Performances of conventional fiber reinforced composites are challenged in thermomechanical loading, when development of interlaminar stresses at the interface becomes the weakest link of the components. Development of functionally graded materials (FGMs) could lead to the reduction of such interlaminar failures, especially at high temperature applications. Therefore, these FGMs have a huge potential for use in many structural applications, particularly under thermomechanical loading. There has been a large number of works already reported on FGM components, starting from manufacturing to stress analysis of such components. Cracks in such FGM components may develop due to variety of reasons during service and need to be addressed while analyzing the performances of such components. This paper reviews the progress made till date on the analysis of structural components made of FGMs with a special emphasis on the analysis of cracked FGM components. In view of the potential use of components made of FGMs in a wide range of applications, it is important to understand the state of the art in this area. This paper thus provides a critical review of works reported in this area with an objective of providing the key challenges and future scopes of development in the direction of analysis of such structure for assessing safety in the presence of cracks.

Static and dynamic analyses of cracked functionally graded structural components: A review

IN THIS PAPER, AUTHORS PRESENT THE STUDY OF FREE VIBRATION OF BENDING MULTIPLE CRACKED FUNCTIONALLY GRADED MATERIAL (FGM) BEAM. VIBRATION EQUATIONS OF MULTIPLE CRACKED FGM BEAM WERE ESTABLISHED BY USING THE ROTATIONAL SPRING MODEL OF CRACKS, DYNAMIC STIFFNESS METHOD (DSM) AND ACTUAL POSITION OF NEUTRAL PLANE. THE FREQUENCY EQUATION OBTAINED WAS IN A SIMPLE FORM, THAT PROVIDES AN EFFECTIVE APPROACH TO STUDY NOT ONLY FREE VIBRATION OF THE BEAMS BUT ALSO INVERSE PROBLEMS LIKE IDENTIFICATION OF MATERIAL AND CRACK PARAMETERS IN STRUCTURE. THE OBTAINED NUMERICAL RESULTS SHOW GOOD AGREEMENT WITH OTHER PREVIOUS PUBLISHED RESULTS. THENCE, NUMERICAL COMPUTATION HAS BEEN CARRIED OUT TO INVESTIGATE THE EFFECT OF EACH CRACK, THE NUMBER OF CRACKS, MATERIAL AND GEOMETRIC PARAMETERS ON THE NATURAL FREQUENCIES OF MULTIPLE CRACKED TIMOSHENKO FGM BEAMS.

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Free vibration analysis of multiple cracked functionally graded timoshenko beams

Over the past two decades, extensive research has been carried out in the field of structural health monitoring for damage detection in structural systems. Some crack detection methods are based on...

Identification of cracks in an Euler–Bernoulli beam using Bayesian inference and closed-form solution of vibration modes:

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.
 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.

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

In this paper, the transverse vibration of cracked nano-beam has been studied based on modified couple stress theory. Crack is modeled by a rotational spring that creates a discontinuity. Frequency equations of cracked nano-beam with some typical boundary conditions are derived and the frequency parameter for different crack positions, crack parameter and length scale parameters value are calculated. According to the results, it can be found that the effects of the crack parameter and crack location on transverse frequency of the cracked nano-beam are significant. In addition, scale effect parameter is one of the important parameter in nanoscale that must be obtained. Finally, the results of special cases show good agreement with the results available in the literature.

Size Effect on Free Transverse Vibration of Cracked Nano-beams using Couple Stress Theory

A complete investigation on the free vibration and stability analysis of beams made of functionally graded materials (FGMs) containing open edge cracks utilizing four beam theories, Euler-Bernoulli, Rayleigh, shear and Timoshenko, is performed here. It is assumed that the material properties vary along the beam thickness exponentially and the cracked beam is modeled as two segments connected by two mass-less springs, extensional and rotational spring. Afterward the equations of motion for the free vibrations and buckling analysis are established and solved analytically for clamped-free boundary conditions. A detailed parametric study is also performed to examine the influences of the location and depth of the crack, material properties and slenderness ratio of the beam on the free vibration and buckling characteristics of cracked FGM beams for each of the four engineering beam theories.

https://www.ije.ir/article_72331_7a2a66e9081466f403433b77af0a25b0.pdf

K Sherafatniaa

Papers

Analytic approach to free vibration and buckling analysis of functionally graded beams with edge cracks using four engineering beam theories