Bending, buckling and free vibration of laminated composite and sandwich beams: A critical review of literature

Present investigation is concerned with the free vibration analysis of functionally graded material (FGM) beams subjected to different sets of boundary conditions. The analysis is based on the classical and first order shear deformation beam theories. Material properties of the beam vary continuously in the thickness direction according to the power-law exponent form. Trial functions denoting the displacement components of the cross-sections of the beam are expressed in simple algebraic polynomial forms. The governing equations are obtained by means of Rayleigh–Ritz method. The objective is to study the effects of constituent volume fractions, slenderness ratios and the beam theories on the natural frequencies. To validate the present analysis, comparison studies are also carried out with the available results from the existing literature.

Free vibration of Euler and Timoshenko functionally graded beams by Rayleigh–Ritz method

An analytical-numerical method is presented that can be used to determine the dynamic behavior of beams, with different boundary conditions, carrying a moving mass. This article demonstrates the transformation of a familiar governing equation into a new, solvable series of ordinary differential equations. The correctness of the results has been ascertained by a comparison, using finite element models, and very good agreement has been obtained. Furthermore, the article shows that the response of structures due to moving mass, which has often been neglected in the past, must be properly taken into account because it often differs significantly from the moving force model.

Closure of "Numerical Solution for Response of Beams With Moving Mass"

Functionally graded materials (FGMs) have attracted much research interest in the industry due to their graded material properties, which result from gradually distributed compositions or structures. In recent years, metallic FGMs have been widely studied, and additive manufacturing (AM) has become an important approach to build metallic FGMs. This paper aims to provide an overview of the research progress in metallic FGMs fabricated by laser metal deposition (LMD), an AM process that is widely used in metallic materials. Firstly, the unique material properties and advantages of FGMs are introduced. Then, typical recent findings in transition path design, fabrication, and characterization for different types of metallic FGMs via LMD are summarized and discussed. Finally, challenges in fabricating metallic FGMs via LMD are discussed, and other related aspects in the area of FGMs such as model representation and numerical simulation are proposed for further investigation.

Additive manufacturing of functionally graded metallic materials using laser metal deposition

Now a days, sandwich beams and plates made of functionally graded (FG) materials are widely used in many engineering industries. Therefore, several modeling techniques and solution methods ...

Modeling and analysis of functionally graded sandwich beams: a review

This paper presents a finite element model based on the first-order shear deformation theory for free vibration and buckling of functionally graded beams. The present element has five nodes and ten degrees-of-freedom. Material properties vary continuously through the beam thickness according to the power-law form. Governing equations are derived with the aid of Lagrange's equations. Natural frequencies and buckling loads are calculated numerically for different end conditions, power-law indices, and span-to-depth ratios. Accuracy of the present element is demonstrated by comparisons with the available results.

Finite element model for vibration and buckling of functionally graded beams based on the first-order shear deformation theory

Modal parameter identification and vibration based damage detection of a multiple cracked cantilever beam

Damages on reinforced concrete buildings due to consecutive earthquakes in Van

This study presents damage localisation in steel cantilever beams including multiple cracks based on changes in the modal curvature and flexibility. Natural frequencies and corresponding mode shapes of circular-hollow-sectional and box-sectional steel cantilever beams are obtained by analytical and experimental models under six damage scenarios. Based on these data, the modal curvature and modal flexibility methods are employed to localise the cracks within the beams. Comparisons are made to show effectiveness of the methods in determination of crack locations.

Vibration-based damage detection in beam structures with multiple cracks: modal curvature vs. modal flexibility methods

This paper presents a finite element model based on the first-order shear deformation theory for free vibration and buckling analyses of functionally graded (FG) sandwich beams. The present element has 3 N + 7 degrees-of-freedom for an N-layer beam. Lagrange's equations are employed for derivation of the equations of motion. Two types of FG sandwich beams are considered: (a) Type A with FG faces and homogeneous ceramic core, and (b) Type B with homogeneous ceramic and metal faces and FG core. Natural frequencies and buckling loads are calculated numerically for different boundary conditions, power-law indices, and span-to-height ratios. Accuracy of the present element is demonstrated by comparisons with the results available, and discussions are made on the results given in graphs and tables for the sandwich beams considered.

Volkan Kahya

Papers

Finite element model for vibration and buckling of functionally graded beams based on the first-order shear deformation theory

Modal parameter identification and vibration based damage detection of a multiple cracked cantilever beam

Damages on reinforced concrete buildings due to consecutive earthquakes in Van

Vibration-based damage detection in beam structures with multiple cracks: modal curvature vs. modal flexibility methods

Vibration and stability analysis of functionally graded sandwich beams by a multi-layer finite element