Modal analysis of cracked continuous Timoshenko beam made of functionally graded material

Khiem, Nguyen Tien; Tran, Hai T.; Nam, Do

doi:10.1080/15397734.2019.1639518

Cited by 12 publications

(5 citation statements)

References 39 publications

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“…Table 3 presented another validation for the result of the present study to that found in the literature. The frequency ratio for cracked to un-cracked FG beam was compared to the results of reference [30] at a/h = 0.2, xc/L = 0.4, k = 1.9 as tabulated in Table 3. According to this table, the results of the present study are a reasonable agreement with the results of Yang and Chen [31].…”

Section: Validationmentioning

confidence: 99%

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Investigation of Transverse Vibration Characteristics of Cracked Axially Moving Functionally Graded Beam Under Thermal Load

Elaikh

Agboola²

2022

Trends Sci

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This article presents a new analysis of the vibration characteristics of open-edge cracks for graded moving beams under thermal load. The material property gradient is based on the distribution of the power law in the direction of the beam thickness. The vibration equation is obtained depending on the precept of Hamilton and resolved by the extension of Galerkin’s approach. A rotational spring is used to represent the cracking in the beam. The effects of the axial velocity, gradient index, thermal load, and cracking parameters on vibration characteristics are observed. Furthermore, the mode shapes of the simple support cracked moving graded beam are determined. The results show that the rise in the axial velocity, the crack depth, and the material property index led to a decrease in the natural frequencies, which indicates the results obtained. HIGHLIGHTS Stability and vibrations analysis of the cracked gradient beams with an axial motion under a uniform temperature rise The effect of axial velocity, gradient index, thermal load, and cracks parameter was studied Galerkin’s technique is developed for vibrational analysis of cracked graded beams with longitudinal motion The Euler-Bernoulli beam model was used taking into account the effect of rotatory inertia GRAPHICAL ABSTRACT

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Section: Validationmentioning

confidence: 99%

“…The density and young's modulus varied through the direction of thickness relying on the power and exponential laws of the volume fraction. Khiem et al [30] established the vibration equation of a cracked FG Timoshenko beam model. The transfer matrix technique has been used to solve the equation of motion.…”

Section: Introductionmentioning

confidence: 99%

Investigation of Transverse Vibration Characteristics of Cracked Axially Moving Functionally Graded Beam Under Thermal Load

Elaikh

Agboola²

2022

Trends Sci

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“…However, there are many measurement techniques for the evaluation of fracture properties of cementitious composites, e.g., [ 63 , 64 , 65 , 66 , 67 , 68 , 69 , 70 , 71 , 72 , 73 , 74 ]. On their basis, it was found that microcracks develop in concrete structures during the loading process, which leads to a gradual loosening of the material.…”

Section: Purpose and Scope Of The Experimental Researchmentioning

confidence: 99%

Studies of Fracture Toughness in Concretes Containing Fly Ash and Silica Fume in the First 28 Days of Curing

Golewski

Gil

2021

Materials

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This paper presents the results of the fracture toughness of concretes containing two mineral additives. During the tests, the method of loading the specimens according to Mode I fracture was used. The research included an evaluation of mechanical parameters of concrete containing noncondensed silica fume (SF) in an amount of 10% and siliceous fly ash (FA) in the following amounts: 0%, 10% and 20%. The experiments were carried out on mature specimens, i.e., after 28 days of curing and specimens at an early age, i.e., after 3 and 7 days of curing. In the course of experiments, the effect of adding SF to the value of the critical stress intensity factor—KIcS in FA concretes in different periods of curing were evaluated. In addition, the basic strength parameters of concrete composites, i.e., compressive strength—fcm and splitting tensile strength—fctm, were measured. A novelty in the presented research is the evaluation of the fracture toughness of concretes with two mineral additives, assessed at an early age. During the tests, the structures of all composites and the nature of macroscopic crack propagation were also assessed. A modern and useful digital image correlation (DIC) technique was used to assess macroscopic cracks. Based on the conducted research, it was found the application of SF to FA concretes contributes to a significant increase in the fracture toughness of these materials at an early age. Moreover, on the basis of the obtained test results, it was found that the values of the critical stress intensity factor of analyzed concretes were convergent qualitatively with their strength parameters. It also has been demonstrated that in the first 28 days of concrete curing, the preferred solution is to replace cement with SF in the amount of 10% or to use a cement binder substitution with a combination of additives in proportions 10% SF + 10% FA. On the other hand, the composition of mineral additives in proportions 10% SF + 20% FA has a negative effect on the fracture mechanics parameters of concretes at an early age. Based on the analysis of the results of microstructural tests and the evaluation of the propagation of macroscopic cracks, it was established that along with the substitution of the cement binder with the combination of mineral additives, the composition of the cement matrix in these composites changes, which implies a different, i.e., quasi-plastic, behavior in the process of damage and destruction of the material.

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“…Although the layered plates exhibit good mechanical performance, it is necessary to reduce immediately the modulus di erence between adjacent layers, which is a major cause of large interlaminar stress [10]. is requirement has led to the development of a novel material, called functionally graded (FG) materials, which can be designed to have continuous mechanical properties [11][12][13]. Due to its outstanding behaviors, FG materials have been applied in various areas, such as piezoelectric ber-reinforced composite [14], heat-resistant materials [15], and nonuniform porous materials [16].…”

Section: Introductionmentioning

confidence: 99%

Efficient Analytical Model for Time-Dependent Behavior of Layered Functionally Graded Plates with Viscoelastic Interlayers

Liu

2022

Mathematical Problems in Engineering

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Layered functionally graded (FG) plate plays an important role in engineering constructions. In this work, an efficient analytical solution is proposed to investigate the time-dependent characters of layered FG plate with viscoelastic interlayers, in which each FG layer is described by the elasticity theory, and the interlayer viscoelasticity is simulated by the generalized Maxwell model. The constitutive equations in the interlayer are simplified, and then, the analytical solutions of stresses and displacements for the layered FG plate are solved by virtue of the efficient recursive matrix method. Some examples are analyzed to investigate the influences of geometric and material characteristics on the long-term behaviors for the FG plate.

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Modal analysis of cracked continuous Timoshenko beam made of functionally graded material

Cited by 12 publications

References 39 publications

Investigation of Transverse Vibration Characteristics of Cracked Axially Moving Functionally Graded Beam Under Thermal Load

Investigation of Transverse Vibration Characteristics of Cracked Axially Moving Functionally Graded Beam Under Thermal Load

Studies of Fracture Toughness in Concretes Containing Fly Ash and Silica Fume in the First 28 Days of Curing

Efficient Analytical Model for Time-Dependent Behavior of Layered Functionally Graded Plates with Viscoelastic Interlayers

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