Vibration of composite-material cylindrical shells with ring and/or stringer stiffeners

Free vibration is analyzed for thin-walled circular cylindrical shells constructed of composite materials and provided with ring and/or stringer stiffeners. Numerical results are presented for graphite-epoxy shells: unstiffened and stiffened with rings only, stringers only, and both rings and stringers.     

Axisymmetric vibration analysis of laminated hollow cylinders with ring stiffeners

This paper presents an axisymmetric vibration analysis of laminated hollow cylinders composed of monoclinic layers and stiffened by ring stiffeners. A successive approximation approach, which is based on a transfer matrix and then an equivalent stiffness matrix formulation, is used to enable three-dimensional solutions to be found. It is assumed that the ring stiffeners are attached to the lateral surfaces of the cylinder and only provide elastic supports in radial direction. These constraints are imposed by using Lagrange multipliers to couple the responses of a number of vibration modes of corresponding cylinders without stiffeners. Using this method the natural frequencies of a stiffened cylinder are found to be the eigenvalues of a constraint matrix and the predictions can be arbitrarily close to the exact three-dimensional solutions.     

Three-dimensional piezoelasticity solution for dynamics of cross-ply cylindrical shells integrated with piezoelectric fiber reinforced composite actuators and sensors

A benchmark three-dimensional (3D) exact piezoelasticity solution is presented for free vibration and steady state forced response of simply supported smart cross-ply circular cylindrical shells of revolutions and panels integrated with surface-bonded or embedded monolithic piezoelectric or piezoelectric fiber reinforced composite (PFRC) layers. The effective properties of PFRC laminas for the 3D case are obtained based on a fully coupled iso-field model. The governing partial differential equations are reduced to ordinary differential equations in the thickness coordinate by expanding all entities for each layer in double Fourier series in span coordinates, which identically satisfy the boundary conditions at the simply-supported ends. These equations with variable coefficients are solved using the modified Frobenius method, wherein the solution is constructed as a product of an exponential function and a power series. The unknown constants of the general solution are finally obtained by employing the transfer matrix method across the layers. Results for natural frequencies and the forced response are presented for single layer piezoelectric and multilayered hybrid composite and sandwich shells of revolution and shell panels integrated with monolithic piezoelectric and PFRC actuator/sensor layers. The present benchmark solution would help assess 2D shell theories for dynamic response of hybrid cylindrical shells.     

Buckling of thin-walled composite structures with intermediate stiffeners

The interactive buckling of prismatic, thin-walled composite columns with open sections, reinforced with intermediate stiffeners and with edge reinforcements, has been considered. The columns are assumed to be simply supported. The nonlinear problem has been solved with the Koiter’s asymptotic theory within the first order approximation. The asymptotic theory of the first order nonlinear approximation allows for simultaneous evaluation of the effect of imperfections and interactions of various modes of buckling on the behaviour of thin-walled structures. This evaluation can be only the lower bound estimation of the load carrying capacity. Detailed calculations have been made for several cases of columns.     

Nonlinear dynamic stability of laminated composite shells integrated with piezoelectric layers in thermal environment

This paper reports the nonlinear dynamic stability characteristics of laminated composite cylindrical (CYL) and spherical (SPH) shells integrated with piezoelectric layers using the finite element method. The shells are subjected to a thermal environment in addition to the in-plane periodic load and the electric load. The theoretical formulation considers Sanders?? approximation for doubly curved shells, and von Kármán type nonlinear strains are incorporated into the first-order shear deformation theory (FSDT). The formulation includes the effects of transverse shear, in-plane and rotatory inertia. The in-plane periodic load is taken as the parametric excitation in the governing equation. The nonlinear matrix amplitude equation is obtained by employing Galerkin??s method. The correctness of the formulation is established by comparing the authors?? results with those available in the published literature. Detailed parametric studies are carried out to investigate the effects of different parameters on the dynamic stability characteristics of laminated composite shells.     

Axisymmetric nonlinear analysis of shallow spherical shells by a combined boundary element and finite difference method

This paper is concerned with the development of the mixed boundary element method and finite element method for the analysis of spherical annular shells under axisymmetric loads. The boundary element techniques are used to solve the equilibrium equation of shells and the central difference operator is adopted to deal with the compatibility equations. Iterative techniques are used throughout the analysis procedure. A number of numerical examples are given in the paper to illustrate the validity of the present approach.     

Analysis of active damping in composite laminate cylindrical shells of revolution with skewed PVDF sensors/actuators

Active damping in a FRP composite cylindrical shell with collocated piezoelectric sensors/actuators is studied. The electrode on the sensors/actuators are spatially shaped to reduce spillover between circumferential modes. A three noded, isoparametric, semianalytical finite element is developed and used to model the cylindrical shell. The element is based on a mixed piezoelectric shell theory which makes a single layer assumption for the displacements and a layerwise assumption for the electric potential. The effects of location of patch of collocated piezoelectric sensors/actuators, percentage length of the shell covered with these patches, fiber angle of the laminae in the composite laminate, stacking sequence of laminae in a laminate and skew angle of the sensor/actuator piezoelectric material, on the system damping for various modes is studied.     

Suppression of nonlinear composite panel flutter with active/passive hybrid piezoelectric networks using finite element method

For the suppression of nonlinear panel flutter, a new optimal active/passive hybrid control design with piezoceramic actuators is proposed using finite element methods. This approach has the advantages of both active (high performance, feedback action) and passive (stable, low power requirement) systems. Piezoceramic actuators are connected in series with an external voltage source and a passive resonant shunt circuit which consists of an inductor and resistor. The shunt circuit should be tuned correctly to suppress the flutter effectively with less control effort as compared to purely active control. To obtain the best effectiveness, active control gains are simultaneously optimized together with the value of the resistor and inductor through a sequential quadratic programming method. The governing equations of the electromechanically coupled composite panel flutter are derived through an extended Hamilton’s principle, and a finite element discretization is carried out. The adopted aerodynamic theory is based on the quasi-steady first-order piston theory, and the von Kármán nonlinear strain–displacement relation is used. Nonlinear modal equations are obtained through a modal reduction technique. Optimal control design is based on linear modal equations of motion, and numerical simulations are based on nonlinear-coupled modal equations. Using the Newmark integration method, suppression results of a hybrid control and a purely active control are presented in the time domain.     

An efficient finite element with layerwise mechanics for smart piezoelectric composite and sandwich shallow shells

In this work, we present a new efficient four-node finite element for shallow multilayered piezoelectric shells, considering layerwise mechanics and electromechanical coupling. The laminate mechanics is based on the zigzag theory that has only seven kinematic degrees of freedom per node. The normal deformation of the piezoelectric layers under the electric field is accounted for without introducing any additional deflection variables. A consistent quadratic variation of the electric potential across the piezoelectric layers with the provision of satisfying the equipotential condition of electroded surfaces is adopted. The performance of the new element is demonstrated for the static response under mechanical and electric potential loads, and for free vibration response of smart shells under different boundary conditions. The predictions are found to be very close to the three dimensional piezoelasticity solutions for hybrid shells made of not only single-material composite substrates, but also sandwich substrates with a soft core for which the equivalent single layer (ESL) theories perform very badly.     

Prediction of energy absorption in composite stiffeners

The energy absorption behavior of composite stiffeners subjected to axial compression has been investigated. Flat plate, angle, and channel specimens were fabricated of T650-35/F584 graphite/epoxy plain-weave fabric and were crush tested under axial compression. A nonlinear finite element approach was used to model the sustained crushing of the flat plate specimens, and a progressive failure model was implemented as part of the finite element analysis to enable investigation of the fundamental mechanisms involved in the crushing behavior. The progressive failure model was based on linear elastic fracture mechanics for prediction of crack growth and a set of failure criteria for predicting fiber/matrix failures that occurred as a result of large deformations. Friction between the specimen and the crushing surface was included in the model. A semi-empirical analysis methodology was developed for prediction of the energy absorption capability of composite stiffeners based on crush tests of flat plate specimens and an understanding of the fundamentals of the energy absorption process.     

An investigation of the buckling behavior of composite elliptical cylindrical shells with piezoelectric layers under axial compression

The paper is focused on the elastic buckling behavior of piezocomposite elliptical cylindrical shell finite element formulation. The formulation is based on the shear deformation theory, and the serendipity quadrilateral eight-node element is used to study the elastic behavior of elliptical cylindrical shells. The strain-displacement relations are accurately accounted for in the formulation. The contributions of work done by the applied load are also incorporated. A constant gain displacement control algorithm coupling the direct and inverse piezoelectric effect is applied to provide active control of composite non-circular shells in a self-monitoring and self-controlling system. The governing equations obtained using the principle of minimum potential energy are solved through an eigenvalue approach. The influences of elliptical cross-sectional parameter and displacement feedback gain (G _d ) values on the critical buckling loads of elliptical cylindrical shells are examined.     

Active damping of geometrically nonlinear vibrations of laminated composite shallow shells using vertically/obliquely reinforced 1-3 piezoelectric composites

This paper addresses the analysis of active constrained layer damping (ACLD) of geometrically nonlinear transient vibrations of laminated thin composite cylindrical shallow shells using vertically reinforced 1-3 piezoelectric composite (PZC). The constraining layer of the ACLD treatment is considered to be made of this 1-3 PZC material. The Golla–Hughes–McTavish (GHM) method has been implemented to model the constrained viscoelastic layer of the ACLD treatment in time domain. The Von Kármán type non-linear strain displacement relations and the first-order shear deformation theory (FSDT) are used for deriving this electromechanical coupled problem. A three dimensional finite element (FE) model of smart composite shallow shells integrated with a patch of such ACLD treatment has been developed to demonstrate the performance of the patch on enhancing the damping characteristics of thin laminated cylindrical shells, in controlling the geometrically nonlinear transient vibrations. The numerical results indicate that the ACLD patch significantly improves the damping characteristics of the shells for suppressing the geometrically nonlinear transient vibrations of the shells. The effect of variation of fiber orientation in the PZC material on the control authority of the ACLD patch has also been investigated.     

Performance of piezoelectric fiber-reinforced composites for active structural-acoustic control of laminated composite plates

This paper deals with the active structural acoustic control of thin laminated composite plates using piezoelectric fiber-reinforced composite (PFRC) material for the constraining layer of active constrained layer damping (ACLD) treatment. A finite element model is developed for the laminated composite plates integrated with the patches of ACLD treatment to describe the coupled structural-acoustic behavior of the plates enclosing an acoustic cavity. The performance of the PFRC layers of the patches has been investigated for active control of sound radiated from thin symmetric and antisymmetric cross-ply and antisymmetric angle-ply laminated composite plates into the acoustic cavity. The significant effect of variation of piezoelectric fiber orientation in the PFRC layer on controlling the structure-borne sound radiated from thin laminated plates has been investigated to determine the fiber angle in the PFRC layer for which the structural-acoustic control authority of the patches becomes maximum.     

Probability of the presence of damage estimated from an active sensor network in a composite panel of multiple stiffeners

Artificial damage in the form of a through-thickness hole in a composite panel of five stiffeners is identified using a guided wave-based damage diagnostic algorithm, which is based on the probability of the presence of damage in the monitoring area estimated using correlation coefficients of Lamb wave signals from an active sensor network. Without defining the detail features of individual wave components, this diagnostic algorithm focuses on the calibrated changes in wave signals due to the presence of damage. The probability of the presence of damage at each grid in the monitoring area is estimated. The area consisting of grids with probability values for the presence of damage above a threshold is subsequently identified for damage identification. The effect of networks of sensing paths and shapes of the affected zone of individual sensing paths on identifying the damage in the composite panel is investigated. The results demonstrate that the diagnostic algorithm, being computationally efficient and amenable to automated processing, can be used to identify damage in highly complex structures.