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The linearity assumption is widely used when acquiring the hydrodynamic coefficients of a floating structure. However, the linear damping is frequently underestimated, especially for the natural frequency. To investigate the sloping seafloor effects on the damping terms of a single module of a semi-submersible Very Large Floating Structure (VLFS), this paper revisits the conventional formulation and further proposes the direct integration method for obtaining the linear and quadratic damping coefficients from free-decay tests. Numerical free-decay simulations of the single module over variable bathymetry are carried out by the CFD numerical tank. Corresponding model tests are also implemented to verify and validate against the numerical solutions. The effects of the sloping seafloor, as well as the water depth, on the hydrodynamic coefficients are investigated based on the validated CFD modeling. Both numerical and experimental results indicate that the acquisition of the linear and quadratic damping coefficients is sensitive to the data-processing and identification approaches. For the case studied in present paper, the identification errors introduced by the conventional method are 1.5 % while they are 0.5 % using the direct integration method. The quadratic damping coefficient for heave mode decreases about 10.4 % when the sloping angle increases from 0 to 6 deg.

This article analytically investigates a (2+1)-dimensional generalized Yu-Toda-Sasa-Fukuyama equation. We secure the solutions of this equation via the engagement of Lie symmetry reductions alongside direct integration techniques. We gain non-topological 1-soliton as well as periodic function solutions of the equation. Series solution of the underlying equation is also achieved by exploiting power series technique. Furthermore, the utilization of ( G ′ / G ) -expansion method is done in procuring some closed-form solutions of the equation. Graphical exhibition of the dynamical character of the gained results is given in a bid to have a sound understanding of the physical phenomena of the underlying model. Conclusively, we give the conserved vectors of the aforementioned equation by employing both the standard multiplier approach as well as the Ibragimov’s conservation theorem.

Surface integral equation (SIE) methods are of great interest for the efficient electromagnetic modeling of various devices, from integrated circuits to antenna arrays. Existing acceleration algorithms for SIEs, such as the adaptive integral method (AIM), enable the fast approximation of interactions between well-separated mesh elements. Nearby interactions involve the singularity of the kernel, and must instead be computed accurately with direct integration at each frequency of interest, which can be computationally expensive. We propose a novel algorithm for reducing the cost-per-frequency of near-region computations for both homogeneous and layered background media. In the proposed extended AIM (AIMx), the SIE operators are decomposed into a frequency-independent term containing the singularity of the kernel, and a nonsingular frequency-dependent term. Direct integration is only required for the frequency-independent term, and can be reused at each frequency, leading to significantly faster frequency sweeps. The frequency-dependent term is captured with good accuracy via fast Fourier transform (FFT)-based acceleration even in the near region, as confirmed with an error analysis. The accuracy and efficiency of the proposed method are demonstrated through numerical examples drawn from several applications, and CPU times are significantly reduced by factors ranging from three to 16., 15 pages, 18 figures, accepted for publication in the IEEE Transactions on Antennas and Propagation

Developing efficient platinum (Pt)-based electrocatalysts is enormously significant for fuel cells. Herein, we report an integrated electrocatalyst of ultralow-Pt alloy encapsulated into nitrogen-doped nanocarbon architecture for efficient oxygen reduction reaction. This hybrid Pt-based catalyst achieves a mass activity of 3.46 A mgpt−1 at the potential of 0.9 V vs. RHE with a negligible stability decay after 10,000 cycles. More importantly, this half-cell activity can be expressed at full cell level with a high Pt utilization of 10.22 W mgPt−1cathode and remarkable durability after 30,000 cycles in single-cell. Experimental and theoretical investigations reveal that a highly strained Pt structure with an optimal Pt-O binding energy is induced by the incorporation of Co/Ni into Pt lattice, which would account for the improved reaction kinetics. The synergistic catalysis due to nitrogen-doped nanocarbon architecture and active Pt component is responsible for the enhanced catalytic activity. Meanwhile, the strong metal-support interaction and optimized hydrophilic properties of nanocarbon matrix facilitate efficient mass transport and water management. This work may provide significant insights in designing the low-Pt integrated electrocatalysts for fuel cells and beyond.

The knowledge of the steady-state security region is essential for secure operation of the integrated energy system (IES). The two-time-scale feature of the IES is explored to facilitate construction of its exact steady-state security region. Conditions allowing decomposition of the IES into fast and slow subsystems are established. A complete characterization of the IES steady-state security region via the stable equilibrium manifold of the fast subsystem and the slow subsystem is derived and theoretically proven. This characterization can significantly facilitate construction of the IES steady-state security region (SSR) and is derived under the AC power flow model and gas flow model without any model approximation and simplification. Numerical studies are conducted to validate the derived characterization of the SSR and to illustrate the advantages of the proposed characterization in terms of robustness and reduced computational burden. Numerical studies show that exploring the fast and slow subsystems can lead to fast computation of feasible solutions with a 20-fold speed up in calculation time, as compared with the direct integration of the original IES system. Hence, the proposed two-time-scale method appears to be fast and yet accurate.

Roads and railway tracks are a major focus of interest in transport infrastructure monitoring. Settlement in a road or railway track profile changes the dynamic excitation applied to passing vehicles. This, in turn, results in a changed dynamic response in the original source of loading, such as a passing vehicle. These changes in dynamic excitation make it possible to detect damage in transport infrastructure from the vehicle response. In this paper, the profile is calculated using accelerations in a passing vehicle and used to monitor transport infrastructure.

Prediction of the response of nonlinear dynamical systems under interacting parametric and external excitations is important in designing systems such as sensors, amplifiers or energy harvesters, to achieve the desired performance. This paper concerns the nonlinear forced Mathieu equation, with linear damping and a 2:1 ratio between the parametric and external excitation frequencies. The Method of Varying Amplitudes (MVA) is employed to derive approximate analytical expressions for the response of the system. Both single-term and double-term solutions are developed: it is seen that, employing the double-term approximation, the MVA can accurately predict the response of the system over a wide range of frequencies and system parameters, showing a maximum of 0.2% deviation from numerical results obtained by direct integration of the equation of motion. This is in contrast with most of the available theoretical approaches such as the conventional Method of Multiple Scales, which can predict the response accurately only for a narrow range of system parameters and excitation frequencies. Furthermore, it is seen that the response is bounded, and analytical expressions for the frequency and amplitude of the upper bound are developed: this is unlike other methods which predict unbounded response, unless nonlinear damping is considered. Analytical expressions for the response are developed, and results are verified with numerical results obtained from direct integration of the equation of motion. Numerical examples are presented, showing good agreement with results obtained by the MVA.

An investigation of dynamic behaviors of a sandwich plate containing an imperfect two dimensional functionally graded (2D-FG) core surrounded by two faces on a two-parameter elastic foundation and subjected to a moving load is carried out in this paper. The present sandwich solid is composed of a porous 2D-FG core covered by two homogenous layers. It is assumed that the middle layer has micro voids dispersed uniformly and unevenly through the layer thickness. The fundamental equations are governed within the framework of first-order-shear deformation theory by utilizing Hamilton’s principle, von-Karman geometrical nonlinearity and the principal of mixtures. Newmark direct integration procedure is implemented to transform the dynamic equations into a static form and then the kinetic dynamic relaxation numerical technique in conjunction with the finite difference discretization method are employed to solve the nonlinear partial differential governing equations. Finally, the effects of porosity fraction and scattering patterns, boundary constrains, the variation of materials’ grading indexes and elastic foundation constants on the transient performances of the plate are studied in detail.

The article discusses a new approach to modeling the behavior of structures under the influence of dynamic loads, including loads from ground and underground transport. The approach is to apply the direct integration method, as well as the SBFEM method to calculate the forces in load-bearing building structures under dynamic influences, taking into account a number of factors - the damping properties of the subgrade, physical nonlinearity of soils and the passage of waves in the soil space. The article presents the main theoretical premises, the results of a numerical experiment of a real monolithic building, built in the zone of influence of the subway.

Surface location error (SLE) caused by the forced vibration is one of the main factors limiting machining accuracy in stable milling. This paper presents a novel scheme with high precision and high efficiency to predict SLE based on the Newton polynomial-Chebyshev nodes. The dynamic model embodying the forced and regenerative excitations is first derived from the simplified milling process. After describing the response of the system with the direct integration format, the Newton polynomial frame is chosen to spread the self-excited and forced-excited elements successively in each equidistant time interval to obtain the separate output of tool vibration displacements with a close form. Then, the coefficient matrix which is not affected by the change of time is established in each spindle speed location to calculate SLE. Three examples which have been verified by the experiments are introduced to capture the optimal approximated order with exhibiting the characteristic of the proposed methods. It is observed that the prediction accuracy of the high-order methods drop seriously for the absence of Runge effect. In order to avoid this unwanted phenomenon, the origin uniform time joints are modified by a nonlinear sampling technique based on Chebyshev nodes to establish the novel coefficient matrix with fewer calculated loads for SLE prediction, and a series of comparisons illuminate the proposed modified method performs satisfactorily.

Diamond has been forecasted as an excellent substrate material for acoustic devices and microelectromechanical systems owing to its exceptional mechanical and acoustic properties. The integration of piezoelectric thin films on diamond can realize devices operating in the GHz frequency range, which has great relevance in the 5G communication systems. The heterostructures, based on lead zirconate titanate (PZT) and diamond, could be highly promising for the aforesaid applications. However, the direct integration of PZT on diamond is problematic due to the formation of undesired pyrochlore phase and the mismatch in their thermal expansion coefficients. Thus, PZT/diamond heterostructures are often fabricated using a buffer layer. But the recent reports indicated that the direct integration of PZT on diamond is possible without any buffer layer, which is highly promising. This comprehensive review discusses various aspects, including the possibilities and challenges in the fabrication of PZT/diamond heterostructures.

This article is primarily concerned with finite-time convergence (FTC) and predefined-time convergence (PTC) design for a class of general zeroing neural network (ZNN) by constructing different activation functions (AFs). Based on the limit comparison test for improper integrals, some useful theoretical criteria are proposed to determine whether a nonlinear-activated ZNN model has FTC, PTC, or not. This novel method can avoid the valuation loss of the zoom method and the unsolvable barrier of the direct integration method that are widely used in the previous ZNN design. According to these convergence criteria, some instructive corollaries are derived to design valuable AFs to make ZNN models with FTC or PTC more easily. By taking a matrix-inversion ZNN model, some commonly used AFs are used to verify the usability of the criteria. In addition, some new AFs are constructed to further design some better ZNN models with superior FTC or PTC. Finally, convergence types of the ZNN model based on different AFs are visualized in numerical experiments.

This numerical study exclusively focused on the direct two point diagonally multistep block method of order four (2DDM4) in the form of Adams-type formulas. The proposed predictor–corrector scheme was applied in this study to compute two equally spaced numerical solutions for the third-order two point and multipoint boundary value problems (BVPs) subject to Robin boundary conditions concurrently at each step. The optimization of the computational costs was taken into consideration by not resolving the equation into a set of first-order differential equations. Instead, its implementation involved the use of shooting technique, which included the Newton divided difference formula employed for the iterative part, for the estimation of the initial guess. Apart from studying the local truncation error, the study also included the method analysis, including the order, stability, and convergence. The results of eight numerical problems demonstrated and highlighted competitive computational cost attained by the scheme, as compared to the existing method.

In this study, an on-the-fly artificial neural network (ANN) framework has been developed for the tabulation of chemical reaction terms in direct numerical simulations (DNS) of premixed and igniting flames. The procedure does not require any preliminary knowledge to generate samples for ANN training; the whole training process is based on the detailed simulation results and takes place on-the-fly, so that the obtained ANN model is perfectly adapted to the specific problem considered. The framework combines direct integration (DI) and ANN model in an efficient way to overcome the extrapolation issue of the monolithic ANN model. Auto-ignition processes as well as the characteristics of established flames can be very well predicted using the ANN model. In the final simulations, involving a case with 3D turbulent hot-spot ignition, and a flame propagating in a turbulent flow, the developed procedure reduces the computational times by a factor of almost 5, while keeping the error for all species below 1 % compared to the standard, monolithic DI solution.

A reliability analysis framework for the stochastic simulation of slope progressive failure is proposed in the current work. Progressive failure is addressed as a local failure propagation process that takes place along individual segments upon a critical slip surface. The probabilities of progressive failure are evaluated by transition probabilities and Markov chains theory. Slope stability computations are performed by elastoplastic finite element models. The point estimate method is used for the direct integration of geotechnical uncertainty within stability computations. For the various safety states during local failure advancement, progressive failure probabilities are expressed through a transition probability matrix. The effect of certain factors, such as the cross-correlation between shear strength components, the performance function’s probability distribution, and the initial stress ratio at rest, are also investigated and discussed.

Stability presents a critical issue for real-time hybrid simulation. Actuator delay might destabilize the real-time test without proper compensation. Previous research often assumed real-time hybrid simulation as a continuous-time system; however, it is more appropriately treated as a discrete-time system because of application of digital devices and integration algorithms. By using the Lyapunov–Krasovskii theory, this study explores the convoluted effect of integration algorithms and actuator delay on the stability of real-time hybrid simulation. Both theoretical and numerical analysis results demonstrate that (1) the direct integration algorithm is preferably used for real-time hybrid simulation because of its computational efficiency; (2) the stability analysis of real-time hybrid simulation highly depends on actuator delay models, and the actuator model that accounts for time-varying characteristic will lead to more conservative stability; and (3) the integration step is constrained by the algorithm and structural frequencies. Moreover, when the step is small, the stability of the discrete-time system will approach that of the corresponding continuous-time system. The study establishes a bridge between continuous- and discrete-time systems for stability analysis of real-time hybrid simulation.

Circular and ring plates on a continuous changeable elastic bed are considered. It is assumed that the bed response is described by the Winkler model with a changeable bedding coefficient. An analytical method for axisymmetric bending calculations of plates loaded by a transverse continuously distributed replaceable load is proposed. The method is based on the solution of the corresponding differential bending equation with exchangeable coefficients found by direct integration. The exact solution is expressed through dimensionless fundamental function given in the form of power series of dimensionless parameters with exchangeable coefficients. Recurrence integral relations were obtained to determine the exchangeable coefficients of the series. As a result, formulas for deflections and internal forces, which fully characterize the plate’s stress-strain state, in the case where the given load and bed factor are arbitrary continuous functions, are obtained in analytical form. The method can be applied for any given limit conditions on the plate contours. In fact, calculations for axisymmetric bending of plates are reduced to determination of unknown integration constants from the given limit conditions and numerical realization of the obtained solutions. The derived general formulas are adaped for the practical case with the bedding factor and load given by polynomials. It is shown that, in this case, the dimensionless fundamental functions can be represented by power series. To calculate the coefficients of the power series, the corresponding recurrence relations are derived. Compared with approximate methods, the proposed analytical method allows one to obtain a more realistic bending behavior, being a lucrative alternative to the application of approximate methods when solving this class of problems.

To characterize the particle mass flow rate of gas–solid two-phase flow, a model of particle mass flow rate based on the comprehensive application of transferred current and induced current signals from an electrostatic sensor is proposed in this article. Compared with the characterization model of the particle mass flow rate using the transferred current signal or induced current signal separately, the proposed model can make full use of the characteristics of the two signals. The induced and transferred current signals are extracted from the electrostatic sensor based on the time-domain waveform characteristic method and the direct integration function method, respectively. According to the sensitivity of the time-domain characteristics of the transferred current signal (the radial motion of particles) and the macroscopic stability of the frequency-domain characteristics of the induced current signal (the axial motion of particles), the new signal characteristic value based on the two signals is used to establish a comprehensive signal characterization model (CSCM) of the particle mass flow rate. The coefficients in the model are fit using the Levenberg–Marquardt (LM) method. The experimental results show that the proposed model has higher accuracy and stability than the separate signal model under the experimental conditions in this article.

In order to predict the performance of designed electric machines, and also based on which the high efficiency of the drive systems can be obtained, the accurate calculation of the iron loss is necessary. Taking modeling accuracy versus modeling complexity into account, this article proposes a general and accurate iron loss calculation method considering harmonics based on the loss surface (LS) hysteresis model and finite-element method (FEM). Compared with the previous triangular wave excitation, this article uses the data under sinusoidal wave excitation to establish the LS model, which is more convenient for engineering application. A specimen is tested for different flux densities with harmonics, the extensive results verify the modeling method. Due to a powerful hysteresis model, the iron loss calculation can be realized by the direct integration of hysteresis loops. A separated iron loss calculation package is developed, and it is combined with the commercial finite-element software to compute the iron loss distribution. The method that combines the LS model and FEM is proved feasible by comparing the calculated iron loss with the measured one for the Epstein frame.

Introduction: This paper reviews the analytical method of assessing the seismic and extreme load resistance of buildings with a complex macrostructure that includes elastic-plastic inserts operating in shear. Methods: We analyze a number of studies that rationalize the choice of models for simulating complex elastic-plastic deformation in a mechanical system with several degrees of freedom, as well as studies that review the durability and resilience of buildings with a complex macrostructure based on non-linear shear links when subjected to dynamic and extreme impact. We also consider the methods of structural analysis regarding buildings with elastic-plastic inserts, accounting for the plastic hinged joints of metal frames. Results: We apply the analytical method to linear and non-linear systems with n degrees of freedom. We propose a mathematical equation that describes the nature of shear link response to seismic and extreme loads. Our method makes it possible to obtain an analytical solution for structures with proportionate and disproportionate damping by using the direct integration algorithm. Discussion: Most structures with a broad range of construction material properties require a disproportionate damping model. In this study, we solve equations by using the direct integration algorithm based on disproportionate damping. Under high dynamic load, the reinforcement of shear inserts operates in a plastic state.

This paper proposes a time-dependent probability method to predict the time-variant pounding risk, owing to this reason that the required separation gap width fails to accommodate the relative movement between two adjacent decks, of bridge systems subjected to non-stationary stochastic seismic excitations. Firstly the pseudo excitation method in random theory is utilized to transform the motion equation of system under the non-stationary stochastic seismic excitations into the transient response equation under deterministic external loads. And then the high precision direct integration method (HPDIM) is also employed to reduce the large number of transient analysis into two times for overcoming the challenges of strenuous computing effort. The time-dependent pounding system probability of bridges is derived by the combination of extreme value distribution theory and matrix-based system probability theory. Finally based on the proposed time-dependent probability method the numerical analysis of a real two span simply-supported beam bridge subjected to spatial and non-stationary ground motions is conducted herein for the pounding risk assessment. The results of this study provides in-depth insight into the time-dependent pounding probability of bridge systems subjected to spatially varying and non-stationary ground motions.

In this paper, the considered two-DOF system consists of a linear oscillator (LO) under external harmonic excitation and an attached lightweight nonlinear energy sink (NES) with local potential and geometrically nonlinear damping. With the application of complex-averaging method, the steady-state dynamical behavior of the system is investigated by the slow invariant manifold, folding singularities and equilibrium points. Different scenarios of strongly modulated responses are presented based on the geometry of SIM, and the numerical simulation results are in consistent with the analytical prediction. The incremental harmonic balance method is applied to detect the frequency response curves of the system around the fundamental resonance, and the accuracy of the theoretical analysis is fully verified by the numerical results obtained by direct integration of equations of motion of the system. It is demonstrated that the increase in external forcing amplitude, global nonlinear stiffness and local nonlinear stiffness can drive the frequency response curves move toward the right and widen the frequency bandwidth of the coexistence of multiple steady-state response regimes, while the increase in nonlinear damping the reverse. The numerical simulation results also show that the addition of geometrically nonlinear damping and local potential in the proposed NES can drastically enhance the capacity of the nonlinear vibration absorber to suppress the shock-induced response of the LO, and the proposed NES is effective for a comparatively broad range of applied impulsive energies, particularly for the high impulsive energies.

For a pulsating free surface source in a three-dimensional finite depth fluid domain, the Green function of the source presented by John [F. John, On the motion of floating bodies II. Simple harmonic motions, Communs. Pure Appl. Math. 3 (1950) 45-101] is superposed as the Rankine source potential, an image source potential and a wave integral in the infinite domain $(0, \infty)$. When the source point together with a field point is on the free surface, John's integral and its gradient are not convergent since the integration $\int^\infty_\kappa$ of the corresponding integrands does not tend to zero in a uniform manner as $\kappa$ tends to $\infty$. Thus evaluation of the Green function is not based on direct integration of the wave integral but is obtained by approximation expansions in earlier investigations. In the present study, five images of the source with respect to the free surface mirror and the water bed mirror in relation to the image method are employed to reformulate the wave integral. Therefore the free surface Green function of the source is decomposed into the Rankine potential, the five image source potentials and a new wave integral, of which the integrand is approximated by a smooth and rapidly decaying function. The gradient of the Green function is further formulated so that the same integration stability with the wave integral is demonstrated. The significance of the present research is that the improved wave integration of the Green function and its gradient becomes convergent. Therefore evaluation of the Green function is obtained through the integration of the integrand in a straightforward manner. The application of the scheme to a floating body or a submerged body motion in regular waves shows that the approximation is sufficiently accurate to compute linear wave loads in practice., Comment: 24 pages, 7 figures

The direct integration of electrocatalysts with photovoltaic materials provides a strategy for photoelectrochemically powering chemical transformations and storing intermittent solar energy as fuel...

In this paper, a method to calculate the first two moments (mean and variance) of the stochastic time response as well as the frequency functions of large FE models with probabilistic uncertainties in the physical parameters is proposed. This method is based on coupling of second order perturbation method and component mode synthesis methods. Various component mode synthesis methods are used to optimally reduce the size of the model. The analysis of dynamic response of stochastic finite element system can be done in the frequency domain using the frequency transfer functions and in the time domain by a direct integration of the equations of motion, using numerical procedures. The statistical first two moments of dynamic response of the reduced system are obtained by the second order perturbation method. Numerical applications have been developed to highlight effectiveness of the method developed to analyze the stochastic response of large structures.

An analytical solution is presented for the 3D static response of variable stiffness non-uniform composite beams. Based on Euler-Bernoulli theory, a set of governing differential equations are obtained, in which four degrees of freedom are fully coupled. For the variable stiffness beam, the governing field equations have variable coefficients reflecting the stiffness variation along the beam. Using the direct integration technique, the general analytical solution is derived in the integral form and the closed-form expressions of the obtained solutions are presented employing a series expansion approximation. The series expansion representation enables the proposed approach to be applicable for variable stiffness composite beams with arbitrary span-wise variation of properties. As an alternative solution, the Chebyshev collocation method is applied to the proposed formulation to verify the results obtained from the analytical solution. A number of variable stiffness composite beams made by fibre steering with various boundary conditions and stacking sequences are considered as the test cases. The static response are presented based on the analytical solution and Chebyshev collocation method and excellent agreement is observed for all test cases. The proposed model presents a reliable and efficient approach for capturing the complicated behaviour of variable stiffness non-uniform composite beams.

The existing non-paraxial expression of audio sounds generated by a parametric array loudspeaker (pal) is hard to calculate due to the fivefold integral in it. A rigorous solution of the Westervelt equation under the quasilinear approximation is developed in this paper for circular PALs by using the spherical harmonics expansion, which simplifies the expression into a series of threefold summations with uncoupled angular and radial components. The angular component is determined by Legendre polynomials and the radial one is an integral involving spherical Bessel functions, which converge rapidly. Compared to the direct integration over the whole space, the spherical expansion is rigorous, exact, and can be calculated efficiently. The simulations show the proposed expression can obtain the same accurate results with a speed of at least 15 times faster than the existing one.

In a previous paper, one of us (UL) constructed an exact analytical expression for the irregular (Jost) solution, off the energy shell, for the Hulthen potential by using the method of ordinary differential equation along with the properties of certain special functions of mathematical physics. In the present text, closed form expressions for the off-shell irregular solution and half-off-shell Tmatrix for motion in the Hulthen potential are re-derived by using the direct integration approach to the problem under consideration. We demonstrate the usefulness of our expressions through some model calculations and achieve excellent agreement between bound-and scattering-state observables and standard results.

This paper compares different full-discretization methods for milling stability analysis by using different high-order polynomials to interpolate both state term and delayed term (HFDMs) from the aspects of accuracy and efficiency. The dynamic model of milling process with consideration of regeneration effect is described by time periodic delay-differential equation (DDE) in the state-space. Different high-order interpolation polynomials are used to approximate the state term and delayed term. The state transition matrix is obtained on the basis of direct integration scheme. The rates of convergence of different HFDMs are compared with those of the benchmark methods using different process parameter points, the results indicate that it is difficult to evaluate the accuracy of different HFDMs through the convergence rate analysis of limited process parameter points. Then, mean differences and variances between the referenced and predicted critical depths of cut are employed for accuracy analysis. The 3rd-2nd HFDM is, on the whole, proved to be more accurate than the other methods. The efficiencies of different HFDMs are also verified through time-consuming study for both single degree of freedom (1-DOF) and two degree of freedom (2-DOF) milling system. The 3rd-2nd HFDM is proved to be an efficient method by comparing with the other methods. Besides, the HFDMs are available for predicting the stability lobe diagrams under both large immersion condition and low immersion condition.

Layer-by-layer manufacturing of composite mechanisms allows fast and cost-effective fabrication of customized robots in millimeter and centimeter scales which is promising for research fields that rely on frequent and numerous physical iterations. Due to the limited number of components that can be directly integrated in composite structures, however, often an assembly step is necessary which diminishes the benefits of this manufacturing method. Inspired by the Japanese craft of cutting (kiri-) paper (-gami), Kirigami, we introduce quasi-2D and highly stretchable functional Kirigami layers for direct integration into the composite mechanisms. Depending on the material and geometrical design; functional Kirigami layers can perform as flat springs, stretchable electronics, sensors or actuators. These components will facilitate the design and manufacturing of composite robots for different applications. To illustrate the effectiveness of these components, we designed and realized a foldable composite inchworm robot with three Kirigami layers serving as actuator, sensor and contact pad with directional friction. We elaborate on the working principle of each layer and report on their combined performance in the robot.

In this work, nonlinear free vibration of electrostatically actuated micromechanical system has been investigated. These nonlinear solutions are analytically derived. An undamped spring-mass model and dynamic equation of motion are employed for the parallel-plate microelectrostatic actuator. The first analytical approximate period and periodic solution of the mentioned problems are constructed with the help of Galerkin’s method and coupling of Galerkin’s with Newton’s method. In addition, the second and third analytical approximate solutions are also derived. The “exact” solutions are obtained from direct integration. In this work, the well-known static and dynamic pull-in parameters are discussed. Phase trajectory becomes non-periodic with the dynamic pull-in point. The approximate and “exact” solutions of period, phase trajectory, and time-dependent displacement of microelectrostatic actuators at various physical parameters are obtained and compared. It is found that the analytical approximate solutions are not only an explicit expression but also have excellent precision for a wide range of nonlinear vibration with different amplitudes.

We present our computationally efficient approach to modeling tunable graphene-based active metadevices, where the integral multivariate surface conductivity is reformulated in the time and frequency domains with physically interpretable and fast-to-compute integration-free terms. The derivation is built on an expansion to power series of $ {z}= -\text {exp}(-\mu /k_{B}T)$ that converges very fast for non-zero chemical potential values. The model reveals interesting decomposition of graphene response into a universal constant term plus a damped oscillator (digamma functions in the frequency domain) plus non-oscillating correction terms for near-zero potentials. The number of terms in that series is analyzed theoretically for a given accuracy. In practice, only a few series terms are required, making our approach very efficient for simulation of active metasurfaces compared with direct integration of Kubo’s formulas. A simple performance test comparing run times with our code versus the numerical integration of the original Kubo’s formulas demonstrates a speedup exceeding 103. The proposed models can be critical for the initial ellipsometric characterization of graphene and advanced global optimization of graphene-controlled metadevices.

The development of advanced, human like tactile sensing capabilities is one of the key challenges for next generation robots or prosthetics. Tactile sensors arrays will need to exhibit the desired sensing capabilities, show robustness to external influences as well as good approaches for the integration of large amounts of sensors. We present a tactile sensor array technology, based on the fabrication of a flexible interconnection substrate containing directly integrated tactile sensors. This approach has several advantages: interconnection substrate technology is widely available making upscaling of sensor arrays easy to a large amount of sensors and/or large sensing areas, the direct integration of sensors allows for a simple and very compact approach to densely packed sensor arrays and the structured flexible substrate enables integration into complex, three-dimensional bodies. We present sensors with a size of 600 μm and arrays of up to 12 x 12 individually addressable sensors. The sensors have a wide measurement range; free membrane deformation results in a high sensitivity of 2.6 kPa⁻¹ respectively 2600 N⁻¹ for small applied pressures (0-0.6 kPa) whereas deforming polymer studs extend the measurement range for larger applied pressures (5-25 kPa) with a sensitivity of 0.022 kPa⁻¹ respectively 22 N⁻¹. A statistical study of six sensor arrays from three wafers showed repeatable performance of the fabricated structures and robustness tests proved the stable sensing conditions over 10'000 cycles., Journal of Microelectromechanical Systems, 30 (6), ISSN:1057-7157, ISSN:1941-0158

Conformal Loadbearing Antenna Structures (CLAS) take advantage of a combination of structural and electromagnetic functions. CLAS have been developed as an advanced replacement for conventional antennas (such as blades, wires and dishes) to improve the structural efficiency, as well as the electromagnetic and aerodynamic performance of a platform. The CLAS concept permits the direct integration of microwave radiating elements in the structural skin of a platform. Therefore, the antenna will be subjected to structural loading and will deform accordingly. The effects of these structural-induced deformations on the resonant frequency of the antenna will be reported in this paper. This paper will investigate the performance of a carbon veil patch antenna when it is subject to static in-plane. The work presented will include the effects of in-plane loading on the resonant behavior of the patch antenna when the carbon veil is fully bonded and when it is disbonded by the parent structure. This paper will also discuss the effects of substrate delamination on the RF response of the patch antenna. The RF characteristics of the antenna will be modelled using ANSYS High Frequency Structure Simulator (HFSS).

Η παρούσα διδακτορική διατριβή αποτελεί συμβολή στην ανάπτυξη εξελιγμένων θεωριών δοκού για την ανάλυση ραβδωτών φορέων. Οι εξελιγμένες θεωρίες δοκού που αναπτύχθηκαν λαμβάνουν υπόψη φαινόμενα γενικευμένης στρέβλωσης (διατμητική υστέρηση λόγω κάμψης και στρέψης), διαστρέβλωσης (παραμόρφωση διατομής – distortion), ενώ πραγματοποιείται και γεωμετρικά μη γραμμική δυναμική ανάλυση δοκών σταθερής ή μεταβλητής διατομής, λαμβάνοντας υπόψη φαινόμενα ανώτερης τάξης όπως η περιστροφική και στρεβλωτική αδράνεια, η μη γραμμικότητα εξωτερικής φόρτισης, οι όροι Wagner και η βράχυνση λόγω στρέψης. Οι εν λόγω καινοτόμες θεωρίες συνδυάζουν την αυξημένη ακρίβεια με τα εγγενή πλεονεκτήματα των στοιχείων δοκού, οδηγώντας στην ανάπτυξη εξελιγμένων υπολογιστικών εργαλείων για την ανάλυση ραβδωτών φορέων.Η γενικευμένη στρέβλωση λαμβάνεται υπόψη, με την εισαγωγή ανεξάρτητων παραμέτρων, που εκφράζουν την «ένταση» της στρέβλωσης στο μήκος της δοκού. Οι παράμετροι αυτές πολλαπλασιάζουν αντίστοιχες συναρτήσεις στρέβλωσης, που προκύπτουν από ισάριθμα διδιάστατα προβλήματα συνοριακών τιμών στο χωρίο της διατομής. Στην παρούσα διατριβή αντιμετωπίζεται το πρόβλημα παραβίασης της συνοριακής συνθήκης μηδενισμού της διατμητικής τάσης στην παράπλευρη επιφάνεια της δοκού (ισορροπία σε επίπεδο υλικού σημείου) από τις τάσεις που προκύπτουν από το υιοθετούμενο πεδίο μετατοπίσεων. Προτείνεται διαδικασία «διόρθωσης» του τασικού πεδίου με χρήση της εξίσωσης διαμήκους τοπικής ισορροπίας. Μέσω της διόρθωσης αυτής βελτιώνεται η ακρίβεια των παραγόμενων αποτελεσμάτων χωρίς αύξηση των κινηματικών αγνώστων και διατηρείται κατά το μέγιστο δυνατό βαθμό η απλότητα της διατύπωσης.Όσον αφορά στη διαστρέβλωση (distortion), παράγεται κατάλληλη βάση συναρτήσεων διαστρέβλωσης/στρέβλωσης μέσω επαναληπτικού σχήματος ισορροπίας στο χωρίο της διατομής. Το σχήμα αυτό παράγεται χρησιμοποιώντας τις εξισώσεις τοπικής ισορροπίας της θεωρίας ελαστικότητας. Η προσέγγιση αυτή παρουσιάζει πλεονεκτήματα έναντι των αντίστοιχων προσεγγίσεων της διεθνούς βιβλιογραφίας που βασίζονται στην Ανάλυση Ιδιομορφών (ανεξάρτητος προσδιορισμός αξονικών, καμπτικών, στρεπτικών μορφών διαστρέβλωσης/στρέβλωσης). Συνεπώς, διατυπώνεται θεωρία δοκού με το μικρότερο δυνατό αγνώστων παραμέτρων διαστρέβλωσης που αντιπροσωπεύουν εξίσου όλους τους μηχανισμούς αντίστασης.Στη συνέχεια οι ως άνω θεωρίες ενσωματώνονται στη μητρωική ανάλυση ραβδωτών φορέων. Παράγονται καινοτόμα τρισδιάστατα στοιχεία δοκού τυχούσας διατομής που περιλαμβάνουν διατμητικές παραμορφώσεις, γενικευμένη στρέβλωση (μητρώο στιβαρότητας 20×20) και διαστρέβλωση (μητρώο στιβαρότητας 32×32) μαζί με τα αντίστοιχα διανύσματα ισοδύναμης επικόμβιας φόρτισης. Τα εν λόγω στοιχεία δοκού ενσωματώνονται σε υπολογιστικό εργαλείο που βασίζεται στoν αλγόριθμο της Μεθόδου Άμεσης Στιβαρότητας (ΜΑΣ, Direct Stiffness Method – DSM) διαμορφώνοντας εξελιγμένο υπολογιστικό εργαλείο για την ανάλυση πλαισιωτών φορέων. Προκειμένου να αρθεί η αδυναμία μετασχηματισμού των επικόμβιων Βαθμών Ελευθερίας (ΒΕ) ανώτερης τάξης σε μέλη συνδεδεμένα υπό γωνία, αναπτύσσεται μεθοδολογία μετασχηματισμού που λαμβάνει υπόψη τις συνθήκες μετάδοσης διαστρέβλωσης/στρέβλωσης στους κόμβους του πλαισίου.Παρουσιάζεται επίσης γενική μεθοδολογία για τη γεωμετρικά μη γραμμική δυναμική ανάλυση δοκών σταθερής και μεταβλητής διατομής. Όσον αφορά στις πρισματικές δοκούς, εξετάζεται η πλέον γενική περίπτωση διατομής, ενώ όσον αφορά στην περίπτωση μεταβλητής διατομής, εξετάζεται η συνήθης περίπτωση της διπλά συμμετρικής διατομής με ομαλό νόμο μεταβολής. Η δοκός υπόκειται σε τυχούσα εξωτερική χρονικά μεταβαλλόμενη φόρτιση, συνοριακές και αρχικές συνθήκες και αναπτύσσει μετρίως μεγάλες μετατοπίσεις και στρεπτικές στροφές. Το μη γραμμικό φαινόμενο της αλλαγής μοχλοβραχίονα του εξωτερικού φορτίου, η επιρροή της περιστροφικής και στρεβλωτικής αδράνειας, των συντελεστών Wagner, καθώς και του φαινομένου βράχυνσης λόγω στρέψης λαμβάνονται υπόψη.Στην παρούσα διατριβή, τα προβλήματα συνοριακών και αρχικών τιμών επιλύονται αριθμητικά χρησιμοποιώντας τη Μέθοδο Συνοριακών Στοιχείων (ΜΣΣ, Boundary Element Method – BEM) και τη Μέθοδο Αναλογικής Εξίσωσης (ΜΑΕ, Analog Equation Method – AEM), η οποία αποτελεί εξέλιξη της BEM. Η AEM αντιμετωπίζει τις εγγενείς αδυναμίες της BEM και προσφέρεται για την επίλυση μεγάλου εύρους προβλημάτων μηχανικής που ορίζονται από χρονικά εξαρτώμενες ή/και μη γραμμικές διαφορικές εξισώσεις ή εξισώσεις με μεταβλητούς συντελεστές.Βάσει των διαδικασιών που αναπτύσσονται, μελετώνται αντιπροσωπευτικά αριθμητικά παραδείγματα. Η ακρίβεια και αξιοπιστία των προτεινόμενων μεθόδων επιβεβαιώνονται με υπάρχουσες αναλυτικές και αριθμητικές λύσεις, πειραματικά αποτελέσματα καθώς και με προσομοιώματα στερεών πεπερασμένων στοιχείων και πεπερασμένων στοιχείων κελύφους.

A consistent co-rotational formulation and numerical procedure for the dynamic analysis of planar Timoshenko beam is presented in detail to demonstrate the finite element analysis techniques of co-rotational formulation for nonlinear dynamic analysis of beam structures. The inertia nodal forces and deformation nodal forces are systematically derived by consistent linearization of the fully geometrically nonlinear beam theory by using the d’Alembert principle and the virtual work principle. The nodal coordinates, incremental displacements and rotations, velocities, accelerations and the equations of motion of the system are defined in terms of a fixed global coordinate system, while the total strains in the beam element are measured in element coordinates which are constructed at the current configuration of the beam element. A practical numerical procedure is proposed to determine the current end cross-section coordinates, element coordinates, and element deformations corresponding to an incremental displacement. An incremental-iterative method based on the Newmark direct integration method and the Newton-Raphson method is employed here for the solution of the 284nonlinear dynamic equilibrium equations. Numerical examples are presented to demonstrate the effectiveness of the proposed method and investigate the effect of the shear deformafion on the dynamic response of the beam structures.

A ferromagnetic heix magnetized axially or radially is apparently the simplest helical undulator. Four helices with alternating magnetization can provide a stronger helical field than the conventional planar Halbach arrays. Such undulators and micro undulators seem promising for various powerful HF sources. The method of direct integration of the fields of elementary magnets is used for analytical calculation of the fields of infinitely thin, longitudinally and radially uniformly magnetized helices of arbitrary length. Subsequent integration allows finding the field of a helix with finite transverse dimensions. The analytical magnitude of the field for an infinite helix is close to the numerically calculated one for a helix with a relatively small number of periods 5-10.

Elastic response spectra that take into account the effects of soil-structure interaction on soft soils are developed. The response spectra are calculated utilizing a 3DOF system including deformations of the superstructure and foundation. The equations of motion of the system are solved using direct integration under normalized earthquake records. Statistical processing of the results is implemented resulting in response spectra for “short and dense buildings with low interaction”, “short and dense buildings with high interaction”, “tall and light buildings with low interaction” and “tall and light buildings with high interaction”. The resulting response spectra are smoothed and discussed.

Fracture mechanics parameters are used for numerical and analytical risk assessment of residual life of a cracked oil drilling rig welded pipe. Number of cycles to the critical crack length, obtained by direct integration of Paris law, verified by using extended Finite Element Method, are related to the number of cycles needed for 10 years of exploitation, to assess probability and risk due to fatigue crack growth.

This paper presents the combination of two boundary element techniques whose principal aim is the transformation of domain integrals into boundary integrals: the radial integration method (RIM) and the direct integration boundary element method (DIBEM). RIM performs this transformation using a suitable change of variables. When used in problems with unknown variables, the RIM employs radial basis functions, following a similar procedure to the Dual Reciprocity Method, in which the primal variable is interpolated. DIBEM differentiates itself from other methods by interpolating the whole kernel of the domain integral, including not only the primal variable but also the fundamental solution. Here, the RIM is used to substitute the primitive auxiliary interpolation function employed exclusively to transform the domain integral into boundary integral in the DIBEM approach. Evaluation of the efficacy of the proposed composition is done solving the Helmholtz equation, including the direct frequency response and the eigenvalue problem. The expected advantages are confirmed by numerical tests performed: the computational cost is strongly reduced and an increase in accuracy is observed, particularly if coarser meshes are used.

After long-term service in deep ocean, pipelines are usually suffered from corrosions, which may greatly influence the Vortex-Induced Vibration (VIV) behavior of pipes. Thus, we investigate the VIV of defective pipelines. The geometric nonlinearity due to large deformation of pipes and nonlinearity in vortex-induced force are simulated. This nonlinear vibration system is simulated with finite element method and solved by direct integration method with incremental algorithm. Two kinds of defects, corrosion pits and volumetric flaws, and their effects of depth and range on VIV responses are investigated. A new finite element is developed to simulate corrosion pits. Defects are found to aggravate VIV displacement response only if environmental flow rate is less than resonance flow rate. As the defect depth grows, the stress responses increase, however, the increase of the defect range reduces the stress response at corroded part. The volumetric flaws affect VIV response stronger than the corrosion pits.

This paper evaluates nonlinear free vibrations of Levy plates using Weak-Form variational principle in algebraic polynomial displacement functions. The energy functional of the plate problem was formulated using Weak-Form variational technique on the integral function of the Von Karman thin plate differential equations. The displacement functions were developed based on static deflection configurations of orthogonal beam network. The process of repeated direct integration on compatibility equation was used to determine the algebraic expressions for stress function. The amplitude of deflection which directly influences the geometric nonlinearity of the plate was determined using integration process on energy functional based on static equilibrium equations. The modal combination method was used to develop the stiffness and mass matrices respectively from the expressions of energy functional based on dynamic equilibrium equations. The numerical values of amplitudes of deflection at various aspect ratios were computed. Also, the first four nonlinear natural frequencies at various aspect ratios were numerically computed. The validation of the present study’s results using the results from previous work found in literature shows satisfactory convergence, with an absolute mean error of 0.186 %. Conclusively, the application of Weak-Form variational principle in polynomial displacement functions provides satisfactory approximation to nonlinear dynamic analysis of Levy plates.

This paper describes a novel method to determine a road profile through the analysis of accelerations in a passing vehicle. A direct integration algorithm is proposed to determine the profile from the measured vehicle acceleration response. A sprung mass model and a half-car model are used to represent the vehicles in separate analyses. Combining the direct integration algorithm with the Cross Entropy (CE) optimisation method, a vehicle fleet monitoring concept is proposed for the monitoring of roads and/or bridges. In this approach, the profile can be calculated using accelerations from multiple vehicles without prior knowledge of the vehicle properties. Numerical results show that calculated profiles are the same as the ‘true’ profiles which were used to generate the ‘simulated measured’ accelerations. University College Dublin China Scholarship Council

This paper introduces an induction machine-based flywheel energy storage system (FESS) for direct integration with a variable-speed wind generator (VSWG). The aim is to connect the FESS at the DC bus level of a permanent magnet synchronous generator-based VSWG in order to stabilize the DC bus voltage as well as the power flowing into the grid. A rotor flux-oriented control strategy is proposed for the FESS converter based on the actual speed of the flywheel rotor. Since mechanical speed sensors are prone to failure and increase the maintenance cost of the system, a sensorless technique is proposed to estimate the rotor speed through a specially synthesized high-gain observer (HGO). The proposed observer achieves accurate tracking of the flywheel speed and flux and reduces the adverse effects of variations in the rated rotor resistance. Simulation results obtained using the MATLAB-Simulink environment are presented to illustrate the theoretical synthesis and analysis of the proposed FOC and sensorless HGO control strategies.

In the paper (Kolay and Ricles 2019) under discussion, the authors have presented the development of a new and improved one-parameter family of explicit direct integration algorithms for solving li...

Microfabrication, electrical characterisation, and mathematical modelling of a non-spiral planar microcoil useful for wireless power transfer applications in biomedical devices are presented in this work. The fabrication method using the existing very-large-scale integration manufacturing process requires a single mask level, and a single metal level without any via enables direct integration with a complementary metal oxide semiconductor sensing circuitry. An analytical model of magnetic field distribution in a non-spiral microcoil is developed for the first time in this work, which satisfies the form of a Bessel function of the first kind. An electrical model of the non-spiral planar microcoil is also developed and compared with experimental results. Experimental results are in good agreement with the theoretical model. Based on the experimental results, using optimised coil geometry, a wireless power transfer link suitable for biomedical wireless power transfer applications is studied. The maximum possible value of coupling factor of the wireless link is found to be 60% for a small separation between the coil and the magnet whereas the minimum value of coupling factor is found to be below 10% for large separations. It is found that introducing Neodymium magnetic shield layer at the receiving coil enhances the coupling factor significantly.

In practical engineering, fuzzy failure criteria can reflect the actual conditions of the normal use and durability of structures. Therefore, this topic has garnered considerable research attention. First, a fuzzy set and a membership function were proposed in this study. A fuzzy reliability mathematical model of structures was obtained by means of the fuzzy random event probability. Second, the distribution forms of common membership functions were introduced, and the optimal membership function was selected based on the Akaike information criterion. Third, considering the difficulty of calculating multiple integrals in the fuzzy reliability mathematical model, a direct integration method based on dual neural networks was introduced. This method provides a new approach for calculating structural reliability with the fuzzy failure criteria. Finally, the proposed method was verified by numerical examples. The results showed that this method could solve structural fuzzy reliability problems with multidimensional random variables with high computational efficiency and accuracy.

High-density, point-of-load (PoL) power conversion and power delivery are required to continue scaling electronic systems with increased functionality, more bandwidth, and smaller sizes. To meet the demands of these highly complex and miniaturized electronic systems, new 3-D integration schemes of advanced passive and active components are needed to enable the next-generation power distribution networks (PDNs). In addition, shorter interconnect lengths are required to provide low losses and better transient response in switch-based power conversion systems. Tantalum capacitors have the potential to provide some of the highest volumetric densities of any current capacitor technology, but are generally bulky components with low frequency stability, limiting their use in future 3-D power systems. In this paper, a process for the embedding and integration of ultrathin, high-density tantalum capacitors with improved frequency stability is demonstrated. The 5-V capacitors show a density of $1~\mu \text{F}$ /mm2 at 1 MHz with only a 100- $\mu \text{m}$ thickness, and are shown to be capable of direct integration on silicon for short interconnect length of $ . The electrical performance of the capacitors is tested after integration and shows that they retain high capacitance density and low equivalent series resistance (ESR), while also providing low leakage currents. The combination of low loss, high volumetric density, and 3-D integration capability make the capacitors an ideal candidate for next-generation power modules.

Photonic metasurfaces, that is, two-dimensional arrangements of designed plasmonic or dielectric resonant scatterers, have been established as a successful concept for controlling light fields at the nanoscale. While the majority of research so far has concentrated on passive metasurfaces, the direct integration of nanoscale emitters into the metasurface architecture offers unique opportunities ranging from fundamental investigations of complex light-matter interactions to the creation of flat sources of tailored light fields. While the integration of emitters in metasurfaces as well as many fundamental effects occurring in such structures were initially studied in the realm of nanoplasmonics, the field has recently gained significant momentum following the development of Mie-resonant dielectric metasurfaces. Because of their low absorption losses, additional possibilities for emitter integration, and compatibility with semiconductor-based light-emitting devices, all-dielectric systems are promising for highly efficient metasurface light sources. Furthermore, a flurry of new emission phenomena are expected based on their multipolar resonant response. This review reports on the state of the art of light-emitting metasurfaces, covering both plasmonic and all-dielectric systems.