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Abstract This paper deals with the derivation of the exact solutions for the static electro-mechanical response of a simply-supported doubly curved (DC) smart shell, composed of a piezoelectric fiber reinforced composite (PFRC) placed over a laminated substrate. These responses are evaluated when the system is subjected to distributed electrical and mechanical loads. The electro-mechanical governing equations and the associated boundary conditions have been derived here for the curvilinear coordinate system using the variational principle. Closed-form expressions for the mechanical displacement and the electrical potential have been obtained by solving these governing differential equations and simultaneously satisfying the derived boundary conditions. Numerical results have been presented for different shell geometries. The effect of the curvature and the geometric parameters of the PFRC layer over its performance as an actuator are studied and compared for these shells. Also, the effect of varying geometric parameters of the PFRC over its performance as a sensor is studied. Optimal dimensions of the PFRC for use as an actuator and sensor/harvester have been proposed. This study may be considered as a benchmark for use in the numerical and experimental studies involving smart shells. Highlights • Exact solutions for the governing equations modelling the electro-mechanical response of smart shells have been derived. • Electrical and mechanical governing equations have been solved without any assumptions over the displacement fields. • Effect of curvature over the performance of piezoelectric layer as an actuator and sensor/harvester has been studied. • Effect of size of the piezoelectric layer on its performance has been investigated. • This paper serves as a benchmark for verifying numerical and experimental models. [ABSTRACT FROM AUTHOR]

Geometrically nonlinear vibration control of fiber reinforced magneto-electro-elastic or multiferroic fibrous composite plates using active constrained layer damping treatment has been investigated. The piezoelectric (BaTiO 3 ) fibers are embedded in the magnetostrictive (CoFe 2 O 4 ) matrix forming magneto-electro-elastic or multiferroic smart composite. A three-dimensional finite element model of such fiber reinforced magneto-electro-elastic plates integrated with the active constrained layer damping patches is developed. Influence of electro-elastic, magneto-elastic and electromagnetic coupled fields on the vibration has been studied. The Golla–Hughes–McTavish method in time domain is employed for modeling a constrained viscoelastic layer of the active constrained layer damping treatment. The von Kármán type nonlinear strain-displacement relations are incorporated for developing a three-dimensional finite element model. Effect of fiber volume fraction, fiber orientation and boundary conditions on the control of geometrically nonlinear vibration of the fiber reinforced magneto-electro-elastic plates is investigated. The performance of the active constrained layer damping treatment due to the variation of piezoelectric fiber orientation angle in the 1–3 Piezoelectric constraining layer of the active constrained layer damping treatment has also been emphasized. [ABSTRACT FROM AUTHOR]

A novel continuous unidirectional piezoelectric fuzzy fiber reinforced composite (PFFRC) comprised of zig-zag single-walled carbon nanotubes and piezoelectric fibers as reinforcements embedded in a conventional polymer matrix has been studied. Effective piezoelectric and elastic properties of this composite have been determined by the method of cell (MOC) approach and the Mori–Tanaka (MT) method. It is found that the effective in-plane piezoelectric coefficient and elastic coefficients of the PFFRC are significantly improved over those of the existing 1–3 piezoelectric composite without reinforced with carbon nanotubes. [ABSTRACT FROM AUTHOR]

Abstract: A novel three-phase shear lag model is derived to study the load transfer characteristics of the short fuzzy fiber reinforced composite (SFFRC) subjected to the thermomechanical loading. The distinctive feature of the SFFRC is that the short carbon fiber reinforcements coated with radially aligned carbon nanotubes (CNTs) are uniformly interlaced in the polymer matrix. The main novelty of the shear lag model derived in this study is that the interactions between the representative volume elements (RVEs) of the SFFRC, the application of the radial and the thermal loads on the RVE, and the radial as well as the axial deformations of different orthotropic constituent phases of the SFFRC have been taken into account. Particular emphasis has been placed on investigating the effect of waviness of CNTs on the load transfer characteristics of the SFFRC when the wavy CNTs are coplanar with either of the two mutually orthogonal planes. In the absence and the presence of the applied radial and thermal loads on the RVE, the shear lag analysis revealed that if the wavy CNTs are coplanar with the axial plane of the carbon fiber such that the amplitudes of the CNTs are parallel to the length of the carbon fiber then the load transfer characteristics of the SFFRC are significantly improved over those of the composite with and without the straight CNTs. The limiting value of the effective aspect ratio of the carbon fiber is also found for the efficient load transfer to the carbon fiber. [Copyright &y& Elsevier]

Abstract: This paper deals with the investigation of the effect of carbon nanotube (CNT) waviness on the effective coefficient of thermal expansion (CTE) of a novel continuous fuzzy fiber reinforced composite (FFRC). This novel FFRC is composed of carbon fibers, sinusoidally wavy CNTs and epoxy matrix. The sinusoidally wavy CNTs are radially grown on the circumferential surfaces of the carbon fibers. Analytical micromechanics model based on the method of cells (MOC) approach is derived to investigate the influence of the waviness of CNTs on the effective CTEs of the FFRC. The present study reveals that if the amplitudes of the radially grown sinusoidally wavy CNTs are parallel to the axis of the carbon fiber then the thermoelastic properties of the FFRC are significantly improved over those of the FFRC being composed of straight CNTs. [Copyright &y& Elsevier]

Abstract: The effective thermal conductivities of a novel fuzzy fiber reinforced composite (FFRC) have been determined by employing the effective medium approach in conjunction with the composite cylinder assemblage approach. The novel constructional feature of this FFRC is that the uniformly spaced carbon nanotubes (CNTs) are radially grown on the circumferential surfaces of the unidirectional carbon fiber reinforcements. The present study reveals that the transverse thermal conductivities of the FFRC are improved up to ∼1040% and ∼400% over those of the composite without CNTs when the values of CNT volume factions present in the FFRC are 6.88% and 4.27%, respectively. It is also found that the CNT/polymer matrix interfacial thermal resistance does affect the effective thermal conductivities of the FFRC, and the effective values of thermal conductivities of the FFRC are improved with the increase in the values of carbon fiber volume fraction and temperature. [Copyright &y& Elsevier]

We present the finite element (FE) model using the first-order shear deformation theory (FSDT) to investigate the damping performance of laminated hybrid fiber-reinforced composite (HFRC) smart plates via the active constrained layer damping (ACLD) treatment. A unique feature of the HFRC is that the nanoscale carbon nanotubes (CNTs) are embedded in the matrix phase of carbon fiber composite to improve the overall properties, especially the damping characteristics of the resulting HFRC. Two- and three-phase micromechanical models are employed to determine the effective elastic properties of the base composite and HFRC respectively. The constraining layer of the ACLD treatment is considered to be made of vertically reinforced 1–3 piezoelectric composite (PZC) material. The system consists of a laminated HFRC plate integrated with the two patches of ACLD treatment and the numerical results are computed for three cases: symmetric and anti-symmetric cross-ply, and anti-symmetric angle-ply. The damping performance of the laminated HFRC square plate is significantly enhanced over the laminated base composite plate due to the incorporation of a small amount of CNTs. In particular, the anti-symmetric angle-ply case provides better damping than symmetric/anti-symmetric cross-ply cases. Analysis of the HFRC plate showed that its vibration amplitudes can be attenuated from ∼ 8 to ∼ 16% by adding a small amount CNTs. The effect of in-plane and transverse actuation of 1–3 PZC on the damping characteristics of the overall plate was also studied. We found that the transverse actuation significantly influences the damping performance of the overall plate. The outcomes of our study provide substantial evidence that the addition of a small amount of CNTs in the conventional composite structure can improve its damping performance significantly. This is practically possible in view of the recent research activities in the field of fabrication of large-scale CNT-based hybrid composite structures. • FE model is developed to study the damping performance of laminated CNT-based hybrid composite plates. • Micromechanical models are developed to determine the effective elastic properties of hybrid composites. • Damping performance of laminated HFRC plate is significantly enhanced due to the incorporation of small amount of CNTs. • Transverse actuation significantly influences the damping performance of overall plate. [ABSTRACT FROM AUTHOR]

Abstract: The effective properties of a continuous fuzzy fiber-reinforced composite have been determined by employing the method of cells approach and the finite element (FE) method. The novel constructional feature of this fuzzy fiber-reinforced composite is that the uniformly aligned carbon nanotubes (CNTs) are radially grown on the surface of the horizontal carbon fibers. The effective properties of this fuzzy fiber-reinforced composite are estimated with and without the consideration of an interphase formed due to non-boned interaction between a CNT and the polymer matrix. Effective elastic properties of the fuzzy fiber-reinforced composite estimated by the method of cells approach have been compared with those predicted by the FE method. It has been found that the transverse effective properties of this composite are significantly improved due to the radial growing of CNTs on the surface of the carbon fiber. It is also found that the consideration of the CNT/matrix interphase has a negligible effect on the effective elastic properties of the fuzzy fiber-reinforced composite. [Copyright &y& Elsevier]

Abstract: A novel short fuzzy fiber-reinforced composite reinforced with aligned short carbon fibers and carbon nanotubes (CNTs) has been analyzed in this study. The constructional feature of this composite is that the uniformly aligned CNTs are radially grown on the circumferential surfaces of short carbon fibers. Micromechanical model based on the Mori–Tanaka method is derived to estimate the effective elastic properties of the short fuzzy fiber-reinforced composite. Effective elastic properties of the short fuzzy fiber-reinforced composite estimated by the Mori–Tanaka method have been compared with those predicted by the finite element (FE) method. The effective properties of the short fuzzy fiber-reinforced composite are estimated in the presence and the absence of an interphase between a CNT and the polymer matrix formed due to non-bonded van der Waals interaction between them. It has been found that the transverse effective properties of this composite are significantly improved due to the radial growing of CNTs on the circumferential surface of the short carbon fibers and the CNT/ polymer matrix interphase has negligible effect on the effective properties of the short fuzzy fiber-reinforced composite. Effects of the different types of zig–zag CNTs and the variation of their volume fraction on the effective properties of the short fuzzy fiber-reinforced composite are also investigated. [Copyright &y& Elsevier]

Abstract: In this paper, a nonlinear static finite element analysis of simply supported smart functionally graded (FG) plates in the presence/absence of the thermal environment has been presented. The substrate FG plate is integrated with the patches of piezoelectric fiber reinforced composite (PFRC) material which act as the distributed actuators of the plate. The material properties of the FG substrate plate are assumed to be temperature dependent and graded along the thickness direction according to a simple power-law distribution in terms of the volume fractions of the constituents. The derivation of this nonlinear thermo-electro-mechanical coupled finite element model is based on the first order shear deformation theory and the Von Karman type geometric nonlinearity. The numerical solutions of the nonlinear equations of the finite element model are obtained by employing the direct iteration method. The numerical illustrations suggest the potential use of the distributed actuator made of the PFRC material for active control of nonlinear deformations of smart FG structures. The effects of volume fraction index of the FG material of the substrate plates and the locations of the PFRC patches on the control authority of the patches are investigated. Emphasis has also been placed on investigating the effect of variation of piezoelectric fiber orientation angle in the PFRC patches on their actuation capability for counteracting the large deflections of FG plates. [Copyright &y& Elsevier]

The effective coefficients of piezoelectric fiber-reinforced composites (PFRC) have been determined through micromechanical analyzes. The method of cells (MOC) and the strength of materials (SM) approach have been employed to predict the coefficients. A constant electric field is considered in the direction transverse to the fiber direction and is assumed to be the same both in the fiber and the matrix. MOC and SM predictions for the effective piezoelectric coefficient of the PFRC assessing the actuating capability in the fiber direction are in excellent agreement. It has been found for the piezoelectric fibers considered that, when the fiber volume fraction exceeds a critical fiber volume fraction, this effective piezoelectric coefficient becomes significantly larger than the corresponding coefficient of the piezoelectric material of the fiber. The methods also show the excellent matching of the predictions of the effective elastic constants and the dielectric constant of the PFRC in the useful range of fiber volume fraction. [ABSTRACT FROM AUTHOR]

This paper is concerned with the analysis of active constrained layer damping (ACLD) of geometrically nonlinear vibrations of doubly curved sandwich shells with facings composed of fuzzy fiber reinforced composite (FFRC). FFRC is a novel composite where the short carbon nanotubes (CNTs) which are either straight or wavy are radially grown on the periphery of the long continuous carbon fiber reinforcements. The plane of waviness of the CNTs is coplanar with the plane of carbon fiber. The constraining layer of the ACLD treatment is composed of the vertically/obliquely reinforced 1–3 piezoelectric composites (PZCs) while the constrained viscoelastic layer has been sandwiched between the substrate and the PZC layer. The Golla–Hughes–McTavish (GHM) method has been implemented to model the constrained viscoelastic layer of the ACLD treatment in time domain. A three dimensional finite element (FE) model of smart doubly curved FFRC sandwich shells integrated with ACLD patches has been developed to investigate the performance of these patches for controlling the geometrically nonlinear vibrations of these shells. This study reveals that the performance of the ACLD patches for controlling the geometrically nonlinear vibrations of the doubly curved sandwich shells is better in the case of the facings composed of laminated FFRC than that in the case of the facings made of conventional orthotropic laminated composite. The research carried out in this paper brings to light that even the wavy CNTs can be properly utilized for attaining structural benefits from the exceptional elastic properties of CNTs. [ABSTRACT FROM AUTHOR]