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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]

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]

Abstract: Uncertainty propagation in multi-parameter complex structures possess significant computational challenges. This paper investigates the possibility of using the High Dimensional Model Representation (HDMR) approach when uncertain system parameters are modeled using fuzzy variables. In particular, the application of HDMR is proposed for fuzzy finite element analysis of linear dynamical systems. The HDMR expansion is an efficient formulation for high-dimensional mapping in complex systems if the higher order variable correlations are weak, thereby permitting the input–output relationship behavior to be captured by the terms of low-order. The computational effort to determine the expansion functions using the method scales polynomically with the number of variables rather than exponentially. This logic is based on the fundamental assumption underlying the HDMR representation that only low-order correlations among the input variables are likely to have significant impacts upon the outputs for most high-dimensional complex systems. The proposed method is first illustrated for multi-parameter nonlinear mathematical test functions with fuzzy variables. The method is then integrated with a commercial finite element software (ADINA). Modal analysis of a simplified aircraft wing with fuzzy parameters has been used to illustrate the generality of the proposed approach. In the numerical examples, triangular membership functions have been used and the results have been validated against direct Monte Carlo simulations. It is shown that using the proposed HDMR approach, the number of finite element function calls can be reduced without significantly compromising the accuracy. [ABSTRACT FROM AUTHOR]

Abstract: We present an experimental investigation of a single-plane automatic balancer that is fitted to a rigid rotor. Two balls, which are free to travel around a circular race, are used to compensate for the mass imbalance in the plane of the device. The experimental rig possesses both cylindrical and conical rigid body modes and the performance of the automatic balancer is assessed for a variety of different levels of imbalance. A non-planar mathematical model that also includes the observed effect of support anisotropy is developed and numerical simulations are compared with the experimental findings. In the highly supercritical frequency range the balls act to balance the rotor and a good quantitative match is found between the model and the experimental data. However, during the rigid body resonances the dynamics of the ball balancer is highly nonlinear and for this speed range the agreement between theory and experiment is mainly qualitative. Nevertheless, the model is able to successfully reproduce many of the solution types that are found experimentally. [ABSTRACT FROM AUTHOR]

Abstract: This paper investigates the hyperelastic behaviour of single wall carbon nanotubes (SWCNTs) by means of a finite element-based lattice approach. A one-term incompressible Ogden-type hyperelastic model is chosen to describe the mechanical response of SWCNTs under tensile loading. In order to determine the material constants of the model, numerical tests are conducted on a representative arrangement of carbon atoms, establishing equality between the Ogden strain–energy and the variation of the Tersoff–Brenner interatomic potential. The material constants determined here are then used in numerical simulations carried out on SWCNTs models. A good predictive capability of the present model is found when the obtained results are compared to published data. A first conclusion obtained from the present work suggests that a value of 0.147nm for the Cuivalent diameter is suitable for the hyperelastic description of SWCNTs. A second conclusion reveals a prediction of 0.51 for the breaking strain of SWCNTs under tension, which is in excellent agreement with results obtained from molecular dynamics simulations and continuum theory. [ABSTRACT FROM AUTHOR]

Over the decades, vibration-based condition monitoring has become well accepted and widely used to identify faults in rotating machines. However, the quantification of faults may require a significant number of tests to be carried out which may be time consuming and costly, if not impossible, by experiments alone. In the recent past, it has been observed that model-based identification has played a significant role in the rapid resolution and quantification of faults. The paper seeks to give an overview of the recent developments in this field which has considerable practical importance. [Copyright &y& Elsevier]

In this paper, the dynamics of a tailored composite rotating blade with curved tips are investigated, with a view to improving the dynamic behaviour of the blade in flight. The blade tip is curved either in the out-of-plane or in the in-plane directions. The composite blade is modelled by using the exact beam formulation, and the cross-sectional properties of the blade are obtained using the variational asymptotic method. The resulting nonlinear partial differential equations are discretised using a time-space scheme, and the stationary and rotating frequencies of the blade are obtained from the eigenvalues of the linearised system. Three case studies are considered here each of them representing one of the main elastic couplings that might happen in a composite blade. These three elastic couplings are the flap-twist, lag-twist, and extension-twist couplings. All these couplings are very important in the blade design as they can affect the twist and hence the dynamics of the blade. The blade tip length and curvature value are two main parameters that this paper is focused on. It is shown that the curved tip of the blade affects the blade frequencies by adding extra couplings, and therefore could be used as a potential morphing concept for tuning the frequencies, enhancing the aeroelastic stability or performance of the blade in flight. [ABSTRACT FROM AUTHOR]

• General nonlocal theory with two parameters is used for the porous FG nanobeam. • The nonlocal parameters cause softening and hardening behavior. • Reddy's beam theory is used to model higher-order transverse shear strains. • Material variations in the length and thickness directions are investigated. • The porosity volume fraction and the length to thickness ratio are varied. A comprehensive vibrational analysis of bi-directional functionally graded (2D-FG) rotating nanobeams with porosities is studied for the first time. The beam is modeled based on general nonlocal theory (GNT) where the beam governing equations are derived depending on two different nonlocal parameters. Unlike Eringen's conventional form of nonlocal theory, the general nonlocal theory can reveal both hardening and softening behaviors of the material. Here, the attenuation functions are altered in both transverse and longitudinal directions of 2D-FG nanobeam. This feature, which has a significant effect on the vibrational characteristics, has not been considered in previous studies. Moreover, to estimate the effects of the higher-order transverse shear strains on the vibration of the nanobeam, Reddy's beam theory (RBT), which includes higher-order shear deformation, is employed. The material properties of the 2D-FG rotating nanobeam vary both in the length and thickness directions according to a power law. The generalized differential quadrature method (GDQM) is used to predict the vibration response. Also, the effects of material variation along the length and thickness directions, the rotating velocity of the nanobeam, the porosity volume fraction and the length to thickness ratio of the rotating nanobeam are illustrated and discussed in detail. The investigations performed in this study expose new phenomena for the vibration of nanobeams. [ABSTRACT FROM AUTHOR]

• Dynamics of viscoelastic AFG beams with axial and spinning motion is studied. • Numerical and analytical methods for determining the stability threshold are given. • Divergence and flutter analysis for the system are performed. • Influence of viscosity and axial load on the stability evolution is discussed. • Mass-addition and stiffness-hardening effects of material gradation are found. For the first time, the structural dynamics and vibrational stability of a viscoelastic axially functionally graded (AFG) beam with both spinning and axial motions subjected to an axial load are analyzed, with the aim to enhance the performance of bi-gyroscopic systems. A detailed parametric study is also performed to emphasize the influence of various key factors such as material distribution type, viscosity coefficient, and coupled rotation and axial translation on the dynamical characteristics of the system. The material properties of the system are assumed to vary linearly or exponentially in the longitudinal direction with viscoelastic effects. Adopting the Laplace transform and a Galerkin discretization scheme, the critical axial and spin velocities of the system are obtained. An analytical approach is applied to identify the instability thresholds. Stability maps are examined, and for the first time in this paper, it is demonstrated that the stability evolution of the system can be altered by fine-tuning of axial grading or viscosity of the material. The variation of density and elastic modulus gradient parameters are found to have opposite effects on the divergence and flutter boundaries of the system. Furthermore, the results indicate that the destabilizing effect of the axial compressive load can be significantly alleviated by the simultaneous determination of density and elastic modulus gradation in the axial direction of the system. [ABSTRACT FROM AUTHOR]

• Nonlinear model updating using multivalued global correlation analysis is proposed. • Correlations between multivalued Frequency Response Curves(FRCs) are conducted. • Numerical study is conducted for a nonlinear model with 8 bifurcation points. • The method is validated with an experimental nonlinear beam with multivalued FRCs. Model updating using multivalued Frequency Response Curves (FRCs) is an important approach to construct a strongly nonlinear model. Residues between the predicted and measured FRCs are usually computed for updating, while the updating precision may be impacted by the measurement noise at local DOFs. In this paper, based on multivalued Global Shape Curve Criterion (GSCC) and Global Amplitude Curve Criterion (GACC), a novel nonlinear model updating method is proposed, to utilize global correlations to update complex nonlinear models. Through arclength-based separation, multivalued GSCCs/GACCs are quantified between multivalued FRCs obtained from prediction and measurement. Afterwards, a correlation-map is established to exclude false global correlation characteristics within multivalued correlations. Analytical sensitivities of the retained true global correlations to nonlinear parameters are derived and finally model updating is conducted. A simulation study is performed on a numerical nonlinear model. Updating successfully handles complex multivalued FRCs with up to 8 bifurcations. The proposed updating further indirectly identifies a strong magnet nonlinearity of a real beam test rig, through multivalued responses measured at Mode 3. The updated results show the validity and superiority of the proposed method. [ABSTRACT FROM AUTHOR]

Corrugated panels have many potential applications in civil, mechanical and aerospace engineering. The research on morphing aircraft requires the derivation of deformation limits of corrugated panels, which can be used as the constraint conditions for the design and optimisation of morphing structures. The relationship between the local and global strains of the equivalent models for corrugated panels is derived, which makes the prediction of the maximum strain available. Thus, from the maximum strain criterion, the global strain limit is evaluated under different load conditions. The results from the proposed analytical method are compared to those from detailed finite element models, which indicates a good agreement for all of the analysed cases. The influence of the geometric parameters of the corrugation shape is also investigated. [ABSTRACT FROM AUTHOR]

• The effects of structural joint variability on modal parameters are experimentally studied. • A stochastic generic joint element is introduced to represent variability in joint. • Bayesian model updating is used to identify joint model parameters from measured data. • Bayesian model updating is used to identify joint parameters from measured data. Dynamic properties of the contact interfaces in joints and mechanical connections have a great influence on the overall dynamic properties of assembled structures. Uncertainty and nonlinearity are two major effects of contact interfaces which introduce challenges in accurate modeling. Randomness in surface roughness quality, surface finish and contact preload are the main sources of variability in the contact interfaces. On the other side, slip and slap are two mechanisms responsible for nonlinear behavior of joints. Stochastic linear/nonlinear models need to be developed for such uncertain structures to be used in dynamic response analysis or system parameter identification. In this paper, variability in linear behavior of an assembled structure containing a bolted lap-joint is investigated by using experimental results. A stochastic model is then constructed for the structure by employing a stochastic generic joint model and the uncertainty in the joint model parameters is identified by using a Bayesian identification approach. [ABSTRACT FROM AUTHOR]

In this paper, the effect of various parameters of a specific rotor blade cross-section on the effectiveness of a twist morphing concept is investigated. Then, by considering different constraints, a cross-section consistent with this morphing concept with high lag-twist coupling and low extension-twist, is developed. This lag bending-torsion coupling is used to change the twist of the blade during the flight, while the high values of extension-twist coupling is avoided. To this end, a concentrated mass is added to the blade, where its chordwise location varies in flight. When the mass moves in the chordwise direction, a local lag bending is introduced into the blade. This in-plane bending moment then changes the blade twist distribution through lag-twist coupling induced through stiffness tailoring in the blade cross-section. Therefore, this coupling plays an important role in this morphing concept. The one-dimensional dynamics of the blade is modelled by using the geometrically exact fully intrinsic bean equations while the 2D cross-sectional stiffness values are determined by using the VABS software. First, a blade which resembles the BO-105 main rotor blade in the fundamental frequencies is designed. Then, the effect of various parameters of the cross-section on the fundamental frequencies, the lag-twist coupling, and the extension-twist coupling are determined. It is found that the skin of the spar has the highest contribution to both the extension-twist and the lag-twist coupling. Finally, a cross-section compatible with the proposed morphing concept is designed and it is demonstrated that the twist of the blade may be changed significantly. [ABSTRACT FROM AUTHOR]

In this paper, the aeroelastic stability of a composite hingeless rotor blade with a chordwise movable mass is investigated. The point mass is located near the tip of the blade and its chordwise location is variable with respect to the elastic axis and can be moved during the flight. This movable mass is added to the blade to actuate the blade twist during flight. By actuating the mass in the chord direction of the blade during the flight, a bending moment which is the result of the centrifugal force of the mass and its offset is induced on the blade. This bending moment induces twist in the blade, due to bend-twist coupling in the composite lamination. The blade is modelled by using the geometrically exact fully intrinsic beam equations along with the variational asymptotic beam sectional analysis. The aerodynamic loads are simulated by using the two-dimensional strip theory combined with a uniform inflow. The nonlinear partial differential aeroelastic equations are discretized by a time-space scheme, and the converged results are compared with those reported in the literature and a very good match is observed. The results show that by positioning the mass near the tip of the blade, and also by using the ply angle of about 30 degree in this configuration, the highest possible twist change is achieved when the mass moves from the leading edge to the trailing edge of the blade. Moreover, the spanwise location of the mass slightly changes the stability boundaries, while the chordwise movement significantly affects the aeroelastic instability. [ABSTRACT FROM AUTHOR]

In this paper, the potential effectiveness of a nonlinear energy sink (NES) to absorb the energy from a wing that is vibrating as a result of flying in a gusty environment is investigated. The structural dynamics of the wing is simulated using a rigid airfoil mounted on two linear/nonlinear springs to represent the bending and torsional stiffness of the wing. The wing is subjected to a combination of gust and aerodynamic loads. The unsteady aerodynamic lift and moment are modelled using Wagner's theory. Furthermore, the gust loads are obtained by assuming two different gust profiles, e.g. sharp-edged and 1-cosine gust profiles. A nonlinear energy sink, which comprises of a concentrated mass, damper and a nonlinear spring, is attached to the wing, and its effectiveness to absorb the gust energy is investigated. The coupled nonlinear aeroelastic equations are integrated numerically to determine the response of the wing. To verify the developed aeroelastic model, the obtained results are compared with the available results in the literature and an excellent agreement is observed. The results highlight that adding the NES to the wing is capable of reducing the gust oscillation amplitude of the wing significantly when the NES parameters are chosen accordingly. [ABSTRACT FROM AUTHOR]

• Correlation analysis of strongly nonlinear frequency responses is proposed. • Correlation functions with complex multivalued behavior are computed. • Real and fake correlations within the multivalued responses are extracted. • Correlation analysis is conducted for responses with different multivalued behavior. Global correlation analysis is an important technique to quantify both the shape and amplitude differences between two response vectors. In linear dynamic systems, differences between two Frequency Response Functions (FRFs) are quantified as scalar number curves of the Global Shape Criterion (GSC) and the Global Amplitude Criterion (GAC), to represent FRF similarities at different frequencies. From linear to nonlinear, responses are usually obtained at different frequencies to form the Frequency Response Curve (FRC), replacing the FRF for dynamic analysis. Extending the concept of global correlation analysis from linear FRFs to nonlinear FRCs could quantify shape and amplitude similarities between nonlinear models. However, global correlation analysis for multivalued FRCs with a strong nonlinearity is hard to conduct, as strongly nonlinear correlation functions have complex multivalued phenomena with real/fake characteristics. In this paper, the Global Shape Curve Criterion (GSCC) and Global Amplitude Curve Criterion (GACC) are proposed for the correlation analysis of strongly nonlinear FRCs, which can quantify the similarity between two FRCs with different and complex multivalued phenomena. Through the arclength-based separation, multivalued FRCs are separated to single-valued response branches, in order to compute single-valued correlation functions that form the multivalued correlation function. The computed correlations contain the GSCC and GACC, which separately represent shape and amplitude differences between two FRCs at each frequency. The multivalued correlation function is represented as a Correlation-Map (C-MAP) to extract real correlation characteristics, for accurate correlation analysis. The multivalued correlation analysis is first verified on a 3 DOF model with a strong nonlinearity. Differences between the reference and initial multivalued FRCs are successfully quantified as scalar curves and the GACC may be more sensitive than the GSCC on models with a local nonlinearity. Then, the proposed method is further validated on an experimental 3 DOF model. Very complex 15-valued correlation functions between FRCs with different multivalued phenomena are established. Even so, the real correlations are still successfully extracted by the C-MAP. These show the validity and superiority of the proposed method. [ABSTRACT FROM AUTHOR]

• An arclength-based response matching method is proposed to match multivalued responses. • A model updating technique for structures with strong nonlinearities is presented. • The proposed method can handle the linear and strongly nonlinear responses at the same time. • Multi-valued frequency response data with both stable and unstable responses are used for model updating. Model updating of strongly nonlinear systems is a vital tool to establish the precise nonlinear model from the multivalued responses and one major step in the updating process is the matching of the predicted and measured multivalued responses. However, when the multivalued behavior of the predicted and measured responses varies widely, the traditional multivalued response matching methods perform poorly. In this paper, a novel arclength-based multivalued response matching technique is proposed, which can help to update the model from linear to strongly nonlinear and handle both stable and unstable responses. The arclength is obtained from the continuation and the multivalued response is parameterized and transferred from the frequency domain to the arclength domain. The Arclength-Response curve is single-valued and can be easily separated into several parts based on feature points. Transferring the separation results back to the frequency domain, the full multivalued response is divided to single-valued Frequency-Response curves, where single-valued predicted and tested responses may be directly matched. A 2 DOF strong nonlinear model is first updated for verification. Using the proposed method, the linear response is directly updated based on the multivalued response with both softening and hardening regions. The error in the final updated parameters is below 1% and the proposed updating method performs better than two traditional methods. A real 3 DOF nonlinear model with a non-smooth strong nonlinearity with the hardening region is then used for validation. The stable and unstable responses of the system are measured from a shaker voltage-based constant frequency test and model updating is then conducted from linear to strongly nonlinear. During the updating process, the complex nonlinear behavior has six bifurcation points on one predicted response curve, but the updated responses fit the real ones well after 18 iterations. These results show the validity and superiority of the proposed method. [ABSTRACT FROM AUTHOR]

This article presents the application of finite-element fuzzy model updating to the DLR AIRMOD structure. The proposed approach is initially demonstrated on a simulated mass-spring system with three degrees of freedom. Considering the effect of the assembly process on variability measurements, modal tests were carried out for the repeatedly disassembled and reassembled DLR AIRMOD structure. The histograms of the measured data attributed to the uncertainty of the structural components in terms of mass and stiffness are utilised to obtain the membership functions of the chosen fuzzy outputs and to determine the updated membership functions of the uncertain input parameters represented by fuzzy variables. In this regard, a fuzzy parameter is introduced to represent a set of interval parameters through the membership function, and a meta model (kriging, in this work) is used to speed up the updating. The use of non-probabilistic models, i.e. interval and fuzzy models, for updating models with uncertainties is often more practical when the large quantities of test data that are necessary for probabilistic model updating are unavailable. [ABSTRACT FROM AUTHOR]

This study presents the Ritz formulation, which is based on boundary characteristic orthogonal polynomials (BCOPs), for the two-phase integro-differential form of the Eringen's nonlocal elasticity model. This approach is named the nonlocal Ritz method (NL-RM). This feature greatly reduces the computational cost compared to the nonlocal finite-element method (NL-FEM). Another advantage of this approach is that, unlike NL-FEM, the nonlocal mass and stiffness matrices are independent of the mesh distribution. Here, these formulations are applied to study the static-bending and free-dynamic analyses of the Kirchhoff plate model. In this paper, novel 2D BCOPs of the plate are derived as coordinate functions. These polynomials are generated using a modified Gram-Schmidt process and satisfy the given geometrical boundary conditions as well as the natural boundary conditions. The accuracy and convergence of the presented model, demonstrated through several numerical examples, are discussed. A concise argument on the advantages of NL-RM compared to NL-FEM is also provided. [ABSTRACT FROM AUTHOR]

• Updating strongly nonlinear models using fixed frequency tests is proposed. • Fixed frequency tests with continuation also measure unstable multivalued responses. • Multivalued responses of nonlinear models with fixed frequency excitation predicted. • Proposed updating method achieves higher precision than only using stable responses. Model updating using multivalued responses is an important approach to construct strongly nonlinear models. During updating, swept frequency tests are usually used to measure the multivalued responses, but the measured responses only contain the stable branches. Accordingly, updating mainly uses these stable responses for the nonlinear model construction. Unstable responses are rarely tested or participate in the updating process, which may lead to errors in the constructed model with strong nonlinearities. Recently, fixed frequency tests using a continuation scheme have been used to measure fully multivalued responses, including both the stable and unstable branches, for structures with the strong nonlinearity. However, the measured responses were then transformed to equivalent swept frequency tests for the existing updating schemes, where this transformation may induce errors in the updating process. In this paper, a novel method for strong nonlinear model updating using the results of the fixed frequency test is proposed. Such updating is based on the directly measured data of the fixed frequency tests and can handle both the stable and unstable responses. Fixed frequency continuation using the Multi-Harmonic Balance Method (MHBM) is developed to predict the multivalued responses and their sensitivities. The multivalued responses of the prediction and measurement are directly matched in sensitivity-based updating. The proposed method is numerically verified on a 2 DOF nonlinear model. Using the proposed method, the nonlinear model is updated from linear to strongly nonlinear and the updated parameters all converge to the simulated values after 7 iterations. The proposed method is then experimentally validated on a 3 DOF nonlinear system with a non-smooth nonlinearity. A nonlinear model with a 7th order polynomial stiffness represents the equivalent system and is directly updated based on the fixed frequency test results. The updated responses are generally a good fit to the tested responses. Compared with updating using only the stable responses, the proposed updating method achieves higher precision and its updated responses are closer to the tested responses. These results show the validity and superiority of the proposed method. [ABSTRACT FROM AUTHOR]

This work presents a conceptually simple experiment consisting of a cantilever beam with a nonlinear spring at the tip. The configuration allows manipulation of the relative spacing between the modal frequencies of the underlying linear structure, and this permits the deliberate introduction of internal resonance. A 3:1 resonance is studied in detail; the response around the first mode shows a classic stiffening response, with the addition of more complex dynamic behaviour and an isola region. Quasiperiodic responses are also observed but in this work the focus remains on periodic responses. Predictions using Normal Form analysis and continuation methods show good agreement with experimental observations. The experiment provides valuable insight into frequency responses of nonlinear modal structures, and the implications of nonlinearity for vibration tests. [ABSTRACT FROM AUTHOR]

In this paper the analytical analysis of an adaptively tuned piezoelectric vibration based energy harvester is presented. A bimorph piezoelectric energy harvester is suspended between two electrodes, subjected to a same DC voltage. The resonance frequency of the system is controllable by the applied DC voltage, and the harvested power is maximized by controlling the natural frequency of the system to cope with vibration sources which have varying excitation frequencies. The nonlinear governing differential equation of motion is derived based on Euler Bernoulli theory, and due to the softening nonlinearity of the electrostatic force, the harvester is capable of working over a broad frequency range. The steady state harmonic solution is obtained using the harmonic balance method and results are verified numerically. The results show that the harvester can be tuned to give a resonance response over a wide range of frequencies, and shows the great potential of this hybrid system. [ABSTRACT FROM AUTHOR]

Corrugation has long been seen as a simple and effective means of forming lightweight structures with high anisotropic behaviour, stability under buckling load and energy absorption capability. This has been exploited in diverse industrial applications and academic research. In recent years, there have been numerous innovative developments to corrugated structures, involving more elaborate and ingenious corrugation geometries and combination of corrugations with advanced materials. This development has been largely led by the research interest in morphing structures, which seek to exploit the extreme anisotropy of a corrugated panel, using the flexible degrees of freedom to allow a structure’s shape to change, whilst bearing load in other degrees of freedom. This paper presents a comprehensive review of the literature on corrugated structures, with applications ranging from traditional engineering structures such as corrugated steel beams through to morphing aircraft wing structures. As such it provides an important reference for researchers to have a broad but succinct perception of the mechanical behaviour of these structures. Such a perception is highly required in the multidisciplinary design of corrugated structures for the application in morphing aircraft. [ABSTRACT FROM AUTHOR]

Polynomial chaos solution for the frequency response of linear non-proportionally damped dynamic systems has been considered. It has been observed that for lightly damped systems the convergence of the solution can be very poor in the vicinity of the deterministic resonance frequencies. To address this, Aitken׳s transformation and its generalizations are suggested. The proposed approach is successfully applied to the sequences defined by the first two moments of the responses, and this process significantly accelerates the polynomial chaos convergence. In particular, a 2-dof system with respectively 1 and 2 parameter uncertainties has been studied. The first two moments of the frequency response were calculated by Monte Carlo simulation, polynomial chaos expansion and Aitken׳s transformation of the polynomial chaos expansion. Whereas 200 polynomials are required to have a good agreement with Monte Carlo results around the deterministic eigenfrequencies, less than 50 polynomials transformed by the Aitken׳s method are enough. This latter result is improved if a generalization of Aitken׳s method (recursive Aitken׳s transformation, Shank׳s transformation) is applied. With the proposed convergence acceleration, polynomial chaos may be reconsidered as an efficient method to estimate the first two moments of a random dynamic response. [ABSTRACT FROM AUTHOR]

Recent research in the field of finite element model updating (FEM) advocates the adoption of Bayesian analysis techniques to dealing with the uncertainties associated with these models. However, Bayesian formulations require the evaluation of the Posterior Distribution Function which may not be available in analytical form. This is the case in FEM updating. In such cases sampling methods can provide good approximations of the Posterior distribution when implemented in the Bayesian context. Markov Chain Monte Carlo (MCMC) algorithms are the most popular sampling tools used to sample probability distributions. However, the efficiency of these algorithms is affected by the complexity of the systems (the size of the parameter space). The Hybrid Monte Carlo (HMC) offers a very important MCMC approach to dealing with higher-dimensional complex problems. The HMC uses the molecular dynamics (MD) steps as the global Monte Carlo (MC) moves to reach areas of high probability where the gradient of the log-density of the Posterior acts as a guide during the search process. However, the acceptance rate of HMC is sensitive to the system size as well as the time step used to evaluate the MD trajectory. To overcome this limitation we propose the use of the Shadow Hybrid Monte Carlo (SHMC) algorithm. The SHMC algorithm is a modified version of the Hybrid Monte Carlo (HMC) and designed to improve sampling for large-system sizes and time steps. This is done by sampling from a modified Hamiltonian function instead of the normal Hamiltonian function. In this paper, the efficiency and accuracy of the SHMC method is tested on the updating of two real structures; an unsymmetrical H-shaped beam structure and a GARTEUR SM-AG19 structure and is compared to the application of the HMC algorithm on the same structures. [ABSTRACT FROM AUTHOR]

Abstract: The probability structure of the response and energy harvested from a nonlinear oscillator subjected to white noise excitation is investigated by solution of the corresponding Fokker–Planck (FP) equation. The nonlinear oscillator is the classical double well potential Duffing oscillator corresponding to the first mode vibration of a cantilever beam suspended between permanent magnets and with bonded piezoelectric patches for purposes of energy harvesting. The FP equation of the coupled electromechanical system of equations is derived. The finite element method is used to solve the FP equation giving the joint probability density functions of the response as well as the voltage generated from the piezoelectric patches. The FE method is also applied to the nonlinear inductive energy harvester of Daqaq and the results are compared. The mean square response and voltage are obtained for different white noise intensities. The effects of the system parameters on the mean square voltage are studied. It is observed that the energy harvested can be enhanced by suitable choice of the excitation intensity and the parameters. The results of the FP approach agree very well with Monte Carlo Simulation (MCS) results. [Copyright &y& Elsevier]

Abstract: A novel approach for uncertainty propagation and response statistics estimation of randomly parametrized structural dynamic systems is developed in this paper. The frequency domain response of a stochastic finite element system is resolved at randomly sampled design points in the input stochastic space with an infinite series expansion using preconditioned stochastic Krylov bases. The system response is expressed in the eigenvector space of the structural system weighted with finite order rational functions of the input random variables, termed spectral functions. The higher the order of the spectral functions, the more accurate is the order of approximation of the stochastic system response. However, this increased accuracy comes at a computational cost. This cost is mitigated by using a Bayesian metamodel. The proposed approach is used to the analyze the stochastic vibration response of a corrugated panel with random elastic parameters. The results obtained with the proposed hybrid approach are compared with direct Monte Carlo simulations, which have been considered as the benchmark solution. [Copyright &y& Elsevier]

Abstract: The dynamic characteristics of damped viscoelastic nonlocal beams are studied in this paper. The Kelvin–Voigt and three-parameter standard viscoelastic models, velocity-dependent external damping and nonlocal Euler–Bernoulli beam theory are employed to establish the governing equations of motion for the bending vibration of nanobeams. A transfer function method (TFM) is developed to obtain closed-form and uniform solution for the vibration analysis of Euler–Bernoulli beams with different boundary conditions. New analytical expressions for critical viscoelastic parameters, damping parameters and limiting frequencies are obtained. Considering a carbon nanotube as a numerical example, the effects of the nonlocal and viscoelastic constants on the natural frequencies and damping factors are discussed. The results demonstrate the efficiency of the proposed modeling and analysis methods for free vibration analysis of viscoelastic damped nonlocal Euler–Bernoulli beams. [Copyright &y& Elsevier]

Abstract: The probabilistic characterisation of a frequency response function can be very valuable for structural design and control. Unfortunately, obtaining a sufficiently large sample for wide ranges of vibration can easily become unaffordable. A variety of modelling assumptions can dramatically add to the computational cost: nonproportional damping, multiscale material properties, and high-resolution finite element analysis are some examples. This paper explores Bayesian emulators as surrogates for expensive finite element models in structural dynamics. We demonstrate the effectiveness of the method by performing uncertainty analysis of the frequency response of a nonproportionally damped plate made of a carbon fibre/epoxy composite material. [Copyright &y& Elsevier]

Abstract: Morphing aircraft concepts aim to enhance the aircraft performance over multiple missions by designing time variant wing configurations. The morphing concepts require wing skins that are flexible enough to allow large in-plane stretching and high bending stiffness to resist the aerodynamic loads. In this study, an optimization problem is formed to enhance the in-plane flexibility and bending stiffness of wing skins made of composite laminate. Initially, the optimal fiber and elastomer materials for highly flexible fiber reinforced elastomer laminates are studied using materials available in the literature. The minor Poisson’s ratio of the laminate is almost zero for all the fiber and elastomer combinations. In the next stage, the effects of boundary conditions and aspect ratio on the out-of-plane deflection of the laminate are studied. Finally, an optimization is performed to minimize the in-plane stiffness and maximize the bending stiffness by spatially varying the volume fraction of fibers of a laminate. The optimization results show that the in-plane flexibility and bending stiffness of the laminate with a variable fiber distribution is 30–40% higher than for the uniform fiber distribution. [Copyright &y& Elsevier]

Abstract: This paper investigates the effects of spatially uncertain material properties on the aeroelastic response predictions (e.g., rotating frequencies, vibratory loads, etc.) of composite helicopter rotor. Initially, the spatial uncertainty is modeled as discrete random variables along the blade span and uncertainty analysis is performed with direct Monte Carlo simulations (MCS). Uncertainty effects on the rotating frequencies vary with the higher-order modes in a non-linear way. Each modal frequency is found to be more sensitive to the uncertainty at certain sections of the rotor blade than uncertainty at other sections. Uncertainty effects on the vibratory hub load predictions are studied in the next stage. To reduce the computational expense of stochastic aeroelastic analysis, a high-dimensional model representation (HDMR) method is developed to approximate the aeroelastic response as functions of blade stiffness properties which are modeled as random fields. Karhunen–Loève expansion and a lower-order expansion are used to represent the input and outputs, respectively, in the HDMR formulation which is similar to the spectral stochastic finite element method. The proposed method involves the approximation of the system response with lower-dimensional HDMR, the response surface generation of HDMR component functions, and Monte Carlo simulation. The proposed approach decouples the computationally expensive aeroelastic simulations and uncertainty analysis. MCS, performed with computationally less expensive HDMR models, shows that spatial uncertainty has considerable influence on the vibratory hub load predictions. [Copyright &y& Elsevier]

Abstract: A model for quantifying the performance of acoustic emission (AE) systems on plate-like structures is presented. Employing a linear transfer function approach the model is applicable to both isotropic and anisotropic materials. The model requires several inputs including source waveforms, phase velocity and attenuation. It is recognised that these variables may not be readily available, thus efficient measurement techniques are presented for obtaining phase velocity and attenuation in a form that can be exploited directly in the model. Inspired by previously documented methods, the application of these techniques is examined and some important implications for propagation characterisation in plates are discussed. Example measurements are made on isotropic and anisotropic plates and, where possible, comparisons with numerical solutions are made. By inputting experimentally obtained data into the model, quantitative system metrics are examined for different threshold values and sensor locations. By producing plots describing areas of hit success and source location error, the ability to measure the performance of different AE system configurations is demonstrated. This quantitative approach will help to place AE testing on a more solid foundation, underpinning its use in industrial AE applications. [Copyright &y& Elsevier]

• Micro-slip behaviour of bolted joint is demonstrated using a detailed FE model. • An Equivalent model capable of predicting Micro-slip behaviour is developed. • An identification scheme based on the behaviour of the contact interface is proposed. • The parameters of equivalent model are identified using detailed model predictions. The dynamic response of individual components in an assembled structure shows high accuracy compared to experimental measurements of the system response. However, when it comes to assemblies, the conventional linear approaches fail to deliver good accuracy, due to the uncertain linear and nonlinear mechanisms in the contact interface of the joints. Therefore, the inherent dynamics of the contact interfaces needs to be considered in modeling assembled structures. In this paper the prediction of the nonlinear dynamic response in a bolted flange joint was obtained in two ways. First, a 3D detailed finite element model capable of representing the micro-slip mechanism was made using a quasi-static time stepping analysis. The linear characteristics and nonlinear mechanisms developing in the contact interface of a bolted joint are investigated by using the 3D detailed model. Moreover, the natural frequencies of the assembled structure (representing the linear response) and the micro-slip behavior in terms of hysteresis loops (representing the nonlinear response) are obtained using the detailed model. Second, an equivalent model composed of beam elements and an appropriate joint model is then constructed for the assembled structure. An identification approach is proposed, and the parameters of the joint model are identified using both linear and nonlinear characteristics, i.e. natural frequencies and hysteresis loops. Comparing the hysteresis loops obtained from the detailed and equivalent models verifies the accuracy of the joint model used to represent the contact interface and the identification approach proposed for parameter quantification. [ABSTRACT FROM AUTHOR]

In this study, the aeroelastic instability of a wing with an initial out-of-plane curvature is determined. The structural dynamics of the wing is modelled by using the geometrically exact beam equations, and the aerodynamic loads are determined using an incompressible unsteady aerodynamic model. The wing is considered to have initial out-of-plane curvature, and the effect of the curvature on the flutter velocity and flutter frequency of the wing is determined. Two curved wing cases are considered here. In the first case, the length of the wing is assumed to be constant and therefore, as the wing is curved, the projected area of the wing decreases. In the second case, the wing is assumed to have a constant projected area and therefore different curvature angles result from different wing lengths. When the wing is designed to have an initial out-of-plane curvature, the wing dynamics change, and therefore the aeroelastic stability of the curved wing is also affected. It is shown that as the initial curvature of the wing increases, initially the flutter velocity decreases but then increases, and finally a sudden jump occurs in the flutter velocity due to the change of the coupled modes contributing to flutter. Moreover, the flutter frequency also first decreases as the curvature of the wing increases, and then there is a sudden jump in the frequency, and from this point again the frequency decreases. Finally, results highlighting the importance of the initial curvature and the length of the curved segment on the stability velocity and frequency of the curved wing are presented. [ABSTRACT FROM AUTHOR]