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Analytical elastic–plastic analysis is presented to investigate the in-plane deformation of the reentrant honeycomb structures subjected to tension or compression. An analytical elastic–plastic def...

The stress-intensity factors of box beams under torsion and crack propagation under torsion or/and bending moment are discussed here. This study is motivated by a previous work [1] that derived a c...

Panel methods are frequently applied to aerodynamic shape optimization problems due to their fast turnaround time and ability to model arbitrary geometries. Despite being advantageous for design optimization, we have found that panel methods can predict nonphysical results for unconventional geometries. This paper presents robust methods to solve optimization problems using panel methods that are not susceptible to numerical errors. Important factors are highlighted with regard to choice in boundary conditions, induced drag calculation, wake modeling, and regularization. Two parameterization methods are introduced where wing geometry is defined locally by airfoils at discrete spanwise positions and regularized by filtering along the span. Such methods of defining the geometry locally enlarge the design space and allow the optimizer to converge to reliable designs. Results also suggest the following: 1) enforcing a Dirichlet boundary condition rather than a Neumann formulation provides significant cost savings in gradient calculations, 2) far-field force calculations should be adopted for optimization problems as numerical errors in surface pressure integration have a strong influence on the gradients, and 3) the additional design freedom of a B-spline parameterization can be disadvantageous as the low fidelity of the inviscid model cannot correctly capture aerodynamic properties of irregular airfoil geometries.

Light-activated shape memory polymer (LaSMP) is a novel actuator with dynamic Young’s modulus and strain when exposed to ultraviolet lights, which can be used in noncontact vibration control. This ...

Dynamically extendable blade chord sections show promise for reducing helicopter rotor loads. A rotor model\ud based on elastic beam concept, and capable to predict helicopter power, is utilized. A four bladed rigid rotor\ud with the shape similar to the UH-60A rotor, is used as baseline for comparisons. For the control of the 4/rev\ud vertical hub force, it is not beneficial to actuate the extendable chord at hover and low speed flight. At a high\ud speed of 270km/h, the extendable chord, with a width of 10% rotor radius and responded to 10% of chord\ud length, obtained a maximum force reduction of 89.4%. The magnitude of the dynamic chord needs to be\ud optimized according to the flight state. The performance can be enhanced by increasing the extension or\ud width of the dynamic chord. The dynamically extendable chord was not suitable for reducing the 2/rev blade\ud flapwise root bending moment. A 3/rev dynamic chord though showed great potential in reducing the 3/rev\ud flapwise root bending moment and the 4/rev rotor rolling and pitching moments, simultaneously. The\ud effectiveness of a 5/rev dynamic chord in reducing the 4/rev rotor rolling or pitching moment degraded\ud significantly compared with a 3/rev actuated. To control the 4/rev target load originating from the 3/rev\ud flapwise root bending moment, the phase difference for the maximum rotor rolling and pitching moment\ud reduction was 180o\ud for the 5/rev dynamic chord. Based on the analyses, it is recommended to use the 4/rev\ud dynamically extendable chord to reduce the 4/rev vertical hub force, and use the 3/rev dynamic chord to\ud reduce the 3/rev blade flapwise root bending moment and 4/rev rotor rolling and pitching moments.

Flexoelectric materials subject to inhomogeneous electric field can actuate and control flexible structures based on the converse flexoelectric effect. An atomic force microscope (AFM) probe placed...

A new structural design method is developed in this paper to improve the surface accuracy and enhance the performance of large deployable mesh reflectors. A self-standing truss with hard points (SS...

We investigate in this Paper the nonlinear aeroelastic response of large horizontal axis wind turbines under a stochastically simulated turbulent wind field, which is instantaneously sampled by the...

The responses of a NACA0012 airfoil and a large-aspect-ratio wing, subjected to gust excitation about high mean angles of attack, close to stall, are presented here. Reynolds-averaged Navier–Stokes...

In this paper, a method to obtain effective continuum beam stiffness properties of tensegrity towers with n struts in each bay is developed. Long tensegrity towers for space applications can be mod...

A multifield variational beam sectional analysis is proposed based on the Hellinger–Reissner principle for anisotropic beams with arbitrary cross-sectional geometries and material distributions. Bo...

Analytical expressions for the energy release rate and mode-mixity phase angle are derived for a sandwich composite double-cantilever beam fracture specimen with the face sheets reinforced by stiff plates. The sandwich beam is considered symmetric, with identical top and bottom facesheets. Only a pure moment loading is considered. The J-integral coupled with laminate beam theory is employed to derive closed-form expression for the energy releaserate in terms of the applied moments, geometry, and material properties .A scalar quantityωis obtained to express the mode-mixity phase angle. It is shown that ω is independent of the applied loading conditions. The value of ω is found to be moderately influenced by reinforcement thicknesses.

Thin-walled beams exhibit a nonlinear response to bending moments due to the progressive flattening of the cross-section, a behavior commonly referred to as the Brazier effect. Most approaches to model this effect are limited to either circular cross-sections or to cross-sections made of isotropic materials. This article proposes an efficient two-step method of predicting the nonlinear collapse of thin-walled cross-sections of arbitrary geometry with isotropic and orthotropic materials. The procedure relies on representing the cross-section by two-dimensional nonlinear corotating beam elements with imposed in-plane loads proportional to the curvature, combined with a finite strip buckling analysis based on the deformed cross-section. By comparison with existing analytical and numerical modeling approaches, it is demonstrated that the present method can capture the cross-section flattening and critical moment for buckling of thin-walled structures commonly found in the industry.

The transient blast response of a sandwich panel that consists of a compressible core with in-plane rigidity using the extended high-order sandwich panel theory is presented and compared with elasticity closed-form solutions. The mathematical formulation of the extended high-order sandwich panel theory for the transient dynamic response of sandwich plates is described along with a numerical investigation. The extended high-order sandwich panel theory formulation takes into account the shear resistance of the core and its compressibility, which is envisaged through nonidentical displacements of the upper and the lower facesheets and its in-plane rigidity. The equations of motion and the appropriate boundary conditions are derived using the Hamilton’s principle. A numerical investigation is conducted on a simply supported sandwich panel, and its results are compared with a benchmark elasticity closed-form solution. The results include deformed shapes at the first millisecond at various time steps; displacem...

This paper presents a complete set of analytical expressions for the stiffness constants of a generalized Euler–Bernoulli beam theory for homogeneous, anisotropic, prismatic beams with arbitrary cross-sectional shapes. These expressions are extracted from exact solutions of the linear equations of three-dimensional elasticity for the cases of loading by axial forces, torques, and bending moments about two orthogonal directions. Closed-form expressions are derived for the extensional stiffness and the extension-related coupling terms. Expressions for the remaining stiffness constants are derived in terms of the torsional stiffness: the expression of which is in terms of a function that needs to be obtained. The resulting expressions reveal both similarities and differences from its isotropic and orthotropic counterparts. For elliptical, anisotropic cross sections and rectangular, orthotropic cross sections, all stiffness constants are known in closed form. These closed-form expressions constitute a standar...

A = beam cross-sectional area, m B = Boley parameter c = specific heat, J∕kg · K E = modulus of elasticity, N∕m h = thin-walled beam thickness, m I = moment of inertia, m k = thermal conductivity,W∕m · K l = beam length, m MT = thermal bending moment, N · m N = shape function O; x; y; z = beam coordinate q = absorbed solar heat flux of beam surface,W∕m R = thin-walled beam radius, m S0 = magnitude of solar heat flux, W∕m S0 = solar heat flux vector T = temperature, K Ta = average temperature, K Ta = steady-state average temperature, K Ta = uncoupled average temperature, K Tp = perturbation temperature, K Tp = steady-state perturbation temperature, K Tp = uncoupled perturbation temperature, K T0 = initial temperature, K t = time, s tT = characteristic thermal time, s tω = the fundamental structural period, s t0 = initial time, s W = generalized displacement, m w = displacement in z direction, m w = steady-state quasi-static displacement at beam free end, m wdyn = maximum dynamic displacement in z direction, m wst = maximum quasi-static displacement in z direction, m w = uncoupled displacement in z direction, m αs = absorptivity of beam surface αT = thermal expansion coefficient e = emissivity of beam surface θ = steady-state quasi-static bending angle at beam free end, rad θy = beam bending angle about y axis, rad θ0 = solar heat flux incident angle, rad μ = damping, N · s∕m ρ = material density, kg∕m σ = Stefan–Boltzmann constant 5.67 × 10−8,W∕m2 · K φ = circumferential angle along the midline of beam cross section, rad

S OLUTIONS to the problems of the deformation of laminated cylindrical shells of finite dimensionsmust satisfy the prescribed boundary conditions, which introduce complexities that are far more difficult to handle; among them being asymmetrically placed boundary conditions, for example clamped-free conditions. Balaraman et al. [1] obtained closed-form solutions for internally pressurized, asymmetrically laminated, cylindrical shells of finite length under the framework of the classical lamination theory (CLT) and the Love–Timoshenko kinematic relations, although the presented numerical results were for unsymmetric cross-ply shells only [1]. Admissible boundary conditions were derived by Chaudhuri et al. [2] for an arbitrarily laminated, internally pressurized, cylindrical shell of finite length under the framework of Donnell’s, Love–Timoshenko’s, and Sanders’ kinematic relations, and the CLT. Chaudhuri et al. [3] derived a closed-form solution for arbitrarily laminated cylindrical shells with both ends simply supported, and subjected to uniform internal pressure, under the framework of the CLT and Love–Timoshenko’s kinematic relations. Abu-Arja and Chaudhuri [4,5] and Chaudhuri and Abu-Arja [6] presented closed-form solutions of cross-ply and angle-ply cylindrical shells under internal pressure based on the constant shear-angle theory (CST), also known as the first-order shear deformation theory (FSDT). In what follows, a hitherto unavailable closed-form solution for an unsymmetric cross-ply, cantilever, cylindrical shell of finite length, which is under uniform internal pressure, using Love–Timoshenko’s kinematic relations under the framework of CLT is presented. II. Formulation of the Problem and Solution Methodology

L ARGE flexible structures composited of thin-walled beams, such as antennae, solar arrays, etc., are extensively used in space applications. These structures may undergo thermally-induced deformations or even vibrations due to the change of orbital heating [1]. To suppress these adverse responses one may use passive control methods to obtain a good design [2]. However, active methods are still needed to achieve precise control in transient manner. Many popular active shape control methods usually use piezoelectric actuators [3]. In this way, cautions should be paid on the interface debounding failure, because the control force is transferred by the tight bounding between the actuator and the structure. Because the thermally-induced response is principally due to the change of thermal environment it could be reliably and economically suppressed if one can control the temperature distribution of the structure. In this manner, the control force induced by thermal expansion strains is generated naturallywithin the structure instead of being transferred through the shear force. Thus, the interface debounding is unlikely to happen. Haftka and Adelman [4] were probably the first to have the idea of shape control by imposing prescribed temperatures on the control elements. They pointed out that the corresponding thermal stresses are self-equilibrating and smaller than those associated with applied forces. Therefore, one need not worry about small inaccuracies in equilibrating control forces, which lead to the drift in position or orientation. In addition, the solar energy could be a natural source of heating. Similar to the idea in [4] thermal bending moments have been applied to control the vibration of cantilevers, ignoring the longitudinal heat conduction and radiation boundary condition [5,6]. Irschik and Ziegler [7] and Irschik and Pichler [8] gave theoretical models of both the static and dynamic shape control by imposing thermal strains. However, the practical realization of the required thermal strains is still unresolved [9]. In present Note, we investigate the practical implementation of quasi-static shape control for thin-walled structures by using heaters. For this purpose, a nonlinear optimization problem is formulated to determine the required control heat fluxes. Because radiation is considered for this transient problem the Fourier finite element [10] is adopted to reduce the computational cost. Besides, an efficient optimization heuristic is constructed to find the good placement of heaters that minimizes the total control energy.

Closed-form algebraic expressions for the energy-release rate and the mode mixity are obtained for a debonded sandwich (trimaterial). The most general case of an “asymmetric” sandwich is considered (i.e., the bottom face sheet not necessarily of the same material or thickness as the top face sheet). The energy-release rate is obtained by use of the J-integral, and the expression is derived in terms of the forces and moments at the debond section. Regarding the mode mixity, a closed-form expression is derived in terms of the geometry, material, and applied loading, and it is proven that, in the trimaterial case, just as in the bimaterial case, the mode mixity can be obtained in terms of a single scalar quantity ω, which is independent of loading; the ω value for a particular geometry and material can be extracted from a numerical solution for one loading combination. Thus, this analysis extends the existing formulas in the literature, which are for either a delamination in a homogeneous composite or an int...

Robust linear control, combined with model-reduction methodologies, is investigated for gust rejection on large, very flexible aircraft using trailing-edge control surfaces. Controllers are designed on linearizations of the nonlinear aeroelastic equations, and the closed-loop response of both the linearized and nonlinear system to discrete gust distributions is compared to the open-loop dynamics. Results show that an ℋ∞ controller performs well on a relatively large linearized system, with 9% load alleviation in root bending moments for the critical gust length. When applied to the nonlinear model of the same vehicle, the robust controller gives a good performance in response to short gusts, including the critical length, with even better load reductions than the linear case. However, this performance gap decreases as the gust length is increased. It is also shown how standard model-reduction techniques can provide metrics for the selection of a minimum size of the aeroelastic system. Finally, it is shown...

different depths, filled with a range of uniform-sized steel ball bearings, were used as particle dampers. For all the tests, the total particle damper mass was identical. During operation, the tip of the beam was displaced, and after release the beam could vibrate freely. The decay in the vibratory motion of the tip of the beam was measured over a range of centrifugal loads. It was found that there is a zone with a high- and one with a low-damping factor. These zones depend on the ratio between the peak vibration acceleration and the centrifugal loading and have a limit, in terms of the centrifugal loading beyond which no damping occurs. The main parameters that influence the performance ofthe particle dampers are thelength/diameter aspectratioandthe particle size. Animportant finding is that a particle damper with fewer layers (increase in particle size) will still function at a higher centrifugal load, compared with one with more layers.

This paper outlines the structural analysis of an articulated pressurizable structure termed the multibubble. The multibubble is a structurally efficient pressure vessel that pressurizes a volume with substantial spatial freedom. Applications are found in pressure cabins for blended-wing–body aircraft and conformable pressure vessels for liquid gases (e.g., propane) or cryogenic applications. Themultibubble in this paper can be configured in an openor closed-cell configuration and consists of cylindrical and spherical membrane elements equipped with walls and/or reinforcements at the intersections in order to ensure structural integrity. The multibubble allows pressurization loads to be carried through in-plane stresses. To solve for loads and forces in the multibubble, it is shown that the solution simply depends on pressure and geometric variables.

A, B, C, D = stiffness matrices of the second-order asymptotically correct beam theory a = characteristic length of the cross-sectional dimension ai = unit vectors of the reference coordinate system b = half-width of a beam with a rectangular cross section E = Young’s modulus F1 = internal axial force F2, F3 = internal shear forces k1 = initial twist k2, k3 = initial curvatures ‘ = characteristic wavelength of deformation along x1 M1 = internal torque M2,M3 = internal bending moments n = outward-directed unit normal vector R = characteristic radius of initial twist and curvatures R, S, T = submatrices of the generalized Timoshenko flexibility matrix t = thickness of a beam with a rectangular cross section U = sectional strain energy X, Y, G = submatrices of the generalized Timoshenko stiffness matrix x1 = beam axial coordinate x2, x3 = local, Cartesian, cross-sectional coordinates for the beam section

A new methodology for determining redundant reactions of beams is presented in this paper. This methodology is based on the principle of quasi work, which is a powerful pseudoenergy theorem deduced from Tellegen's theorem. It takes topography of a structural system as a variable in addition to the variables involved in conventional energy methods, variational principles, and finite element methods. The concept of topologically similar system lies at the heart of the principle of quasi work. This concept is explored for beams to define topologically similar beams and topologically equivalent beams. The principle of quasi work is validated for beams and subsequently used for determining redundant reactions of indeterminate and continuous beams. Further, a unique concept of reference beam is developed. Equation of deflection curve of this reference beam is used to solve redundant reactions of indeterminate beams. This methodology has an advantage of calculating redundant reactions mostly by simple multiplications without any integrations or differentiations and does not require any prior knowledge of writing bending moment expressions. The method is illustrated through examples. It is possible to develop an interactive graphic computer package for calculating reactions of indeterminate beams.

A recently developed nonlinear approach is adapted and used to predict crack initiation in stringer terminations of discretely assembled composite panels made from skin and stiffeners. A linear elastic fracture mechanics based submodel is used to simulate the crack initiation in the critical regions and the influence of ply drop-off is captured. The von Karman formulation for moderately large deflections in plates is used to capture the nonlinear structural behavior; three-dimensional assemblies are schematized and the effect of eccentricity is included in the simulation. An optimum design criterion is sought and basic guidelines for good design are provided. Furthermore, a method for preliminary assessment of structural strength is proposed and predictions are validated against detailed nonlinear finite element analysis.

The nonlinear constitutive relations of the cellular materials are presented in this paper based on the large deformation analysis of elastic beams in plane. The relations reflect the dependences of equivalent stress, equivalent Young’s modulus, equivalent Poisson’s ratio, and equivalent shear modulus on the deformation. It is found that the modified factors of the linear constitutive relations are associated with the shape and deformation of a considered cellularmaterialandindependentoftheratioofthefacethicknessttolengthl(t=l)ofthematerial.Sotheconstitutive relations can describe the mechanical properties of the cellular materials with the same shape.

In this research, mechanical buckling of circular plates composed of functionally graded materials is considered. Equilibrium and stability equations of a functionally graded material circular plate under uniform radial compression are derived, based on the higher-order shear deformation plate theory. Assuming that the material properties vary as a power form of the thickness coordinate variablez and using the variational method, the system of fundamental partial differential equations is established. A buckling analysis of a functionally graded circular plate under uniform radial compression is carried out and the results are given in closed-form solutions. The results are compared with the buckling loads of plates obtained for a functionally graded circular plate based on the first-order shear deformation plate theory and classical plate theory given in the literature. The study concludes that higher-order shear deformation plate theory accurately predicts the behavior of a functionally graded circular plate, whereas the first-order shear deformation plate theory and classical plate theory overestimate buckling loads.

The static and dynamic interaction between piezoelectric layer and host laminated beam has been investigated using classical laminate theory and first-order shear deformation theory. A finite element model has been developed to study the mechanical and electrical behavior of laminated composite beam with piezoelectric actuators. The numerical results have been compared with those available in the literature in order to validate the accuracy of the model. A design optimization methodology has been developed by combining the finite element model and the sequential quadratic programming technique to improve the structural performance. Further, the optimization algorithm has been improved by performing the sensitivity analysis and analytical gradients of constraints and objective function. Various types of optimization problems including shape control of a beam and mass minimization have been investigated. By careful positioning of the actuators and polarizing them to create bending moment and stretching force when required, a very precise shape control has been achieved as well as considerable reduction in the mass of the structure. It has been observed using the analytical gradients of constraints and objective function analytically can significantly reduce the total number of iteration required to obtain the optimal design.

Adhesively bonded joints are currently of interest to the aerospace field due to the heavy reliance on bonded composite structures in new aircraft designs. In response, tools for joint analysis have been developed and examined in this two-part paper. In Part 1, a higher-order theory, considering an explicit discretization of the joint geometry, was investigated. In Part 2, a method for multiaxial stress analysis of composite joints is developed based on Mortensen's unified approach, with considerable extension to accommodate transverse in-plane strain and hygrothermal loads and most importantly, to compute the in-plane and interlaminar stresses in the adherends. Compared with other analytical methods for bonded joint analysis, the present method is capable of handling more general situations, including various joint geometries, linear and nonlinear adhesives, asymmetric and unbalanced laminates, and various loading and boundary conditions. The method has been implemented within the commercially available HyperSizer® structural analysis software. Through comparison to finite element and analytical results, it is shown that the new HyperSizer joint analysis method is efficient and accurate and can serve as a capable tool for joint analysis in preliminary design, where rapid and generally accurate stress field estimates, as well as joint strengths and margins are needed.

A class of textile core sandwich structure is investigated with respect to their ability to absorb transverse compressive load. To this end, experimental observations are compared to numerical simulations for cores made from precrimped woven wire cloth laminated together via transient liquid-phase bonding. The experimental observations show that this structure exhibits key properties for being a promising load-absorbing structure, for example, impact and blast protection. Matching numerical simulations show that the behavior can be captured with simulations and that a relatively simplified scheme can be used. The simulations also suggest sensitivity to the local topology in absorbing energy, as well as explaining the somewhat unexpected deformation behavior observed experimentally. Multifunctionality, owing to the accessible open space between cells, coupled with attractive compressive behavior is achieved. Nomenclature d = diameter of the truss (wire diameter) E = Young’s modulus of the material comprising the trusses G c = shear modulus of the truss core R = radius of the truss, d/2 r = radius of the connecting element in the woven structure w = opening width (distance between wires) ¯ ρcore = relative density of the truss core σY = yield strength of the material comprising the trusses σ c Y = compressive strength of the truss core τ c Y = shear strength of the truss core

One of the most significant drivers in satellite design is the minimization of mass to reduce the large costs involved in the launch. With technological advances across many fields, it is now widely known that very low-mass satellites can perform a wide variety of missions. However, there is a need for small, efficient, area deployment devices. One possible structural solution for such devices is tape springs. Previous work on tape spring hinges has focused on two-dimensional folds; however, applications exist that incorporate three-dimensional tape spring folds. The properties of three-dimensional tape spring folds are experimentally investigated using a specially designed test rig. The rig is first used to produce comparative two-dimensional data before being used to analyze more complex three-dimensional folds.

Although it has long been recognized that all long thin-walled hollow structures exhibit a nonlinear response to bending moments, the majority of analytical research has focused on circular cross sections. A method of predicting the nonlinear behavior of multibay airfoil sections is presented. Although the approach is simple, the algebraic complexity lends itself toward a solution using algebraic manipulation software. Comparison of the analytical models with finite element analysis shows good correlation and demonstrates the ability of the model in predicting the nonlinear bending response of smooth orthotropic two-bay airfoils. Nomenclature [a ]= shell in-plane compliance matrix C = overall curvature [D ]= shell bending stiffness matrix E =Y oung’s modulus G = shear modulus h = height I = second moment of area l = section Y dimension M = longitudinal bending moment m = cross-sectional bending moment p = cross-sectional reaction force S =w all length U = energy w = cross-section displacement z α = cos(β) β = horizontal wall angles to midplane e = strain κ = cross-sectional curvature λ = element length correction factor µ = I correction factor ν = Poisson’s ratio ψ = distributed Brazier crushing force I. Introduction

Adhesively bonded patch repair has been widely used as an efficient and economical method to extend the service life of cracked structural components. Most of the currently available analysis methods and empirical databases for composite bonded patch repair to flat structures are computationally efficient and easy to use. However, the current knowledge on composite bonded repair for flat structures cannot be directly applied to curved repairs. A novel adhesive element developed by the authors in conjunction with a shell element is employed to investigate the fracture toughness at the crack tip of a cracked cylindrical shell bonded with a composite patch. To validate the present finite element model for curved composite patch repairs, the stress intensity factors in a flat composite patch repair are first computed by the strain energy release rate analysis method and compared with those available in the literature. For the curved patch repairs, a full three-dimensional finite element analysis is also conducted to validate the proposed numerical model. Some selected numerical examples are given to demonstrate the effect of curvature on the fracture toughness of a cracked cylindrical shell bonded with a composite patch subjected to different types of loading.

Photostrictive actuator, which can directly turn light energy into mechanical energy, is a new promising photoactuation technique for active vibration control of flexible structures. It offers the advantage of generating distributed actuation strain without connecting any electric lead wires. Photonic control of flexible cylindrical shells using discrete photostrictive actuators is investigated, and the photoactuation effectiveness is evaluated. A coupled optopiezothermoelastic shell theory is presented that incorporates photovoltaic, pyroelectric, piezoelectric, and thermal effects and has the capability to accurately predict the response of a shell to a command illumination applied to the photostrictive actuators. Expressions for the photogenerated forces and moments have been developed. Governing equations are formulated. Solution procedures based on the modal analysis technique are outlined. The detailed actuator control effectiveness is evaluated with respect to actuator placements. It is shown that by properly positioned the actuators the system performance can be improved. Numerical simulation results also show that the membrane control action is more significant than the bending control action. The circumferential membrane control action dominates, and the photonic control effectiveness is only slightly reduced by the removal of all of the actuator patches along the longitudinal direction.

are the normal strains in the prebuckling state. The buckling anal- ysis for the nondebonded imperfect beams is then similar to that presented earlier for the free-vibration problem. In the case of a generally debonded beam, an exact buckling solution cannot be obtained and approximate treatments should be employed. How- ever, if the beam is with through-length delamination at the kth interface, for example, an exact solution can be obtained, just as it can for the nondebonded imperfect beam, but with K (k)

A higher-order assumed modes analysis for a sandwich plate is developed. The base plate is an isotropic plate with the parallel edges of its span clamped and with its remaining edges free. An isotropic constraining layer sandwiching a viscoelastic core is centrally located over one-third of the span across the plate's chord. Analysis of the base plate uses two-dimensional plate bending and in-plane extension mode shapes based on the Kantorovich-Krylov method. Free-free one-dimensional rod modes are used to approximate in-plane motions in both x and y directions for the constraining plate, and bending displacement compatibility is assumed between base and constraining plates. The Golla-Hughes-McTavish method was used to account for the frequency-dependent complex shear modulus of the viscoelastic core. Natural frequencies, mode shape functions, loss factors, and frequency responses of the sandwich plate were calculated and compared to the results of our previous analysis using one-dimensional beam and rod modes. Fewer modes were needed in the current analysis to achieve the same accuracy as compared to the previous analysis. Experiments were conducted to validate predictions, and the experimental data substantially agree with our results.

Debonding of a piezoelectric actuator or sensor layer in an actively controlled structure may significantly affect its closed-loop control and even collapse the active control. Investigation of the effects of the debonded piezoelectric layer on the control stability of smart structures is very important. A state-equation-based method is presented to investigate the control stability of the beams controlled by partially debonded piezoelectric actuator and sensor layers. An analytical model of a beam with a debonded piezoelectric layer is given, in which the debonding of the piezoelectric layer is modeled by considering the adhesive layers. Both displacement continuity and force equilibrium conditions are imposed at the interfaces between the debonded and perfectly bonded regions. Based on this model, a characteristic equation for the controlled structure with debonded piezoelectric actuators and sensor is derived, from which the eigenvalues of the controlled system can be obtained. The control stability of a controlled mode can be evaluated by examining the sign of the real part of the corresponding eigenvalue. The simulation results show that even a 5% edge debonding of the actuator layer can destabilize the cantilevered beam controlled by an actuator/sensor pair, whereas a beam controlled by a self-sensing actuator layer can tolerate much larger edge debonding of the piezoelectric layer. More significant changes can be found in both the damping coefficient and the frequency of the mode whose frequency is close to one of the modal frequencies of the debonded part of the actuator.

Linearconstitutiveequationsofa thermopiezomagneticmedium involving mechanical, electrical, magnetic, and thermal e elds are presented with the aid of a thermodynamic potential. A thermopiezomagnetic medium can be formed by bonding together a piezoelectric and magnetostrictive composite. Two energy functionals are dee ned. It is shown via Hamilton’ s principle that these functionals yield the equations of motion for the mechanical e eld, Maxwell’ s equilibrium equations for the electrical and magnetic e elds, and the generalized heat equation for the thermal e eld. Finite element equations for the thermopiezomagnetic media are obtained by using the linear constitutive equations in Hamilton’ s principle together with the e nite element approximations. The e nite element equations are utilized on an example two-layer smartstructure, which consistsof a piezoceramic (barium titanate ) layer at the bottom and a magnetoceramic (cobalt ferrite ) layer at the top. An electrostatic e eld applied to the piezoceramic layer causes strain in the structure. This strain then produces magnetic e eld in the magnetoceramic layer.

Two methodologies are outlined for the analytical evaluation of the loss factor in composite laminates and in sandwich structures. One of these methods is based on the analysis of free vibrations, whereas the second approach utilizes mechanics of materials. Both methods yield similar results. The loss factor is predicted both for specially orthotropic as well as for generally orthotropic laminas, subjected to axial stresses and/or transverse shear. The results for the loss factor of the laminas are in good agreement with available experimental data. As follows from the numerical analysis, the loss factor of laminas of the facings is significantly affected by the angle of lamination. The loss factor of a sandwich beam is relatively insensitive to the frequency of vibrations, although the effect of this frequency on the loss factors of constituent materials may alter this conclusion.

An analytical method is presented for delamination analysis of a sandwich beam subjected to an action of a transverseload.Thestress/strainstateof thesandwichbeam including delaminationisdecomposedinto two states: basic state and additional state. The additional state of the delaminated sandwich beam is investigated using the theory ofhigh-ordershearstrain. Theordinarydifferential equationsfordelaminatedand undelaminated zones in theadditional state are obtained. Becauseof stress singularity at delamination frontier, the usual displacement and stresscontinuityconditions between thedelaminated and undelaminatedzonesarenotsuitableforan approximate analytical solution. Therefore, new weak form of continuity condition is suggested. Comparison with a numerical solutionrevealsthattheanalyticalsolutionmethodprovidesgoodaccuracyinbothdelaminatedandundelaminated areas. A new method of calculating energy release rate of delamination growth for a sandwich beam is elaborated on the basis of the developed analytical technique. The considered sample delamination problem shows that, the higher the order of shear strain approximation is, the more precise the approximate analytical solution is.