Review on Vibration Analysis of Functionally Graded Material Structural Components with Cracks

Abstract

Background

A Evolution of material taken place for ages and in today's world even faster. The new concept faces a new set of challenges and is to execute in the real-world researchers need the material of new concepts. The journey that started from the base material of periodic table to composite materials has extended its steps towards functionally graded materials.

Review Factor

This paper reviews the effect of the appearance of a crack in component made of FGM. Wide applicability of FGM makes it more prone to crack during the service period. Therefore, it is necessary to evaluate the risk factors associated with cracks.

Conclusions

FGM beam is most investigated structure made of FGM followed by plates and all. In most of cases, we observed that increase in any parameter of crack reduces the natural frequency of vibration on structure. It was also observed that theories implied also affect the results under the same parameter such as shear order deformation theory which provides greater value followed by Timoshenko, Euler Bernoulli, and Rayleigh in respective order.

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Abbreviations

1,2:

Constituents one and two

V :

Volume

T :

Distance in Z direction

Z :

Thickness

N :

Power law index

E :

Modulus of elasticity

K :

Bulk modulus

C :

Modulus of rigidity

\(v\) :

Poisson’s ratio

TTO:

Tamura–Tomota–Ozawa

\(\sigma\) :

Stress

E :

Strain

Q :

Stress to strain

FGM:

Functionally graded material

GRINSH:

Graded index of refraction separate confinement heterostructure

DSM:

Dynamic stiffness method

LSM:

Line spring model

FSDT:

First-order shear stress theory

DOF:

Degree of freedom

PURs:

Points of unstable region

PDE:

Partial differential equation

BD:

Boundary domain

NURBS:

Non-uniform rational b spline curve

SGT:

Strain gradient theory

SIF:

Stress intensity factor

\({\sigma }_{\text{c}}\) :

Cohesive stress

\(\gamma\) :

Surface energy per unit area

\(x\) :

Gauge length

\({\sigma }_{\text{f}}\) :

Fracture stress

c, d :

Dimensions of cracks

\(\pi\) :

Potential energy

A :

Area

g :

Energy release rate

\({w}_{\text{f}}\) :

Fracture energy

GDQ:

Generalized difference quadrature

3D:

Three dimensional

MCST:

Modified coupled stress theory

CBT:

Classical beam theory

Hinged-h:

Hinged–hinged

Clamped-c:

Clamped–clamped

HSDT:

Higher order shear stress theory

L/d :

Length to depth ratio

LFC:

Local flexibility constant

ODE:

Ordinary differential equation

XIGA:

Extended isogeometric approach

CPT:

Classical plate theory

FEM:

Finite element method

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Sinha, G.P., Kumar, B. Review on Vibration Analysis of Functionally Graded Material Structural Components with Cracks. J. Vib. Eng. Technol. 9, 23–49 (2021). https://doi.org/10.1007/s42417-020-00208-3

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Keywords

  • FGM beam/plates
  • Vibration analysis
  • Cracks
  • Response of frequency