Smart damping of geometrically nonlinear vibrations of functionally graded sandwich plates using 1–3 piezoelectric composites

Geometrically nonlinear dynamic analysis of smart functionally graded (FG) sandwich plates integrated with the patches of active constrained layer damping (ACLD) treatment has been carried out by the finite element method. The constraining layer of the ACLD treatment is considered to be made of vertically/obliquely reinforced 1–3 piezoelectric composite while the constrained layer is made of a viscoelastic material, which is modeled using the Golla–Hughes–McTavish method in the time domain. The top and bottom faces of the substrate sandwich plate are composed of the FG isotropic material whose mechanical properties are assumed to vary according to a standard power-law distribution in terms of the volume fractions of the constituents while the core layer may be either a soft honeycomb material or a hard ceramic material. Several FG sandwich plates with different core configurations are studied to evaluate the numerical results. The numerical results indicate that the ACLD patches significantly improve the damping characteristics of the FG sandwich plates for suppressing their geometrically nonlinear vibrations. Effects of metal- or ceramic-rich top and bottom surfaces, the variation of power-law index on the control authority of the ACLD patches have been investigated. Emphasis has also been placed on investigating the effect of the variation of piezoelectric fiber orientation angle on the performance of the ACLD patches.     

Numerical analysis on near net shape forming of Al–Al3Ni functionally graded material

The results of numerical studies on the near-net shape forming of Al–Al₃Ni functionally graded material (FGM) are presented and are compared with the experiments. FGM billets at an elevated temperature of semi-solid condition are set in a container and are subject to backward extruding, and FGM cups are obtained. Due to the composition gradient of FGM the effective viscosity of semi-melt FGM billet varies spatially. The flow/deformation of semi-melt FGM billet is strongly influenced by the spatial variation of effective viscosity. Some characteristic behaviors of flow/deformation of FGM during the semi-solid process are presented and discussed.     

Autofrettage of layered and functionally graded metal–ceramic composite vessels

The residual compressive stresses induced by the autofrettage process in a metal vessel are limited by metal plasticity. Here we showed that the autofrettage of layered metal–ceramic composite vessels leads to considerably higher residual compressive stresses compared to the counterpart metal vessel. To calculate the residual stresses in a composite vessel, an extension of the Variable Material Properties (X-VMP) method for materials with varying elastic and plastic properties was employed. We also investigated the autofrettage of composite vessels made of functionally graded material (FGM). The significant advantage of this configuration is in avoiding the negative effects of abrupt changes in material properties in a layered vessel – and thus, inherently, in the stress and strain distributions induced by the autofrettage process. A parametric study was carried out to obtain near-optimized distribution of ceramic particles through the vessel thickness that results in maximum residual stresses in an autofrettaged functionally graded composite vessel. Selected finite element results were also presented to establish the validity of the X-VMP method.     

Shear horizontal (SH) waves propagating in piezoelectric–piezomagnetic bilayer system with an imperfect interface

This work considers the propagation of shear horizontal (SH) waves in a bilayer system consisting of a piezoelectric (PE) layer and a piezomagnetic (PM) substrate. The interface between the PE layer and the PM substrate is imperfectly bonded. The surfaces of the bilayer system are free of traction, electrically shorted or open and magnetically open or shorted. The exact dispersion equations are derived. The numerical examples are given to illustrate the effects of the electromagnetic boundary conditions, the imperfect interface, the different PE layers and the thickness ratio on the dispersion behaviors. It is found that (a) the electrical boundary conditions dominate the propagation characteristics of SH waves; (b) the imperfect bonding lowers the phase velocities; (c) the thickness ratio and the properties of PE layers have a significant effect on the dispersion behaviors. The obtained results provide a predictable and theoretical basis for applications of PE–PM composites to acoustic wave devices.     

Study on the machining of Al–SiC functionally graded metal matrix composite using die-sinking EDM

Functionally graded aluminum matrix composites (FGAMCs) are new materials with excellent capabilities for design and development of complex engineering works. In this work, FGAMCs are machined using electrical discharge machining (EDM) with the process input parameters such as pulse current, pulse on time, and zone position in brake disk. Design of experiments is used for the experimental planning with full factorial method. The selected input process parameters are optimized using gray relational analysis to minimize the electrode wear ratio, overcut, power consumption, and surface roughness. The influential studies of input process parameters on the output responses are also conducted. The optimal EDM parameter setting for achieving better output parameters is pulse current at 5 A, pulse on time at 50?µs and 45?mm zone position distance in the brake disk. The pulse current (39.40%) contributed the maximum in minimizing the output responses. Further, the surface morphology is also analyzed on the material to observe the crater formation and the erosion mechanism.     

A crack in a viscoelastic functionally graded material layer embedded between two dissimilar homogeneous viscoelastic layers – antiplane shear analysis

A crack in a viscoelastic functionally graded material (FGM) layer sandwiched between two dissimilar homogeneous viscoelastic layers is studied under antiplane shear conditions. The shear relaxation modulus of the FGM layer follows the power law of viscoelasticity, i.e., = ₀ exp (y/h) [t₀ exp (y/h) /t]^q, where h is a scale length, and ₀,t ₀,, and q are material constants. Note that the FGM layer has position-dependent modulus and relaxation time. The shear relaxation functions of the two homogeneous viscoelastic layers are =₁(t ₁/t)^q for the bottom layer and =₂(t ₂/t)^q for the top layer, where ₁ and ₂ are material constants, and t ₁ and t ₂ are relaxation times. An elastic crack problem of the composite structure is first solved and the `correspondence principle' is used to obtain stress intensity factors (SIFs) for the viscoelastic system. Formulae for SIFs and crack displacement profiles are derived. Several examples are given which include interface cracking between a viscoelastic functionally graded interlayer and a viscoelastic homogeneous material coating. Moreover, a parametric study is conducted considering various material and geometric parameters and loading conditions.     

Influence of linear work hardening on the elastic–plastic behavior of a functionally graded thick-walled tube

For the problem of a functionally graded thick-walled tube subjected to internal pressure, we have already presented the elasticity solution based on the Voigt method in Xin et al. (Int J Mech Sci 89:344–349, 2014). This paper discusses the elastic–plastic problem of the functionally graded thick-walled tube subjected to internal pressure and gives the solution in terms of volume fractions of the constituents. We assume that the tube consists of two linear work hardening elastic–plastic constituents and the volume fraction of one phase is a power function varied in the radical direction. The Lamé constants and yield stress of the constituents of the FGM tube are given rather than Young’s modulus and yield stress with different unknown parameters of the whole material in the existing papers. As the internal pressure increases, the deformations of one phase and two phases from elastic to plastic are analyzed. The present method is valid for materials with different Poisson’s ratios rather than constant Poisson’s ratios usually used in the existing references to obtain the effective Young’s modulus. More importantly, the influences of linear work hardening on plastic behavior are considered in this work.     

Determination of the reduced matrix of the piezoelectric, dielectric, and elastic material constants for a piezoelectric material with C∞ symmetry

We present a procedure for determining the reduced piezoelectric, dielectric, and elastic coefficients for a C(∞) material, including losses, from a single disk sample. Measurements have been made on a Navy III lead zirconate titanate (PZT) ceramic sample and the reduced matrix of coefficients for this material is presented. In addition, we present the transform equations, in reduced matrix form, to other consistent material constant sets. We discuss the propagation of errors in going from one material data set to another and look at the limitations inherent in direct calculations of other useful coefficients from the data.     

Smart control of nonlinear vibrations of doubly curved functionally graded laminated composite shells under a thermal environment using 1–3 piezoelectric composites

This paper addresses the active control of geometrically nonlinear vibrations of doubly curved functionally graded (FG) laminated composite shells integrated with a patch of active constrained layer damping (ACLD) treatment under the thermal environment. Vertically/obliquely reinforced 1-3 piezoelectric composite (PZC) and active fiber composite (AFC) are used as the materials of the constraining layer of the ACLD treatment. Each layer of the substrate FG laminated composite shell is made of fiber-reinforced composite material in which the fibers are longitudinally aligned in the plane parallel to the top or bottom surface of the layer and the layer is assumed to be graded in the thickness direction by way of varying the fiber orientation angle across its thickness according to a power law. The novelty of the present work is that, unlike the traditional laminated composite shells, the FG laminated composite shells are constructed in such a way that the continuous variation of material properties and stresses across the thickness of the shell is achieved. The Golla-Hughes-McTavish (GHM) method has been implemented to model the constrained viscoelastic layer of the ACLD treatment in time domain. Based on the first-order shear deformation theory (FSDT), a finite element (FE) model has been developed to model the open-loop and closed-loop nonlinear dynamics of the overall FG laminated composite shell under a thermal environment. Both symmetric and asymmetric FG laminated composite doubly curved shells are considered for presenting the numerical results. The analysis suggests that the ACLD patch significantly improves the damping characteristics of the doubly curved FG laminated composite shells for suppressing their geometrically nonlinear transient vibrations. It is found that the performance of the ACLD patch with its constraining layer being made of the AFC material is significantly higher than that of the ACLD patch with vertically/obliquely reinforced 1-3 PZC constraining layer. The effects of variation of piezoelectric fiber orientation in both the obliquely reinforced 1-3 PZC and the AFC constraining layers on the control authority of the ACLD patch have also been investigated.     

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

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.     

Infiltration-processed, functionally graded aluminium titanate/zirconia–alumina compositePart II Mechanical properties

The nature and degree of deformation-microfracture damage around Vickers indentations in a layered and graded aluminium titanate (AT)/(alumina–zirconia (AZ)) composite is studied. Samples with a homogeneous layer of AZ and a graded layer of heterogeneous AT/AZ are fabricated by an infiltration route. Depth profiling of the Vickers hardness shows that the hardness of the material is depth dependent with a relatively soft graded layer but a hard homogeneous layer. The microhardness of the graded layer is load dependent with 5.6 GPa as the asymptotic value at high loads. The evolution and accumulation of damage modes beneath Hertzian contacts are examined using "bonded-interface" sections. The stress–strain response of the material is monitored by Hertzian tests. The graded layer exhibits a distinctive "softening" in the stress–strain curve, indicating a microscale quasiplasticity which can be associated with grain debonding, grain sliding, diffuse microcracking, grain push-out and grain bridging. No contact-induced cracks are observed in the graded layer and the micro damage is widely distributed within the shear compression zone around and below the contacts. The capability of the graded material to absorb energy from the loading system and to distribute damage is somewhat akin to that of ceramics with heterogeneous microstructures. © 1998 Kluwer Academic Publishers     

Asymptotical construction of a fully coupled,Reissner–Mindlin model for piezoelectric and piezomagnetic laminates

The variational asymptotic method is used to construct a fully coupled Reissner–Mindlin model for piezoelectric and piezomagnetic laminates with some surfaces parallel to the reference surface coated with electrodes and magnetism. Taking advantage of the smallness of the plate thickness, we asymptotically split the original 3D electromagneto-mechanical problem into a 1D through-the-thickness analysis and a 2D plate analysis, and both are fully-coupled multiphysics analyses. The through-the-thickness analysis serves as a link between the original 3D analysis and the plate analysis by providing a constitutive model for the plate analysis and recovering the 3D field variables in terms of global responses calculated by the plate analysis. The present theory is implemented into the computer program VAPAS (Variational Asymptotic Plate and Shell Analysis). A numerical example of three-layer sandwich plate has been used to validate the present model.     

Compressive properties of sandwiches with functionally graded rubber core and jute–epoxy skins

The compressive behaviour of a new class of sandwich composite made up of jute fiber reinforced epoxy skins and piece-wise linear fly ash reinforced functionally graded (FG) rubber core is investigated in flat-wise mode. FG samples are prepared using conventional casting technique. Presence of gradation is quantified physically by weight method. This paper addresses the effect of weight fraction of fly ash, core to thickness ratio (C/H) and orientation of jute on specific compressive modulus and strength. In each trial five replicates are tested with lower amount of fly ash below the upper skin of sandwich (rubber-up). Results of experimentation are subjected to statistical analysis of variance (ANOVA) to find the influential factor governing the compressive behaviour. Furthermore piece-wise linear gradation is modeled in finite element and strength values are compared with experimental results. Sandwich sample with fly ash content of 40%, C/H of 0·4 and orientations of 30°/60° registered better performance. Specific strength is observed to increase upto 30% filler content followed by stabilization. Finite element results for strength match very well with experimental ones.     

Computation of green’s tensor and wave propagation in the random granular elastic medium

Abstract

A linear differential operator equation involving randomly variable field parameters, characterising the heterogeneous granular elastic medium is considered. The appropriate Green’s tensor is evaluated for the non-deterministic operator equations in the form of Fourier integrals in the frequency space; the exact evaluation is carried out to obtain the 36 components of Green’s tensor. The problem of wave propagation in the random granular elastic medium is then carried out with the help of the associated Green’s tensor. The effect of random variation of parameters on wave propagation in the granular elastic medium is examined. Dispersion equations have been analysed in details.     

Mechanical buckling of two-dimensional functionally graded cylindrical shells surrounded by Winkler–Pasternak elastic foundation

In this research, buckling analysis of a two-dimensional, functionally graded, cylindrical shell that has been embedded in an outer elastic medium in the presence of combined axial and transverse loading based on third-order shear deformation shell theory is numerically investigated. Variations of the shell properties are considered to be continuous through length and thickness. Winkler–Pasternak foundation and simply supported boundary conditions have been applied. The problem has been solved using the generalized differential quadrature method. Geometrical, load, and foundation parameters beside functionally graded power indexes effects on the critical buckling load have been studied.     

The ballistic performance of SiC–AA7075 functionally graded composite produced by powder metallurgy

The potential of silicon carbide reinforced Functionally Gradient Material (FGM) to be used as armor material was investigated under the impact of armor piercing projectile. For this purpose, the SiC–Aluminum Alloy (AA) 7075 functionally graded composite at different thicknesses was produced from the metallic and ceramic powders via powder metallurgy method. Before the ballistic testing, the precipitation hardening behavior of the samples was determined. And also, the microstructural characterizations of the samples were done with the aid of microscopy techniques. Next, the FGM samples were tested using armor piercing projectile to analyze their impact behavior. In the produced samples, some pore formation was detected. The ballistic experiments showed that the investigated FGMs (up to a thickness of 25 mm) did not withstand the impact of the projectile. At the tested samples, some major cracks and plug formation were detected at macrolevel while there were some microcracks, deformed and elongated grains in the regions near to the deformation zone of the samples.