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Abstract In this paper, a nonlocal (strain-driven) finite element model is presented to examine the free vibration and buckling behaviour of functionally graded (FG) nanobeams on the basis of first-order shear deformation theory (FSDBT). The proposed beam element has five nodes and ten degrees of freedom. The material properties of the FG nanobeam are assumed to vary in the thickness direction according to the power-law form. The stretching-bending coupling effect is eliminated by employing the neutral axis concept. Governing equations are deduced with the aid of Hamilton's principle. Buckling loads and natural frequencies are calculated for different nonlocal coefficients, boundary conditions (BCs), power-law indices, and span-to-depth ratios. The accuracy of the proposed element is verified by comparing with available benchmark results in the literature. [ABSTRACT FROM AUTHOR]

Abstract In this study, for the first time, hygro-thermal behaviour of functionally graded (FG) sandwich microbeams based on nonlocal elasticity theory is investigated. Temperature-dependent material properties are considered for the FG microbeam, which are assumed to change continuously through the thickness based on the power-law form. The equations of motion are obtained on the basis of first-order shear deformation beam theory via Hamilton's principle. The size effects are considered in the framework of the nonlocal elasticity theory of Eringen. The detailed variational and finite element procedure for FG sandwich microbeams are presented with a five-noded beam element and numerical examinations are performed. The influence of several parameters such as temperature and moisture gradients, material graduation, nonlocal parameter, face-core-face and span to depth ratios on the critical buckling temperature and the nondimensional fundamental frequencies of the FG sandwich microbeams are analysed. Based on the results of this study, temperature and moisture rise soften the FG sandwich microbeam and result in the reduction of the critical buckling load and vibration frequency. In addition, the FG sandwich microbeam with a thicker ceramic core can resist higher temperature and moisture gradients. [ABSTRACT FROM AUTHOR]

Abstract In this study, a finite element (FE) model is proposed to study the thermal transverse vibrations of cracked nanobeams resting on a double-parameter nonlocal elastic foundation. Hamilton's principal is employed to derive the governing equations for the free vibrations of the nanobeam. The cracked section of the beam is modelled by dividing the cracked element into two classical beam sections connected via a rotational spring positioned at the crack. The Galerkin method of weighted residuals is used to solve the equations of motion and calculate the natural frequencies. The effect of the crack length, crack position, the temperature gradient, the boundary conditions and the foundation stiffness, on the vibration response of the cracked nanobeams supported by elastic foundations is considered by including thermal effects. The FE results are compared to the available benchmark studies in the literature. [ABSTRACT FROM AUTHOR]

A dynamical uncertain system is studied in this paper. Two kinds of uncertainties are addressed, where the uncertain parameters are described through random variables and/or fuzzy variables. A general framework is proposed to deal with both kinds of uncertainty using a polynomial chaos expansion (PCE). It is shown that fuzzy variables may be expanded in terms of polynomial chaos when Legendre polynomials are used. The components of the PCE are a solution of an equation that does not depend on the nature of uncertainty. Once this equation is solved, the post-processing of the data gives the moments of the random response when the uncertainties are random or gives the response interval when the variables are fuzzy. With the PCE approach, it is also possible to deal with mixed uncertainty, when some parameters are random and others are fuzzy. The results provide a fuzzy description of the response statistical moments. [ABSTRACT FROM AUTHOR]

Rigid wings usually fly at sub-optimal conditions generating unnecessary aerodynamic loses represented in flight time, fuel consumption, and unfavourable operational characteristics. High aspect ratio wings have good range and fuel efficiency, but lack manoeuvrability. On the other hand, low aspect ratio wings fly faster and are more manoeuvrable, but have poor aerodynamic performance. Span morphing technology allows integrating both features in a single wing design and allows continuously adjusting the wingspan to match the instantaneous flight conditions and mission objectives. This paper develops, a novel span morphing concept, the G ear drive N A utonomous T win Spar ( GNATSpar ) for a mini-UAV. The GNATSpar can be used to achieve span extensions up to 100% but for demonstration purposes it is used here to achieve span extensions up to 20% to reduce induced drag and increase flight endurance. The GNATSpar is superior to conventional telescopic and articulated structures as it uses the space available in the opposite sides of the wing instead of relying on overlapping structures and bearings. In addition, it has a self-locking actuation mechanism due to the low lead angle of the driving worm gear. Following the preliminary aero-structural sizing of the concept, a physical prototype is developed and tested in the 7 ′ × 5 ′ wind-tunnel at the University of Southampton. Finally, benefits and drawbacks of the design are highlighted and analysed. [ABSTRACT FROM AUTHOR]

The aim of this paper is to investigate bandgap formation in an Euler-Bernoulli nanobeam using the nonlocal strain gradient theory. Such a model enables the capture of both softening and stiffening size-dependent behavior of the nanobeams using two length-scale parameters, namely, a nonlocal parameter and a strain gradient parameter. Hamilton's principle is used to develop the normalized equation of motion yielding a sixth order differential equation. The nanobeam is assumed to be infinitely long and the dispersion of an elastic wave in a single representative periodic unit cell of the structure is used to estimate the bandgap edge frequencies. To this end, two unit cell approaches are employed to obtain the dispersion relations, namely, the homogenization and transfer matrix approaches. Both methods yield similar dispersion curves and showed good agreement with classical cases from the literature. A parametric study was carried out to investigate the effect of several parameters on the bandgap formation in the metamaterial nanobeams. These parameters include, the nonlocal parameter, the strain gradient parameter, the length of the unit cell and the resonator mass to unit cell mass ratio. The study conducted using a purely strain gradient model showed a comparable response to that of the classical macro problem with the usual hardening when increasing the value of the strain gradient length scale. Nonlocal and nonlocal strain gradient models introduced coupling between parameters of the study with the occasional introduction of non-monotonic dispersion curves. Such non-monotonic behavior is believed to be characteristic of large values of the nonlocal length-scale. • Bandgap formation in a nonlocal strain gradient theory nanobeam using local resonators. • Nanobeam is governed by a 6th order differential equation with six boundary conditions and two length-scale parameters. • Transfer matrix and homogenization approaches were used to predict bandgaps. • Effect of length scales, in addition to other parameters on bandgap formation were investigated. [ABSTRACT FROM AUTHOR]

Identifying and tracking dynamic modes in a multi-dimensional parameter space is a problem that presents itself in many engineering disciplines. In a flight dynamics context, the dynamic modes refer to the modes of motion obtained from a linearisation of the aircraft system about a known operating point. Typically dynamic results derived from these linear models are unsorted, where mode indices are unrelated from one operating point to the next. When varying the parameters, or in this case operating point, difficulties in automating the process of relating modes from a linear system derived at one parameter set to the next exists. This paper builds on the work in tracking modes in a structural context, using the Modal Assurance Criterion (MAC) to numerically relate modes from two comparable linear systems. The (MAC) is deployed within a spanning algorithm to discover and identify all modes within all conditions, with their relationship to adjacent/neighbouring conditions. This is tested on a 1-, 2- and 3-dimensional parameter space, twelve state system. [ABSTRACT FROM AUTHOR]

Energy harvesting has many potential applications for structures with broadband excitation, such as aircraft noise and low frequency vibrations from human motion. The advantage with a vibro-impacting system is the capability of converting low frequency response to high frequencies. A coupled beam system is base excited and the influence of different system parameters are studied. Exciting the system at a single resonant frequency highlights the influence of clearance and base excitation amplitude on the beam responses. The frequency sweep study shows the sensitivity of the power generated to the contact stiffness, damping and clearance between the beams. The power generated by the coupled system from the non-linear impact is sensitive to the thickness ratio of the beams and the clearance. The variation in thickness ratio alters the spacing of the natural frequencies of the system which causes modes to interact. This study shows that higher power is produced than the linear system, depending on the dissimilarity in the mode shapes of the interacting close modes. [ABSTRACT FROM AUTHOR]

An aircraft that has been carefully optimised for a single flight condition will tend to perform poorly at other flight conditions. For aircraft such as long-haul airliners, this is not necessarily a problem, since the cruise condition so heavily dominates a typical mission. However, other aircraft such as UAVs, may be expected to perform well at a wide range of flight conditions. Morphing systems may be a solution to this problem, as they allow the aircraft to adapt its shape to produce optimum performance at each flight condition. Optimisation of morphing aerofoils is typically performed separately to the morphing mechanism design. In this work, an optimisation strategy is developed to account for a known possible morphing system within the aerodynamic optimisation process itself. This allows for the limitations of the system to be considered from the start of the design process. The Fishbone Active Camber (FishBAC) camber morphing system is chosen as the example mechanism, and it is shown that the FishBAC can achieve large improvements in performance over non-morphing aerofoils when multiple flight conditions are considered. Additionally, its performance is compared to an aerofoil whose shape can change arbitrarily (as if a perfect morphing mechanism can be designed), and it is shown that the FishBAC performs nearly as well, despite being a relatively simple mechanism. [ABSTRACT FROM AUTHOR]

An energy harvesting concept has been proposed comprising a piezoelectric patch on a vertical cantilever beam with a tip mass. The cantilever beam is excited in the transverse direction at its base. This device is highly nonlinear with two potential wells for large tip masses, when the beam is buckled. For the pre-buckled case considered here, the stiffness is low and hence the displacement response is large, leading to multiple solutions to harmonic excitation that are exploited in the harvesting device. To maximise the energy harvested in systems with multiple solutions the higher amplitude response should be preferred. This paper investigates the amplitude of random noise excitation where the harvester is unable to sustain the high amplitude solution, and at some point will jump to the low amplitude solution. The investigation is performed on a validated model of the harvester and the effect is demonstrated experimentally. [ABSTRACT FROM AUTHOR]

Abstract: The use of modal response residuals and parameterized models forms the framework for parameter subset selection based damage detection. This research explores the novel approach in this class of methods which is characterized by the successive application of the homogeneous modal response residuals. The motivation behind this approach is to restrict the use of unknown weighting factors which are employed in cases with mixed response residuals. Particular attention is given to the parameter-effect symmetry issues and large nonlinear changes in response residuals due to increasing damage observed across multiple damage levels. A case study involving a real aluminum three-dimensional frame structure with a loose joint connection is used to demonstrate the approach and its ability to localize the damaged area. [Copyright &y& Elsevier]

Abstract: This paper investigates the deformation and failure mechanisms of wood at the ultrastructural scale. At this level, wood is composed of a periodic alternation of amorphous and crystalline cellulose fractions, embedded in a soft hemicellulose-lignin matrix. The mechanical response of wood is calculated under tensile loading conditions by means of the computational homogenisation of a representative volume element (RVE) of material. Three potential mechanisms of failure are suggested: axial straining of the crystalline fraction of cellulose, accumulation of plastic strain in the amorphous portion of cellulose and tensile rupture in the hemicellulose-lignin matrix due to cellulose fibres separation. In order to validate the present multi-scale framework, we compare our numerical predictions for the reorientation of cellulose fibres with experimental data, finding a good agreement for a wide range of strains. Furthermore, we assess successfully our numerical predictions for ultimate strains at the instant of failure when compared to experimental values. Numerical simulations show that our model is able to provide new clues into the understanding of how trees and plants optimise their microstructure in order to develop larger strains without apparent damage. A remarkable prediction by our model suggests that the extensibility of the material is maximised for initial microfibril angles (MFA) between 50° and 55°, a range of values found typically in branches of trees, in which the extensibility is an essential requirement. These findings are likely to shed more light into the dissipative mechanisms of wood and natural materials, which are still not well-understood at present. [Copyright &y& Elsevier]

Abstract: Morphing aircraft wing skins require composites with conflicting structural requirements: low in-plane stiffness and high out-of-plane bending stiffness. In this study, composites with curvilinear fiber paths are examined to enhance these conflicting structural requirements. The numerical results show that curved fiber paths can minimize the in-plane stiffness and increase the bending stiffness simultaneously compared to a baseline plate with straight fibers. A flexibility ratio is defined to assess the in-plane and out-of-plane deformation of the plate, simultaneously. A multi-objective optimization is formulated to find optimal curved fiber paths which maximize the flexibility ratio of the morphing wing skin. The optimization is performed with fiber paths represented as independent discrete fibers and continuous curvilinear fibers. The results show a significant increase in the flexibility ratio compared to a baseline plate with straight fibers. The aspect ratio of plate, laminate stacking sequence and in-plane loading direction have considerable influence on the optimal paths of the curved fibers. [Copyright &y& Elsevier]

Abstract: The design of corrugated panels has wide application in engineering. For example corrugated panels are often used in roof structures in civil engineering. More recently corrugated laminates have been suggested as a good solution for morphing aircraft skins due to their extremely anisotropic behaviour. The optimal design of these structures requires simple models of the panels or skins that may be incorporated into multi-disciplinary system models. Thus equivalent material models are required that retain the dependence on the geometric parameters of the corrugated skins or panels. An homogenisation-based analytical model, which could be used for any corrugation shape, is suggested in this paper. This method is based on a simplified geometry for a unit-cell and the stiffness properties of original sheet. This paper outlines such a modelling strategy, gives explicit expressions to calculate the equivalent material properties, and demonstrates the performance of the approach using two popular corrugation shapes. [Copyright &y& Elsevier]

Abstract: This paper is concerned with distributed sensors to measure the response of beam and plate structures. The design of modal sensors for beam structures is well established. The design for plate structures with constant thickness sensors may be achieved by optimizing the shape of the sensor boundary, or by optimizing the effectiveness of the electrode. Most applications consider vibration control, but this paper is concerned with structural health monitoring, where the sensor output is made sensitive to changes in key stiffness parameters, for example in joints. The procedure is based on finite element models of the structures, and thus distributed transducers may be designed for arbitrary beam and plate structures. Simulated examples of a beam and a plate excited by a rotating machine are used to demonstrate the approach. [Copyright &y& Elsevier]

Abstract: Discrepancies between experimentally measured data and computational predictions are unavoidable for complex engineering dynamical systems. To reduce this gap, model updating methods have been developed over the past three decades. Current methods for model updating often use discrete parameters, such as thickness or joint stiffness, for model updating. However, there are many parameters in a numerical model which are spatially distributed in nature. Such parameters include, but are not limited to, thickness, Poisson''s ratio, Young''s modulus, density and damping. In this paper a novel approach is proposed which takes account of the distributed nature of the parameters to be updated, by expressing the parameters as spatially correlated random fields. Based on this assumption, the random fields corresponding to the parameters to be updated have been expanded in a spectral decomposition known as the Karhunen–Loève (KL) expansion. Using the KL expansion, the mass and stiffness matrices are expanded in series in terms of discrete parameters. These parameters in turn are obtained using a sensitivity based optimization approach. A numerical example involving a beam with distributed updating parameters is used to illustrate this new idea. [Copyright &y& Elsevier]

Abstract: Vibrations in rotating machinery cause many problems such as fatigue of the rotating components, excessive noise, or transmission of vibration to the supporting structure. A major source of this vibration is out-of-balance forces and this paper proposes that the rotor response is reduced by suspending the machine on nonlinear springs. In the field of vibration isolation, nonlinear mounts have been proposed which have the same static stiffness as an equivalent linear support, i.e. load bearing capability, but at the same time offer a low dynamic stiffness, i.e. a lower natural frequency. Thus the isolator is effective over an increased frequency range. These mounts are known in the literature as high-static-low-dynamic-stiffness (HSLDS) mechanisms. In this paper, the rotor is suspended on a hardening HSLDS spring to considerably reduce the critical speeds to values far away from the operating speed. The advantages of the nonlinear supports are demonstrated using a simple two degree of freedom rotating machine model consisting of a rigid disk, and shafts, bearings and supports that are flexible but have negligible mass. Following a linear analysis to highlight the benefits of a low dynamic stiffness, an approximate analytical solution of the nonlinear equation of motion is presented. A comparison between the linear and nonlinear response shows the effectiveness of the nonlinear supports. Finally, the problems that occur if the nonlinearity is too strong are highlighted. [Copyright &y& Elsevier]

Abstract: The consideration of uncertainties in numerical models to obtain the probabilistic descriptions of vibration response is becoming more desirable for industrial-scale finite element models. Broadly speaking, there are two aspects to this problem. The first is the quantification of parametric and non-parametric uncertainties associated with the model and the second is the propagation of uncertainties through the model. While the methods of uncertainty propagation have been extensively researched in the past three decades (e.g., the stochastic finite element method), only relatively recently has quantification been considered seriously. This paper considers uncertainty quantification with the aim of gaining more insight into the nature of uncertainties in medium- and high-frequency vibration problems. This paper describes the setup and results from two experimental studies that may be used for this purpose. The first experimental work described in this paper uses a fixed–fixed beam with 12 masses placed at random locations. The total ‘random mass’ is about 2% of the total mass of the beam and this experiment simulates ‘random errors’ in the mass matrix. The second experiment involves a cantilever plate with 10 randomly placed spring-mass oscillators. The oscillating mass of each of the 10 oscillators is about 1% of the mass of the plate. One hundred nominally identical dynamical systems are created and individually tested for each experiment. The probabilistic characteristics of the frequency response functions are discussed in the low, medium and high frequency ranges. The variability in the amplitude of the measured frequency response functions is compared with numerical Monte Carlo simulation results. The data obtained in these experiments may be useful for the validation of uncertainty quantification and propagation methods in structural dynamics. [Copyright &y& Elsevier]

Abstract: Usually different nonlinear time responses due to earthquake ground motion are distinguished by non-localized spectra, such as the response or power spectra. However, these spectra are often not able to explain the large discrepancy among structural responses caused by different earthquake records. The local spectrum, obtained by the wavelet transform, shows the energy distribution in the time-frequency domain, and helps to understand the very different structural responses. By changing the energy distribution in time of several earthquake records, the effect of energy concentration on the structural nonlinear response is demonstrated. This paper proposes the use of the characteristic peak ground acceleration, which is the peak of the signal constructed by only a few special wavelet components of an earthquake record, to quantify the difference between earthquake records, since this measure indicates the magnitude of the energy concentrated around the fundamental period of a structure. [Copyright &y& Elsevier]

Abstract: Model updating is a powerful technique to improve finite element models of structures using measured data. One of the key requirements of updating is a set of candidate parameters that is able to correct the underlying error in the model. Often regions such as joints are very difficult to parameterise satisfactorily using physical design variables such as stiffnesses or dimensions. Parameters arising from generic element and substructure transformations are able to increase the range of candidate parameters, and furthermore are able to correct structural errors. However, unconstrained generic substructure transformations change the connectivity of the model matrices. In many instances retaining the connectivity is desirable and this paper derives constraint equations to do so. The method assumes that substructure eigenvalues are the parameters used in the global updating procedure and that the substructure eigenvector matrix is optimised to enforce the connectivity constraints. The method is demonstrated on a simple L shape test structure, where the substructure is the corner. [Copyright &y& Elsevier]

Abstract: In this paper, a non-local damping model including time and spatial hysteresis effects is used for the dynamic analysis of structures consisting of Euler–Bernoulli beams and Kirchoff plates. Unlike ordinary local damping models, the damping force in a non-local model is obtained as a weighted average of the velocity field over the spatial domain, determined by a kernel function based on distance measures. The resulting equation of motion for the beam or plate structures is an integro-partial-differential equation, rather than the partial-differential equation obtained for a local damping model. Approximate solutions for the complex eigenvalues and modes with non-local damping are obtained using the Galerkin method. Numerical examples demonstrate the efficiency of the proposed method for beam and plate structures with simple boundary conditions, for non-local and non-viscous damping models, and different kernel functions. [Copyright &y& Elsevier]

Abstract: The minimum stiffness of a simple (or point) support that raises a natural frequency of a beam to its upper limit is investigated for different boundary conditions. The approach produces the closed-form solution for the minimum stiffness based on the derivative of a natural frequency with respect to the support position. It is seen that when an intermediate elastic support is positioned properly the effect is similar to a rigid support. The solution process also provides insight into the dynamics of a beam with an intermediate support for more general boundary conditions. The resulting solutions can be used to guide the practical design of a support. [Copyright &y& Elsevier]

The structural modification of dynamical systems is an important issue in a wide range of applications, for example in vibration suppression or in active and passive control. It is well known that for a proportionally (or classically) damped system there always exists a real matrix of eigenvectors which simultaneously diagonalizes the three system matrices of inertia, damping and stiffness, even if the system possesses repeated eigenvalues. For general viscously damped systems the eigenvalue analysis must be performed in state space, and for systems with distinct eigenvalues the corresponding eigenvectors diagonalize the state space matrices. However, with general viscous damping, systems with repeated complex eigenvalues may have insufficient linearly independent complex eigenvectors. These systems are termed defective. In contrast to non-defective (or simple) systems, for defective systems only a Jordan decomposition exists. In this paper conditions on rank 1, rank 2 and higher rank modifications are derived which ensure that the modified system is simple. If none of the eigenvalues of the unmodified system is an eigenvalue of the modified system then every rank 1 modification that produces a pair of repeated complex eigenvalues leads to a defective system. Under the same assumptions there exist higher rank modifications which lead to simple systems. Either these modifications produce a proportionally damped system, or the restrictions on these modifications are rather strict which suggests that in practical cases every rank 2 or higher modification that produces repeated pairs of complex eigenvalues will lead to a defective system. The findings are demonstrated by simulated examples. [Copyright &y& Elsevier]

Abstract: The objective of robust design is to optimise the mean and minimize the variability that results from uncertainty represented by noise factors. The various objective functions and analysis techniques used for the Taguchi based approaches and optimisation methods are reviewed. Most applications of robust design have been concerned with static performance in mechanical engineering and process systems, and applications in structural dynamics are rare. The robust design of a vibration absorber with mass and stiffness uncertainty in the main system is used to demonstrate the robust design approach in dynamics. The results show a significant improvement in performance compared with the conventional solution. [Copyright &y& Elsevier]

Provides a simple method to generate the transformation of second-order systems from state-space representation. Presentation of the equation motion; Transformation to second-order form; Conclusions.

Provides additional insights into a set of second-order ordinary differential equations. Potential applications of an equation from which the characteristic roots and vectors can be determined; Cases where some or all of the eigenvalues and eigenvectors are complex; Brief sketch of the algebra that has been developed to facilitate the solution for characteristic roots of self-adjoint second-order systems.

• The attachment positions of intermediate elastic supports are optimally designed for raising the natural frequency of a plate structure. • The minimum restraint stiffness is investigated for a more economic support design with consideration of the additional support mass. • The natural frequency derivative formulation with regard to the support position variation is first derived with the inclusion of the support mass. • A typical relation is proposed between the support mass and the stiffness to demonstrate effects of the additional support mass on the minimum restraint stiffness of the support. • The researches in this work are more practical in engineering applications. The optimum position and minimum restraint stiffness of a flexible point support to raise a natural frequency of a thin bending plate is investigated, with the inclusion of the corresponding additional support mass. First the derivatives of the natural frequencies of the plate structure are derived with respect to the support movement using a finite element model. Second, the minimum support stiffness is analyzed to raise a plate's natural frequency to a target value by solving a characteristic eigenvalue problem. Then the optimal support design is studied to find the optimal attachment point and the associated minimum stiffness. Several typical examples of plate systems are analyzed with addition of the point supports with non-negligible mass. It appears that including the support mass in the plate vibration analysis can significantly increase the minimum support stiffness required to raise a given natural frequency to its target, whereas the optimal support position remains consistent with the massless support design case. [ABSTRACT FROM AUTHOR]

Outlines an extension to the available direct methods of model updating to estimate both the damping and stiffness matrices of a structure. Minimizing change in the damping and stiffness matrices; Algorithm; Numerical example.

• Comprehensive vibrational analysis of anti-symmetric laminated composite plates. • Vibrational analysis includes an elastic foundation and thermal effects. • HSDT is applied to estimate the effects of the higher-order transverse shear. • Effects of damping, elastic, aspect and slenderness ratios are discussed in detail. • Different anti-symmetric laminates and boundary conditions are considered. In this work, a comprehensive vibrational behavior analysis is performed on anti-symmetric laminated composite plates resting on visco-elastic foundations undergoing thermal effects. Here, the governing equations of motion are developed through Hamilton's principle and Reddy's plate theory as higher-order shear deformation theory (HSDT) is employed to capture high accuracy. Also, the generalized differential quadrature method (GDQM) is used to predict the vibration response and the natural frequencies. The effects of temperature change, Winkler-Pasternak and damping coefficients for the elastic foundation, the elastic ratio, the arrangement of different anti-symmetric laminates, and the aspect and slenderness ratios are observed and discussed in detail. The results are extracted for fully clamped boundary conditions and the effects of other boundary conditions are also illustrated. [ABSTRACT FROM AUTHOR]

• For the first time, the comprehensive wave propagation analysis of 2D-FG rotating nanobeams with porosity is considered. • General nonlocal theory is used to establish the governing equation which exhibits softening and hardening behaviour. • Reddy's beam theory is applied to model the effects of the higher-order transverse shear strains on the wave propagation. • The effects of material variation, porosity, and the length to thickness ratio on the wave propagation are discussed. This paper studies the wave propagation of two-dimensional functionally graded (2D-FG) porous rotating nano-beams for the first time. The rotating nano-beams are made of two different materials, and the material properties of the nano-beams alter both in the thickness and length directions. The general nonlocal theory (GNT) in conjunction with Reddy's beam model are employed to formulate the size-dependent model. The GNT efficiently models the dispersions of acoustic waves when two independent nonlocal fields are modelled for the longitudinal and transverse acoustic waves. The governing equations of motion for the 2D-FG porous rotating nano-beams are established using Hamilton's principle as a function of the axial force due to centrifugal stiffening and displacement. The analytic solution is applied to obtain the results and solve the governing equations. The effect of the features of different parameters such as functionally graded power indexes, porosity, angular velocity, and material variation on the wave propagation characteristics of the rotating nano-beams are discussed in detail. [ABSTRACT FROM AUTHOR]

A novel probabilistic robust design optimization framework is presented using a Bayesian inference framework. The objective of the study is to obtain probabilistic descriptors of the system parameters conditioned on the user-prescribed target probability distributions of the output quantities of interest or figures of merit of a system. A criterion-based identification of a reduced important parameter space is performed from the typically high number of parameters modeling the stochastically parametrized physical system. The criterion can be based on sensitivity indices, design constraints or expert opinion or a combination of these. The posterior probabilities on the reduced or important parameters conditioned on prescribed target distributions of the output quantities of interest are derived using the Bayesian inference framework. The probabilistic optimal design proposed here offers the distinct advantage of prescribing probability bounds of the system performance functions around the optimal design points such that robust operation is ensured. The proposed method has been demonstrated with two numerical examples including the optimal design of a structural dynamic system based on user-prescribed target distribution for the resonance frequency of the system. [ABSTRACT FROM AUTHOR]

This paper proposes the use of an electrostatic device to improve the performance of MEMS piezoelectric harvesters in the presence of manufacturing uncertainties. Different types of uncertain parameters have been considered and randomised according to their experimentally measured statistical properties. It has been demonstrated that manufacturing uncertainty in MEMS harvesters results in a lower output power. Monte Carlo Simulation is used to propagate uncertainty through the MEMS mathematical model. It has been found that the uncertainty effects can result in two sets of samples. The first set of samples are those with resonance frequency higher than nominal values and the second set includes samples with resonance frequencies lower than the nominal value. The device proposed in this paper can compensate for the effects of variability in the harvester by tuning the resonance frequency to the nominal design. This device is composed of a symmetrical arrangement of two electrodes, which decrease the resonance frequency from its nominal value. However, achieving precise symmetrical conditions in the device on a micro-scale is not feasible. Therefore, the effects of an unsymmetrical arrangement due to manufacturing variability are also investigated. The device includes two arch-shaped electrodes that can be used to increase the resonance frequency. [ABSTRACT FROM AUTHOR]

In this paper the torsional vibration of size-dependent viscoelastic nanorods embedded in an elastic medium with different boundary conditions is investigated. The novelty of this study consists of combining the nonlocal theory with the strain and velocity gradient theory to capture both softening and stiffening size-dependent behavior of the nanorods. The viscoelastic behavior is modeled using the so-called Kelvin–Voigt viscoelastic damping model. Three length-scale parameters are incorporated in this newly combined theory, namely, a nonlocal, a strain gradient, and a velocity gradient parameter. The governing equation of motion and its boundary conditions for the vibration analysis of nanorods are derived by employing Hamilton’s principle. It is shown that the expressions of the classical stress and the stress gradient resultants are only defined for different values of the nonlocal and strain gradient parameters. The case where these are equal may seem to result in an inconsistency to the general equation of motion and the related non-classical boundary conditions. A rigorous investigation is conducted to prove that the proposed solution is consistent with physics. Damped eigenvalue solutions are obtained both analytically and numerically using a Locally adaptive Differential Quadrature Method (LaDQM). Analytical results of linear free vibration response are obtained for various length-scales and compared with LaDQM numerical results. [ABSTRACT FROM AUTHOR]

Commercial prosthetic feet weigh about 25% of their equivalent physiological counterparts. The human body is able to overcome the walking asymmetry resulting from this mass imbalance by exerting more energy. It is hypothesised that the passive walking dynamics coupled with roll-over shapes has potential to suggest energy efficient walking solutions. A two link passive walking kinematic model has been proposed to study the gait pattern with unbalanced leg masses. An optimal roll-over shape for the prosthetic foot that minimises the asymmetry in the inter-leg angle and the step period is determined. The proposed mathematical formulation provides insights into the variation of step length and inter-leg angle with respect to the position and location of the centres for mass of both prosthetic and physiological legs. [ABSTRACT FROM AUTHOR]

A variable camber morphing airfoil with compliant ribs and flexible composite skins is studied in a hierarchical modeling framework. The key requirements of a variable camber morphing airfoil are the flexible skin, compliant internal structure and a lightweight actuation system. A biologically inspired, internal structure is adapted to produce continuous camber morphing. The conflicting requirements of the morphing skin, namely low in-plane stiffness and high out-of-plane bending stiffness, are met by designing the composite with curvilinear fiber paths. A coupled aeroelastic simulation and optimization of the proposed 2-D morphing airfoil is computationally complex. Hierarchical computational models of the morphing airfoil are used to decouple the complaint ribs and airfoil skin. In the first level of hierarchy, a fluid-structure interaction is performed with the homogenized beam model of the compliant rib structure and 2-D panel method. In the second level, a finite element model of the camber morphing skin is developed with representative boundary conditions. A multi-objective optimization framework is developed to find the optimal curvilinear fiber paths of the morphing skin to meet the airfoil geometric shape and actuation requirements of the first level. The optimal results show that a significant camber variation and significant changes in aerodynamic properties can be achieved with the compliant skin and airfoil structure considered in this study. The hierarchical modeling framework of the camber morphing airfoil discussed in this paper enhances theoretical understanding of each sub-system and reduces the computational costs. [ABSTRACT FROM AUTHOR]

High Static Low Dynamic Stiffness (HSLDS) mounts consist of nonlinear springs that support a high static load with low static displacement, whilst maintaining locally low stiffness near equilibrium, to give a low natural frequency and consequently good isolation properties. Recent analysis has investigated such devices when the force–displacement relationship is an odd function about the equilibrium position, and analysed the consequences of different shapes of these functions. However many devices that have the HSLDS characteristic do not meet the assumptions of this analysis, in that the force–displacement relationship is generally asymmetric about equilibrium. Furthermore, even devices that do meet this assumption may be subject to significant adjustment error, particularly in the context of air vehicles where manoeuvres such as banked turns can cause an apparent variation in gravitational acceleration, and a consequent variation in the weight of the payload. This change in static load moves the payload away from its intended region of low stiffness. The current paper provides analysis of these situations, and shows that the performance of a mount with a symmetric stiffness–displacement relationship is highly sensitive to errors in the static loading. It is then shown that a mount with an asymmetric stiffness–displacement function can offer significant performance advantages when there are adjustment errors in the loading of the mount. [ABSTRACT FROM AUTHOR]

A model order reduction scheme of the transient response of large-scale randomly parametrized linear finite element system in state space form has been proposed. The reduced order model realization is aimed at preserving the invariant properties of the dynamic system model based on the dominant coupling characteristics of the specified system inputs and outputs. An a - priori model reduction strategy based on the balanced truncation method has been proposed in conjunction with the stochastic spectral Galerkin finite element method. Approximation of the dominant modes of the controllability Gramian has been performed with iterative Arnoldi scheme applied to Lyapunov equations. The reduced order representation of the randomly parametrized dynamical system has been obtained with Arnoldi–Lyapunov vector basis using an implicit time stepping algorithm. The performance and the computational efficacy of the proposed scheme has been illustrated with examples of randomly parametrized advection–diffusion–reaction problem under the action of transient external forcing functions. The convergence of the proposed reduced order scheme has been shown with a-posteriori error estimates. [ABSTRACT FROM AUTHOR]

Morphing aircraft aim to increase the performance of aircraft over multiple flight conditions, by enabling shape changes in flight in order to optimise their aerodynamic properties for the current conditions. The skin of a morphing aircraft is a critical component. It must be compliant in degrees of freedom that are required for actuation, to minimise the actuation loads. However, it must also carry structural loads, and therefore be stiff in load bearing degrees of freedom. This leads to a requirement for extremely anisotropic material systems. A common solution is the use of a corrugated panel. However, previous work on corrugations has not addressed the problem of compressive buckling loads. This work analyses the performance of corrugated panels under buckling loads, and optimises corrugation patterns for the objectives of weight, buckling performance, and actuation compliance. Simplified analytical models that derive properties equivalent to conventional plates are used to obtain approximate estimates of the buckling loads. Furthermore a new mode of buckling, that occurs entirely in-plane and is unique to panels with extreme anisotropy is analysed. The simple models allow optimisation to be performed, and both a single-objective and a multi-objective approach are demonstrated. The results are compared to Finite Element Analysis. [ABSTRACT FROM AUTHOR]

• Energy balancing concept can improve the performance of the actuation system by reducing the external energy consumption. • The integration workflow for the passive energy balancing device is established. • The design variables can be optimised for the load stiffness changes. • An integrated demonstrator was also built to validate the concept. A spiral pulley mechanism can be used to passively balance the energy between the morphing structure and actuation system. Applying the energy balancing concept has the potential to improve the performance of the actuation system by reducing the external energy consumption. In the current study, the integration workflow for the passive energy balancing device is established and is adopted in a variable camber morphing wing. The design variables of the passive energy balancing system are optimised and the effects of the different parameters are discussed together with the adaptability of the passive energy balancing device when the load stiffness changes. An integrated demonstrator was also built to validate the mechanism by measuring the currents in the process of morphing actuation. [ABSTRACT FROM AUTHOR]

Abstract: This paper investigates the extensibility of the wood cell-wall composite in the presence of parametric uncertainty by means of a multi-scale finite element approach. Normally, the three fundamental phases in wood, that is, cellulose, lignin and hemicellulose, present considerable scatter in their microstructure and mechanical properties. Nevertheless, by considering uncertainty in their properties, a significant computational cost is added to the solution of a large set of realisations represented by expensive fully-coupled multi-scale analyses. In order to tackle this high cost, we build a statistical approximation to the output of the computer model. Following this strategy, several micromechanical parameters are perturbed to study their influence on the extensibility of the material under tensile loading conditions. By reducing the cost of performing uncertainty analysis of the homogenised mechanical response, we are able to estimate the 5-th, 50-th, and 95-th percentile of the ultimate tensile strains of the material. We contrast our numerical predictions with experimental data, finding a good agreement for a wide range of initial microfibril angles. [Copyright &y& Elsevier]

Abstract: The ‘heel to toe’ rolling contact has a great influence on the dynamics of biped robots. Here this contact is modelled using the roll-over shape defined in the local co-ordinate system aligned with the stance leg. The roll-over shape is characterised by six constants: forefoot, midfoot and hindfoot gains and length values. A piecewise parabolic polynomial constructed from these six values is able to match the realistic roll-over shape with continuous slope and variable curvature. The effect of these constants and the roll-over shape arc length has been studied on various gait descriptors such as average velocity, step period, inter-leg angle (and hence step length), mechanical energy. The bifurcation diagrams have been plotted for point feet and different gain values. The insight gained by studying the bifurcation diagrams for different gain and length values is not only useful in understanding the stability of the biped walking process but also in the design of prosthetic feet. The discovery of ‘critical values’ for the length and mass ratios for the inter-leg angle δ (and hence step length) bifurcation diagrams, or a ‘critical value’ for forefoot gain in the step period bifurcation diagram, is of particular interest as it would mean a constant step length or step period for a range of acceptable values of forefoot and hindfoot gains. The dependence of the horizontal roll-over shape length and hindfoot/forefoot gains on the actual stance leg angular velocity and angular displacement (θs ) values along with the corresponding existence of critical values has also been demonstrated. [Copyright &y& Elsevier]

Abstract: This paper presents the Zigzag wingbox concept that allows the wing span to be varied by 44% (22% extension and 22% retraction). The Zigzag wingbox consists of a rigid part and a morphing part. The rigid part is a semi-monocoque construction that houses the fuel tank and transfers the aerodynamic loads from the morphing part to the fuselage. The morphing part consists of various morphing partitions where in each partition there are two spars each consisting of two beams hinged together. Each morphing partition is covered by flexible skin and is bounded by two ribs through which the spars are connected. The ribs transfer the loads between the spars of adjacent morphing partitions and serves as the main structure to which the flexible skins are to be attached. The Zigzag wingbox concept is then incorporated in the rectangular wing of a medium altitude long endurance (MALE) UAV to enhance its operational performance and provide roll control. Equivalent modelling and preliminary sizing of the concept are performed to assess its feasibility and quantify its potential benefits. [Copyright &y& Elsevier]

A fault-tolerant control scheme with thruster redundancy is developed and applied to perform attitude tracking manoeuvres for an orbiting flexible spacecraft. Based on the assumption of bounded elastic vibrations, an adaptive sliding mode controller is proposed to guarantee that all the signals of the resulting closed-loop attitude system are uniformly ultimately bounded in the presence of an unknown inertia matrix, bounded disturbances and unknown faults. An H∞ performance index is introduced to describe the disturbance attenuation performance of the closed-loop system. This approach is then extended to the problem of elastic vibration without knowledge of the bounds a priori. The presented approach addresses thruster saturation limits and the desired thruster force is guaranteed to stay within the limit of each thruster. Extensive simulation studies have been conducted to demonstrate the closed-loop performance benefits compared to conventional control schemes. [ABSTRACT FROM AUTHOR]

Abstract: Discrepancies between experimentally measured data and computational predictions are unavoidable for structural dynamic systems. Model updating methods have been developed over the past three decades to reduce this gap. Well established model updating methods exist when both the model and experimental measurements are deterministic in nature. However in reality, experimental results may contain uncertainty, for example arising due to unknown experimental errors, or variability in nominally identical structures. Over the past two decades probabilistic approaches have been developed to incorporate uncertainties in computational models. In this paper, the natural frequencies and the eigenvectors of the system are measured and assumed to be uncertain. A random matrix approach is proposed and closed-form expressions are derived for the mean matrix and the covariance matrix of the updated stiffness matrix. A perturbation technique is used to obtain a usable expression for the covariance matrix. The new method is illustrated by three numerical examples highlighting the influence of the eigenfrequency uncertainties on the mean matrix and the influence of the eigenvector uncertainties on the covariance matrix. [Copyright &y& Elsevier]

Abstract: This paper investigates the uncertainty in the mechanical response of foam-filled honeycomb cores by means of a computational multi-scale approach. A finite element procedure is adopted within a purely kinematical multi-scale constitutive modelling framework to determine the response of a periodic arrangement of aluminium honeycomb core filled with PVC foam. By considering uncertainty in the geometric properties of the microstructure, a significant computational cost is added to the solution of a large set of microscopic equilibrium problems. In order to tackle this high cost, we combine two strategies. Firstly, we make use of symmetry conditions present in a representative volume element of material. Secondly, we build a statistical approximation to the output of the computer model, known as a Gaussian process emulator. Following this double approach, we are able to reduce the cost of performing uncertainty analysis of the mechanical response. In particular, we are able to estimate the 5th, 50th, and 95th percentile of the mechanical response without resorting to more computationally expensive methods such as Monte Carlo simulation. We validate our results by applying a statistical adequacy test to the emulator. [Copyright &y& Elsevier]

Abstract: This paper proposes a hyperelastic finite element-based lattice approach for the description of buckling behaviour in single wall carbon nanotubes (SWCNTs). A one-term incompressible Ogden-type hyperelastic model is adopted to describe the equivalent mechanical response of C–C bonds in SWCNTs under axial compression. The material constants of the model are chosen by matching the linearised response with the elastic constants adopted in the AMBER force field and by establishing equivalence between the Ogden strain energy and the variation of the interatomic strain energy obtained from molecular mechanics simulations. Numerical experiments are carried out and the results are compared to atomistic simulations, demonstrating the predictive capabilities of the present model in capturing initial buckling strain, deformation mechanisms and post-buckling behaviour under very large compressive deformations. [Copyright &y& Elsevier]

Abstract: We present an analysis of a two-plane automatic balancing device for rotating machinery. The mechanism consists of a pair of races that contain balancing balls which move to eliminate imbalance due to rotor eccentricity or principal axis misalignment. A model is developed that includes the effect of support anisotropy and rotor acceleration. The symmetry of the imbalance is considered, and techniques from equivariant bifurcation theory are used to derive a necessary condition for the stability of balanced operation. The unfolding of the solution structure is explored and we investigate mechanical systems in which either the supports or the automatic ball balancer is asymmetric. Here it is shown that, provided the imbalance is small, the balanced state is robust to the considered asymmetries. [Copyright &y& Elsevier]