-Bernoulli curved beam was analysed, and a theoretical analysis of its frequency accuracy was performed (Sun et al, 2020).…”