Soft Boundary Conditions Research Articles

Ultralow-frequency absorption mechanism of a hybrid membrane resonator with acoustic soft boundary condition

Hybrid membrane resonator (HMR) as a typical metamaterial-based absorber with acoustic hard boundary condition (AHBC) has demonstrated excellent noise absorption abilities, but the challenge lies in achieving broadband absorption of ultralow-frequency noise in the tens of Hz to 150 Hz regime. In this research, we investigate systematically the absorption characteristics, absorption mechanisms, and casual optimality of an HMR with three openings in lower surface of the cavity, which functioned as an acoustic soft boundary condition (ASBC). Compared to the well-studied HMR with AHBC, a new absorption mechanism, which states that most energy dissipates occur in the opening region rather than in the membrane, has been found first. As a result, the HMR with ASBC can demonstrate outstanding ultralow-frequency sound absorption performance with a very small thickness, and the full width at half maximum of the HMR can be enlarged over 7 times. Furthermore, the causal inequalities of the absorbers with ideal AHBC and ASBC are derived based on the Cauchy integral and causality principle. The causal optimality of the proposed absorber is also achieved. This research provides valuable guidelines for the design of excellent ultralow-frequency sound absorbers which could contribute to solving the major issue of noise reduction.

Investigation on acoustical performances of micro-perforated panel with soft boundary backing cavity

Low-frequency noise control is still an issue due to its characteristic of having a long wavelength. Therefore, attenuation requires a bulky noise control component, including an acoustic absorber. Conventional absorber materials, such as micro-perforated panels (MPP), are a candidate to circumvent such a problem. However, the requirement of backing cavity depth causes the MPP to work under a quarter wavelength constraint. Eventually, the bulky characteristic of the absorber is persistent. Therefore, this study introduces a soft boundary condition to the MPP to enable the system to work at a lower frequency while the associated dimensions reduce. Open gaps between the backing cavity and rigid surface realize the soft boundary conditions and double-layer MPP is considered to test such a system. The experimental result shows that the soft boundary can enhance at low frequencies (<250 Hz) by 0.3-0.6 points. At the same time, the open gap can slightly increase the resulting absorption performance deficiency at mid-frequency.

A High-Power Density DC Converter for Medium-Voltage DC Distribution Networks

A DC converter is the core equipment of voltage conversion and power distribution in a DC distribution network. Its operating characteristics have a profound impact on the flexible regulation of distributed resources in an active distribution network. It is challenging for the existing single-stage conversion topology to meet the requirements of distributed renewable energy connected to a multi-voltage level, medium-voltage grid. It is necessary to study the multistage transform power unit topology further, which can satisfy high reliability, high efficiency, and wide input range. This paper proposes a high-power density DC converter for medium-voltage DC networks with wide voltage levels. It adopts Buck-LLC integrated modular composition. The input ends of the high isolation resonant power unit are connected in series to provide high voltage endurance, and the output ends are connected in parallel to meet the high-power demand and achieve high-power transmission efficiency. The proposed series dual Buck-LLC resonant power unit topology can adjust the duty cycle of series dual buck circuits to meet the needs of different levels of medium-voltage DC power grids. The soft switching problem within the wide input range of all switching tubes is solved by introducing auxiliary inductors, thereby improving energy transmission efficiency. The auxiliary circuit and control parameters are optimized based on the research of each switching tube’s soft switching boundary conditions. Finally, an experimental prototype of a 6.25~7 kW power unit is designed and developed to prove the proposed topology’s feasibility and effectiveness. Great breakthroughs have been made both in theoretical research and engineering prototype development.

Physics-informed neural networks for mesh deformation with exact boundary enforcement

In this work, we have applied physics-informed neural networks (PINN) for solving mesh deformation problems. We used the collocation PINN method to capture the new positions of the vertex nodes while preserving the connectivity information. We use linear elasticity equations for mesh deformation. To prevent vertex collisions or edge overlap, the mesh movement in this work is conducted in steps with relatively small movements. For moving boundary problems, the exact position of the boundary is essential for having an accurate solution. However, PINNs are frequently unable to satisfy Dirichlet boundary conditions exactly. To overcome this issue, we have used hard boundary condition enforcement to automatically satisfy Dirichlet boundary conditions. Specifically, we first trained a PINN with soft boundary conditions to obtain a particular solution. Then, this solution was tuned with exact boundary positions and a proper distance function by using a new PINN considering only the equation residual. To assess the accuracy of our approach, we used the classical translation and rotation tests and compared them with a proper mesh quality metric considering the change in the element area and shape. The results show the accuracy of this approach is comparable with that of finite element solutions. We also solved different moving boundary problems, resembling commonly used fluid–structure interaction problems. This work provides insight into using PINN for mesh-deformation problems without needing a discretization scheme with reasonable accuracy.

Stiffness of Confinement Controls the Localization of an Object under Crowding: Macroscale Real-World and Microscale Numerical Modelings on the Specificity of Intracellular Positioning

Macroscopic systems that mimic microscopic systems can provide fundamental understanding of how macromolecules (e.g., cellular organelles) are organized in a confined space. We studied the behavior of a large particle interacting with several small particles confined in dishes with hard/soft boundary conditions under mechanical vibration using a cm-scale model. We also performed a numerical simulation for the micro-scale system under Brownian fluctuation with fluctuation–dissipation, as a simple model of living cellular cytoplastic crowding. Under a hard boundary condition, the large sphere preferred the boundary at low crowding but tended to localize to the interior under high crowding. Conversely, when the boundary was soft, the large sphere localized to the interior under low crowding and tended to migrate near the boundary when crowding increased. Interestingly, numerical modeling reproduced similar results for both the experimental hard and soft boundary conditions. Our models revealed that membrane stiffness can affect the organization of biopolymers within a confined space and may help explain cellular dynamics.

Diffraction of a Whispering Gallery Mode at a Jumply Straightening of the Boundary

Diffraction of a high-frequency small-number whispering gallery mode running along a concave boundary, which turns into a flat one so that its curvature experiences a jump, is studied. The cases of rigid (Neumann) and soft (Dirichlet) boundary conditions are considered. Within the framework of the parabolic equation method, a mathematically correct scattering problem is obtained which is solved explicitly and investigated asymptotically in detail. Analytic expressions are found for all emerging wavefields. In particular, an edge wave diverging from the point of non-smoothness of the boundary is described. For the rigid condition, its amplitude is proportional to the magnitude of curvature jump, but not for the soft condition.

Low frequency attenuation of acoustic waves in a perforated pipe.

This paper presents new experimental and numerical evidence that perforations in a pipe wall result in a low-frequency bandgap within which sound waves rapidly attenuate. These perforations are modelled as an acoustically soft boundary condition on the pipe wall and show that a low frequency bandgap is created from 0 Hz. The upper bound of this bandgap is determined by the dimensions and separation of the perforations. An analytical model based on the transfer matrix method is proposed. This model is validated against numerical predictions for the pipe with varying perforation geometries. A numerical study is undertaken to model the effect of perforations with ideal acoustically soft boundary conditions and surrounded with an air gap. Close agreement is found between the numerical and analytical models. Experimental evidence shows that the width of the bandgap is accurately predicted with the numerical and analytical models.

Three-dimensional effects of cascade perforations on rotor–stator interaction noise

One novel trend in reducing aero-engine noise is to utilize the silent flight mechanism of owls by applying perforations on fan stator vanes. Consequently, the establishment of relevant theoretical models is of particular interest. The current efforts made in this regard are just targeting the features based on two-dimensional models without including the three-dimensionality. In this paper, we present a three-dimensional solution for acoustic scattering by annular perforated cascades, and the dipole source corresponding to the unsteady pressure loading on the vanes is identified as the dominant sound source. By the singularity method, the acoustic response is obtained with the soft boundary condition applied on the vane surfaces. It is found that considerable noise reduction can be achieved for rotor–stator interaction with a modest uniform porosity, and accordingly two mechanisms are proposed to understand the effect of porosity on propagating sound. The first is that the perforations allowing a normal velocity across the vane reduce the unsteady loading induced by the incident disturbances. The second is that the three-dimensional interactions among the dipole sources at different positions are also dampened by the soft boundaries, thus the distribution of the unsteady pressure loading on the vanes will also change significantly compared to hard-vane cases. Non-uniform distributions of porosity are investigated further, indicating that perforations in the vane upstream area are more effective in reducing propagating noise. Our method is fully three-dimensional and capable of investigating non-uniform porosity, and thus is able to provide useful guidance for future soft vane designs.

Acoustic energy flux analysis of the bifurcated waveguide by varying outlet boundaries

This communication is devoted to the analysis of the energy flux of a two-dimensional waveguide with planar and non-planar surfaces. The main goal is to analyze the effects of reflected and transmitted energy fluxes of the bifurcated waveguide by varying the different types of outlet boundaries. The upper and lower boundaries of the inlet are taken as flexural in nature, whilst the outlet of the duct is varied by soft, rigid and impedance boundary conditions. The benchmark Mode-Matching (MM) technique is applied to solve the underlying boundary value problem (BVP). The system is excited with two types of incident forcing: fluid-borne incident and structure-borne incident. For a flexible inlet bounded by a membrane, the obtained eigenfunctions are linearly dependent and non-orthogonal in character. For sake of this, generalized orthogonality relations (OR) are developed. Additionally, the application of generalized OR led to the appearance of some dependent sums that are tackled using the fixed membrane edge conditions. The application of edge conditions led to the unique solution of the BVP. In the end, the expressions of reflected and transmitted energy fluxes are obtained and analyzed graphically against frequencies for different structural properties of the waveguide. Furthermore, it is shown that the conserved energy flux is valid, and reconstructed matching conditions are found in good accord.

Evaluation of assumptions in foot and ankle biomechanical models

BackgroundA variety of biomechanical models have been used in studies of foot and ankle disorders. Assumptions about the element types, material properties, and loading and boundary conditions are inherent in every model. It was hypothesized that the choice of these modeling assumptions could have a significant impact on the findings of the model. MethodsWe investigated the assumptions made in a number of biomechanical models of the foot and ankle and evaluated their effects on the results of the studies. Specifically, we focused on: (1) element choice for simulation of ligaments and tendons, (2) material properties of ligaments, cortical and trabecular bones, and encapsulating soft tissue, (3) loading and boundary conditions of the tibia, fibula, tendons, and ground support. FindingsOur principal findings are: (1) the use of isotropic solid elements to model ligaments and tendons is not appropriate because it allows them to transmit unrealistic bending and twisting moments and compressive forces; (2) ignoring the difference in elastic modulus between cortical and trabecular bones creates non-physiological stress distribution in the bones; (3) over-constraining tibial motion prevents anticipated deformity within the foot when simulating foot deformities, such as progressive collapsing foot deformity; (4) neglecting the Achilles tendon force affects almost all kinetic and kinematic parameters through the foot; (5) the axial force applied to the tibia and fibula is not equal to the ground reaction force due to the presence of tendon forces. InterpretationThe predicted outcomes of a foot model are highly sensitive to the model assumptions.

A High-Gain Multilevel dc–dc Converter for Interfacing Electric Vehicle Battery and Inverter

An isolated multilevel bidirectional dc–dc converter is presented in this article to interface the low-voltage (LV) battery and the high-voltage (HV) propulsion inverter in electric vehicles. The proposed topology achieves a HV step-up ratio in the motoring mode by reconfiguring two split capacitor half-bridge circuits in series/parallel through the symmetrical modulation of a voltage bidirectional, two quadrant switch. This reconfiguration generates a high-frequency multilevel voltage output at the dc-bus side of the inverter, which reduces the output filter volume. The dc-bus voltage is regulated by the duty cycle modulation of the intermediary switch in the motoring mode, simplifying the sensing and control. During regenerative braking, the converter is operated with phase shift modulation between the HV half bridges and the LV full bridge to regulate the battery voltage. The presented modulation strategies achieve zero voltage switching for the full-bridge devices over a wide load range. A comprehensive analysis of the proposed multilevel converter in motoring and braking modes along with the design constraints and soft switching boundary conditions is presented in this article. Detailed experimental results on a 1.5-kW laboratory prototype are presented to verify the design approach and illustrate the converter performance.

Generalization and stabilization of exact scattering solutions for spherical symmetric scatterers

In a previous work the authors described a fast high-fidelity computer model for acoustic scattering from multi-layered elastic spheres. This work is now extended with a scaling strategy significantly mitigating the problem of overflow and thus expanding the useful frequency range of the model. Moreover, new boundary conditions and loads are implemented. Most important are the fluid–fluid and solid–solid couplings, which allow a completely general layering of the scattering object. Sound hard and sound soft boundary conditions are implemented for solids and fluids respectively. In addition to the existing acoustic excitation, mechanical excitation in the form of point-excitation and surface excitation are implemented. Attenuation in the form of hysteresis damping as well as viscous fluid layers are also included. Several numerical examples are included, with the purpose of validating the code against existing reference solutions. The examples include air bubbles, a coated steel shell and a point-exited steel shell.

Stochastic local FEM for computational homogenization of heterogeneous materials exhibiting large plastic deformations

Computational homogenization is a powerful tool allowing to obtain homogenized properties of materials on the macroscale from simulations of the underlying microstructure. The response of the microstructure is, however, strongly affected by variations in the microstructure geometry. In particular, we consider heterogeneous materials with randomly distributed non-overlapping inclusions, which radii are also random. In this work we extend the earlier proposed non-deterministic computational homogenization framework to plastic materials, thereby increasing the model versatility and overall realism. We apply novel soft periodic boundary conditions and estimate their effect in case of non-periodic material microstructures. We study macroscopic plasticity signatures like the macroscopic von-Mises stress and make useful conclusions for further constitutive modeling. Simulations demonstrate the effect of the novel boundary conditions, which significantly differ from the standard periodic boundary conditions, and the large influence of parameter variations and hence the importance of the stochastic modeling.

Finite elements for Mindlin and Kirchhoff plates based on a mixed variational principle

AbstractQuadrilateral finite elements with five displacements per corner node built up from four triangular elements are developed by a discretization of the Mindlin plate bending theory and based on a modified form of the mixed variational principle for stresses and displacements. The modified principle separates the contribution of shear deformation by taking the transverse shear strains as free functions. It also gives discrete element governing equations in a canonical form. Similar elements are developed based on the potential energy formulation. The elements can be readily specialized to the Kirchhoff plate theory. The discrete shear strains are transformed back to normal‐fiber rotations for enforcing general boundary conditions. The discretization procedure uses one‐dimensional polynomials instead of two‐dimensional shape functions. The discretization satisfies continuity for w, and continuity for the transverse shear strains. The Mindlin elements are tested with soft and hard boundary conditions. They are naturally free of shear‐locking. They are also capable of reproducing the boundary layer that occurs with some soft boundary conditions. Mindlin elements results tend to those of the Kirchhoff theory as the thickness decreases. Extensive numerical results are obtained for square plates some of which are compared with exact results or results obtained by other methods.

Method to Derive the Hamiltonian of Acoustic Topological Crystalline Insulators

Acoustic systems that are without limitations imposed by the Fermi level have been demonstrated as significant platform for the exploration of fruitful topological phases. By surrounding the nontrivial domain with trivial "environment", the domain-wall topological states have been theoretically and experimentally demonstrated. In this work, based on the topological crystalline insulator with a kagome lattice, we rigorously derive the corresponding Hamiltonian from the traditional acoustics perspective, and exactly reveal the correspondences of the hopping and onsite terms within acoustic systems. Crucially, these results directly indicate that instead of applying the trivial domain, the soft boundary condition precisely corresponds to the theoretical models which always require generalized chiral symmetry. These results provide a general platform to construct desired acoustic topological devices hosting desired topological phenomena for versatile applications.

Variable-Frequency Critical Soft-Switching of Wide-Bandgap Devices for Efficient High-Frequency Nonisolated DC-DC Converters

This paper derives a variable-frequency critical soft-switching control method for nonisolated DC/DC converters using wide-bandgap devices. The critical soft switching control technique under maximum frequency trajectory is introduced to maintain zero voltage switching over a wide range of modulation ratios according to the load variation. The concept prevents turn-on losses that are typically much larger than the turn-off losses in SiC and GaN FETs and the latter can be further reduced by adding external drain-source capacitors. We have derived the boundary conditions for critical soft switching operation. For the reduction of inductor value and volume, a maximum available switching frequency is applied to the converter within the constraints of device requirement and soft switching boundary conditions. We demonstrate experimentally that the proposed concept reduces the power losses in the wide-bandgap devices by a factor of approximately 3, enables an increase of the switching frequency by a factor of about 5, and a decrease of the main inductance by a factor of about 10. Then variable frequency critical soft switching control method is proposed with the constraints to maintain the maximum frequency within soft switching operation. Since our test bench uses off-the-shelf inductors, the inductors are subject to significant high frequency losses. Despite this, the converter efficiency increases by 1%.

Regulating surface wrinkles using light.

Regulating existing micro and nano wrinkle structures into desired configurations is urgently necessary yet remains challenging, especially modulating wrinkle direction and location on demand. In this work, we propose a novel light-controlled strategy for surface wrinkles, which can dynamically and precisely regulate all basic characteristics of wrinkles, including wavelength, amplitude, direction and location (λ, A, θ and Lc), and arbitrarily tune wrinkle topographies in two dimensions (2D). By considering the bidirectional Poisson's effect and soft boundary conditions, a modified theoretical model depicting the relation between stress distributions and the basic characteristics was developed to reveal the mechanical mechanism of the regulation strategy. Furthermore, the resulting 2D ordered wrinkles can be used as a dynamic optical grating and a smart template to reversibly regulate the morphology of various functional materials. This study will pave the way for wrinkle regulation and guide fabrication technology for functional wrinkled surfaces.

Forming-Less Compliance-Free Multistate Memristors as Synaptic Connections for Brain-Inspired Computing

Hardware realization of artificial neural networks (ANNs) requires analogue weights to be encoded into the device conductances via blind update and access operations, leveraging Kirchhoff’s circuit laws. However, most memristive solutions lag behind in this aspect due to numerous device nonidealities, like limited number of addressable states, need for a stringent compliance current control, and an electroforming process. By modulating the oxygen vacancy profile of tin oxide switching elements, here we design and evaluate multistate memristors as synaptic connections for brain-inspired computing. Harnessing the advantages of a forming-less compliance-free operation, our devices display gradual switching transitions across multiple conductance states, sufficing the switching requirements of synaptic connections in an ANN. The soft boundary conditions are analyzed systematically, and spike-based plasticity rules, state-dependent spike-timing-dependent-plasticity (STDP) modulations, ternary digital logic, and analogue updatability schemes are proposed and demonstrated comprehensively to establish the analogue programming window of our memristors.

Simulation Analysis of Electromagnetic Surface Wave Suppression by Soft Surfaces, Including Effects of Resistive and Active Elements

The soft surface is defined by its anisotropic surface impedance, and it has the property of suppressing surface wave propagation for any polarization of the electric field. It can be used as a general design element for reducing scattering or controlling coupling between nearby antennas. In this letter, the suppression capabilities and bandwidth limitations of soft surfaces are analyzed using simulations to draw the following conclusions: First, a soft surface is as good as an ideal perfect magnetic conductor for suppressing vertically polarized surface currents; second, adding loss to the soft surface actually increases coupling between nearby antennas; third, the bandwidth of soft surfaces can be extended using active loading; and fourth, a soft surface boundary condition can suppress coupling below even the expected free-space wave coupling. Several simple examples are illustrated using simulations, including the effect of lossy substrates, designs for active loading, and the effects of soft surfaces on the contributions to coupling between nearby planar antennas.

Symmetry, validation, and scattering matrices for time–domain scattering in waveguides

• Channel waveguide problem with scattering regions are presented. • Exploiting symmetry, Mode-matching solutions are converted to scattering and transfer matrices. • Series of identities are presented for scattering matrix. • Time-domain scattering by incident Gaussian wave packets are computed. We outline a method to compute the solution in the frequency–domain for scattering in a waveguide by exploiting symmetry. The method is illustrated by considering a simple scattering example, where soft hard boundary conditions are alternated. We show how the straightforward mode matching or eigenfunction matching solution can be easily converted to scattering and transmission matrices when symmetry is exploited. We then show how the solution for two scatterers can be found explicitly, using symmetry which allows validation of our subsequent solution by scattering matrices. We also give a series of identities which the scattering matrix must satisfy for further numerical validation. Using these frequency–domain solutions we compute the time-domain scattering by incident Gaussian wave–packets.