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



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.


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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Constituents one and two

V :


T :

Distance in Z direction

Z :


N :

Power law index

E :

Modulus of elasticity

K :

Bulk modulus

C :

Modulus of rigidity

\(v\) :

Poisson’s ratio



\(\sigma\) :


E :


Q :

Stress to strain


Functionally graded material


Graded index of refraction separate confinement heterostructure


Dynamic stiffness method


Line spring model


First-order shear stress theory


Degree of freedom


Points of unstable region


Partial differential equation


Boundary domain


Non-uniform rational b spline curve


Strain gradient theory


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 :


g :

Energy release rate

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

Fracture energy


Generalized difference quadrature


Three dimensional


Modified coupled stress theory


Classical beam theory






Higher order shear stress theory

L/d :

Length to depth ratio


Local flexibility constant


Ordinary differential equation


Extended isogeometric approach


Classical plate theory


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).

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