Nonlinear Attachment Research Articles

Aggregating nanoparticle transport with nonlinear attachment: Modeling and experimental validation

A conceptual mathematical model was developed to simulate the transport of migrating nanoparticles in homogeneous, water saturated, 1-dimensional porous media. The model assumes that nanoparticles can collide with each other and aggregate. Nanoparticles can be found attached reversibly and/or irreversibly onto the solid matrix of the aquifer or suspended in aqueous phase. Attached particles may either contribute to the acceleration of subsequent particle deposition or hinder it, leading to the ripening or blocking process, respectively. The aggregation process was simulated based on the Smoluchowski Population Balance Equation (PBE) and was coupled with the advection-dispersion-attachment equation (ADA) to form a family of partial differential equations that govern the migration of nanoparticles in porous media. For the solution of the PBE, an efficient finite volume solver was employed that significantly accelerated computation times, by reducing the number of participating equations, while maintaining the required accuracy. The developed model was applied to nanoparticle transport experimental data available in literature. The model successfully matched the breakthrough concentration curves, and estimated the corresponding nanoparticle diameter, proving its ability to capture the physical processes participating in nanoparticle transport.

Advanced Mathematical Model for the Transport of Aggregating Nanoparticles in Water Saturated Porous Media: Nonlinear Attachment and Particle Size‐Dependent Dispersion

AbstractA conceptual mathematical model was developed to describe the migration of aggregating nanoparticles in water saturated, homogeneous porous media with one‐dimensional uniform flow. Nanoparticles can be found suspended in the aqueous phase or attached reversibly and/or irreversibly onto the solid matrix. The Smoluchowski population balance equation (PBE) was used to model the process of particle aggregation and was coupled with the advection‐dispersion‐attachment equation to form a nonlinear transport model. Furthermore, an efficient and accurate solver for the PBE, and an iterative solver for the linear or nonlinear attachment equations were employed. The new numerical model was applied to nanoparticle transport experimental data available in the literature. Although, conventional transport models can be used to describe nanoparticle migration at low ionic strength conditions, such models might not be applicable for high ionic strength conditions, where aggregation becomes a dominant process. Aggregation is significantly affecting the transport characteristics of nanoparticles. Under high ionic strength conditions, the mass retention in the solid matrix of the porous medium increases, and a nonlinear particle attachment behavior may be observed. The proposed model performed remarkably well, successfully capturing numerous physical processes associated with nanoparticle transport, including particle‐size‐dependent dispersion. Ignoring the aggregation process and using conventional colloidal transport models to model nanoparticle transport may lead to erroneous results.

A Framework for Rapidly Predicting the Dynamics of Flexible Solar Arrays in the China Space Station with a Verification Based on On-Orbit Measurement Data

The Chinese space station is a complex structure with large flexible appendages. Obtaining the on-orbit response characteristics of such a structure under different working conditions is a traditional and classic challenge in the field of dynamics. To address the on-orbit dynamics of the China Space Station, the basic equations for dynamic reduction, assembly and data recovery of linear and nonlinear substructures are derived based on the reduction and recovery theory, and a fast coupling analysis framework for flexible systems with nonlinear attachments is formed. This coupling analysis framework is adopted to quickly acquire the dynamic response of the China Space Station during in-orbit operation, thereby guiding the design. Taking SZ-15 radial docking to the Chinese Space Station as the object, the substructure of six nonlinear flexible arrays is reduced, the full flexible dynamic equation of the space station is assembled, and the response of each part of the flexible wing during the docking process is analyzed and recovered. By designing a reasonable and reliable flexible wing test scheme in-orbit, the acceleration at the root and top of the flexible wing during the docking of SZ-15 is obtained. The measured data in-orbit show that the acceleration analysis results of the typical parts of the flexible wing have a good agreement, which verifies the correctness of the fast coupling analysis framework of the flexible system. Hence, the dynamic coupling characteristics analysis of the main structure of the space station and the flexible wing based on this method can better guide the rationality of the design of the dynamic characteristics of the Chinese Space Station.

Intra-community link formation and modularity in ultracold growing hyperbolic networks

Hyperbolic network models offer a straightforward yet powerful method for understanding the small-world, scale-free, highly clustered, and modular characteristics typical of complex systems that are often called as real-world networks. These models involve randomly positioning nodes in a hyperbolic space and connecting them based on a probability that diminishes with distance. In this study, we examine the community structure within networks created by the Popularity Similarity Optimization model, a fundamental hyperbolic model, when the temperature parameter (responsible for tuning the clustering coefficient) is set to the limiting value of zero. We focus on link formation within communities and show their close relation with non-linear preferential attachment processes. Based on this, we derive analytical expressions that significantly improve previous estimates of the expected modularity for partitions formed by equally sized angular sectors in the 2d hyperbolic space. Our formulas can now predict average modularity, confirmed by numerical simulations, with high accuracy over a broader range of model parameters and community sizes relative to the whole network. These results advance our understanding of module formation in hyperbolic networks, highlighting the surprising emergence of communities despite the lack of explicit community formation steps in the model definition.

Physical Reservoir-Based Health Monitoring of a Structure with Nonlinear Attachments

The purpose of this work is to discuss the possibility of the concept of physical reservoir computing (PRC) in the field of structural health monitoring (SHM) by regarding the target structure of SHM as the physical reservoir. To this end, the dynamics of the structure, which is assumed extrinsically linear, is tailored to be strongly nonlinear by installing nonlinear attachments. Our purpose is then to detect the change occurred in this augmented physical reservoir. As one possible methodology to achieve this, we propose in this study to train the output layer to learn a specific nonlinear mapping of the input so that the increase of the error may indicate the change of the reservoir. Numerical experiments are presented to examine the validity of the proposed concept.

An investigation into the interaction between a nonlinear resonance and a fixed anti-resonance in a harmonically excited system

The study of linear mechanical structures with discrete nonlinear attachments is a widespread field in structural dynamics as it is important in many areas of engineering. A common type of nonlinearity is a hardening spring, which can be described by a cubic polynomial representing the force-deflection relationship. The frequency response of a system consisting of a hardening spring and a mass is characterized by an amplitude-dependent resonance frequency, that increases as the displacement of the mass increases. The way in which the resonance of a nonlinear attachment interacts with the resonance of a linear host structure has already been discussed in the literature, however little attention has been paid to the interaction of the nonlinear resonance with a fixed anti-resonance of the host structure. This paper aims to fill this gap by addressing the physical aspects of the interaction between an anti-resonance and a resonance due to a nonlinear resonant attachment. A two-degrees-of-freedom system representing a general structure with two modes of vibration is used as a host structure to which a nonlinear resonant device is attached. The host structure has a fixed anti-resonance prior to the nonlinear device being attached to the structure, and the influence of this device on the anti-resonance is investigated. This is achieved by using the harmonic balance method and a numerical continuation algorithm. In the study, it was found that the anti-resonance interacts with the nonlinear resonance, where some of the peaks bend toward higher frequencies because of the hardening stiffness. Further increasing the nonlinearity, results in an isola being formed inside the main frequency response curve. When the motion is extremely high, quasi-periodic or chaotic-like responses are observed in specific frequency regions.

Vibration control of a pre-twisted rotating beam with nonlinear bi-stable attachments

The influence of the nonlinear bi-stable attachment on the vibration suppression of a pre-twisted rotating cantilever beam is investigated in this study. The kinetic and potential energies of the system, comprising a pre-twisted rotating Euler–Bernoulli beam and the nonlinear bi-stable attachments, are obtained, and the equations of motion are derived using the Rayleigh–Ritz method. The natural frequencies and mode shapes of the beam (without the attachments) obtained using the present formulation are validated with the results obtained from Ansys. Subsequently, the flapwise vibration control of the pre-twisted rotating beam subjected to a base excitation is studied. A parametric study is performed for various amplitudes of base excitation, rotational speeds, and the number and position of the bi-stable attachments. Results show significant vibration suppression capabilities of the nonlinear attachments, and hence the proposed system could potentially be used for rotating beam-type structures such as wind turbine blades.

Measuring the variability of local characteristics in complex networks: Empirical and analytical analysis.

We examine the dynamics for the average degree of a node's neighbors in complex networks. It is a Markov stochastic process, and at each moment of time, this quantity takes on its values in accordance with some probability distribution. We are interested in some characteristics of this distribution: its expectation and its variance, as well as its coefficient of variation. First, we look at several real communities to understand how these values change over time in social networks. The empirical analysis of the behavior of these quantities for real networks shows that the coefficient of variation remains at high level as the network grows. This means that the standard deviation and the mean degree of the neighbors are comparable. Then, we examine the evolution of these three quantities over time for networks obtained as simulations of one of the well-known varieties of the Barabási-Albert model, the growth model with nonlinear preferential attachment (NPA) and a fixed number of attached links at each iteration. We analytically show that the coefficient of variation for the average degree of a node's neighbors tends to zero in such networks (albeit very slowly). Thus, we establish that the behavior of the average degree of neighbors in Barabási-Albert networks differs from its behavior in real networks. In this regard, we propose a model based on the NPA mechanism with the rule of random number of edges added at each iteration in which the dynamics of the average degree of neighbors is comparable to its dynamics in real networks.

The response of linear oscillators coupled to MDOF nonlinear attachment with combined seismic excitation

The response of linear oscillators coupled to MDOF nonlinear attachment with combined seismic excitation

Biomechanical analysis of Instrumented decompression and Interbody fusion procedures in Lumbar spine: a finite element analysis study.

Interbody fusions have become increasingly popular to achieve good fusion rates. Also, unilateral instrumentation is favored to minimize soft tissue injury with limited hardware. Limited finite element studies are available in the literature to validate these clinical implications. A three-dimensional, non-linear ligamentous attachment finite element model of L3-L4 was created and validated. The intact L3-L4 model was modified to simulate procedures like laminectomy with bilateral pedicle screw Instrumentation, transforaminal, and posterior lumbar interbody fusion (TLIF and PLIF, respectively) with unilateral and bilateral pedicle screw instrumentation. Compared to instrumented laminectomy, interbody procedures showed a considerable reduction in range of motion (RoM) in extension and torsion (6% and 12% difference, respectively). Both TLIF and PLIF showed comparable RoM in all movements with < 5% difference in reduction of RoM between them. Bilateral instrumentation showed a more significant decrease in RoM (> 5% difference) in the entire range of motion except in torsion when compared to unilateral instrumentation. The maximum difference in reduction in RoM was noted in lateral bending (24% and 26% for PLIF and TLIF, respectively), while the least difference in Left torsion (0.6% and 3.6% for PLIF and TLIF, respectively) in comparing bilateral with unilateral instrumentation. Interbody fusion procedures were found to be biomechanically more stable in extension and torsion than the instrumented laminectomy. Single-level TLIF and PLIF achieved a similar reduction in RoM with a < 5% difference. Bilateral screw fixation proved biomechanically superior to unilateral fixation in the entire range of motion except in torsion.

An Investigation into the Trend Stationarity of Local Characteristics in Media and Social Networks

We studied the evolution of complex social networks over time. The elements of the networks are users, and the connections correspond to the interactions between them. At a particular moment in time, each node of a complex network has such characteristics as its degree, as well as the total degree of its neighbors. Obviously, in the process of network growth, these characteristics are constantly changing due to the fact that new edges are attached to this node or its neighbors. In this paper, we study the dynamics of these characteristics over time for networks generated on the basis of a nonlinear preferential attachment mechanism, and we find both the asymptotics of their expected values and the characteristics of their spread around the mean. In addition, we analyze the behavior of these local characteristics for three real social networks. The applicability of the findings to actual problems in the study of social media in the digital humanities is discussed.

Nonlinear energy sink coupled with a nonlinear oscillator

This study investigates the energy flow characteristics of a nonlinear energy sink when coupled with a nonlinear oscillator. The primary system comprises of an oscillator with cubic stiffness and is coupled with an essentially nonlinear oscillator with cubic stiffness, which is suitably tuned such that the flow of energy is unidirectional towards the nonlinear attachment. The mechanisms and conditions for unidirectional energy transfer is investigated analytically to gain insights into achieving enhanced efficiency through proper tuning of the system parameters. Computational studies have been carried out to investigate resonance capture in the system in contrast with the modal response of the underlying Hamiltonian system.

A Light for a Light

AbstractHow does loss tear a hole in the world and produce a collective remaking of a new social order in which grief-work is not contained singularly but is a process done in feminist, queer, and Black and Brown ensemble? Interested in how we deliberately incorporate loss into collective grief-work, this article pulls from feminist and queer theorists of color who move across social and psychical constructions of sorrow. Highlighting contemporary art by minoritarian artists such as Eva Margarita Reyes and Pedro Lopez, who embrace loss, the author argues that grief-work is a communal labor we undergo together in acts of intimate meditation, suffering, spillage, and transformation. Happening in feminist and queer ensemble, grief-work is a deliberate decision to assemble in nonlinear feelings and attachments; it is an intention to work together to defend not only the dead but also the living, tending to immaterial energies that shift the fecund terrain of both life and death.

The Uses of Mourning

The Uses of Mourning

Nonlinear multiple scattering of flexural waves in elastic beams: Frequency conversion and non-reciprocal effects

Multiple scattering from a cluster of nonlinear point attachments on a beam is formulated and analyzed. The nonlinear equation of motion is solved using a perturbation strategy. The analytical solution is implemented for two common mass–spring–damper systems and for either nonlinear stiffness or nonlinear damping of power-law dependence. The nonlinearity generates harmonic waves at frequencies that are multiples of the incident-wave frequency, and also shifts the linear response of the fundamental frequency. In addition to asymmetric reflection, which is also achievable using linear scatterers with damping, the cluster of nonlinear scatterers can produce asymmetric transmission, thus breaking reciprocity of the system. Analytical results for a single scatterer are presented and validated using Finite Element Method simulations with perfect agreement. A two-scatterer nonlinear cluster acts as a filter that is tunable by the incident amplitude and a three-scatterer cluster that acts as a non-reciprocal frequency converter are considered, demonstrating the potential of the proposed framework for the design of nonlinear scatterer clusters with more complicated scattering properties.

Discrete breathers and discrete oscillating kink solution in the mass-in-mass chain in the state of acoustic vacuum

The present study is concerned with the dynamics of special localized solutions emerging in the mass-in-mass anharmonic oscillatory chain in the state of acoustic vacuum. Each outer element of the chain incorporates an additional, purely nonlinear mass attachment. Using the homogeneity of the system under consideration, we use the separation of time and space and reduce the analysis of standing wave solutions supported by the chain to the analysis of an algebraic system. An analytical study of the latter revealed the distinct types of static discrete breather solutions as well as the discrete oscillating kinks. Along with the analytical description of their spatial wave profiles, we also establish their zones of existence in the space of system parameters. The stability properties of these solutions are assessed through the linear stability analysis (Floquet). All analytical models are supported by the numerical simulations of the full model.

Identification of multiple local nonlinear attachments using a single measurement case

This research focuses on the construction of representative mathematical models for the dynamics of multiple local nonlinear attachments installed on the same primary structure. Specifically, the applicability of the recently developed characteristic nonlinear system identification (CNSI) to multiple attachments and attachments tuned to modes higher than the first linear mode of the primary structure is investigated. The CNSI procedure is a data-driven approach that produces a mathematical model for the dynamics of local nonlinear attachments directly from experimental measurements with the only knowledge of the mass of the attachment and the general frequency content required. The applicability of the CNSI method for multiple attachments is demonstrated using a two-story tower with one local nonlinear attachment installed on each floor in two configurations. In the first configuration, both attachments are tuned to interact with the first mode of the tower. In the second configuration, the linear stiffness of the attachment installed on the first floor is increased, such that it interacts with the second mode instead of the first. The resulting models are numerically integrated, and the resulting displacements are directly compared with the experimental measurements. This comparison provides validation of the success and strength of the CNSI method for identifying multiple nonlinear attachments using a single measurement case. The method is particularly suitable for transient response data, and it is unlikely that the method would work with harmonic and random excitation responses. The method also might not be ideal for systems having inflexible impacts or asymmetric restoring forces.

Dynamics and wave propagation in nonlinear piezoelectric metastructures

This paper reports dynamical effects in one-dimensional locally resonant piezoelectric metastructures leveraged by nonlinear electrical attachments featuring either combined quadratic and quartic, or essentially quartic potentials. The nonlinear electromechanical unit cell is built upon a linear host oscillator coupled to a nonlinear electrical circuit via piezoelectricity. Semi-analytical harmonic balance (HB)-based dispersion relations are derived to predict the location and edges of the nonlinear attenuation band. Numerical responses show that weakly and moderately nonlinear piezoelectric metastructures (NPMSs) promote a class of nonlinear attenuation band where a bandgap and a wave supratransmission band coexist, while also imparting nonlinear attenuation at the resonances around the underlying linear bandgap. Besides, strongly nonlinear regimes are shown to elicit broadband chaotic attenuation. Negative capacitance (NC)-based essentially cubic piezoelectric attachments are found to expand the aforementioned effects over a broader bandwidth. Excellent agreement is found between the predictions of the HB-based dispersion relations and the nonlinear transmissibility functions of undamped and weakly damped NPMSs at weakly and moderately nonlinear regimes, even in the presence of NC circuits. This research is expected to pave the way toward fully tunable smart periodic metastructures for vibration control via nonlinear piezoelectric attachments.

Damage detection in nonlinear vibrating structures using model updating

This paper presents two distinct model updating strategies for dynamical systems with local nonlinearities based on acceleration time history responses measured spatially across the vibrating structure. Both linear and nonlinear parameters are calibrated by minimizing the selected metric based on measured and predicted response using the newly proposed variant of differential search algorithm named as multi-cluster hybrid adaptive differential search (MCHADS) algorithm. The first model updating strategy involves the decoupling of linear and nonlinear characteristics of the system. In this scheme, we first establish the dynamic stiffness matrix using input and output measurements and then the underlying linear system is alone updated using it. Later, localization of the nonlinear attachment is attempted using the inverse property of the FRF of the nonlinear system and the established dynamic stiffness matrix of the underlying linear system from the previous step. Once the linear system is updated and with the already identified location(s) of nonlinear attachment(s), the nonlinear parameters are identified by formulating it as an optimization problem using the proposed MCHADS algorithm. The major advantage of the first approach is the reduction of the complex problem of nonlinear model updating to linear model updating. The second approach involves updating both linear and nonlinear parameters simultaneously using the proposed MCHADS algorithm. Investigations have been carried out by solving several numerically simulated examples and also with the experimental data of a benchmark problem to evaluate the effectiveness of the two proposed nonlinear model updating strategies. Further, investigations are also carried out to evaluate the capability of the model updating approaches towards damage identification in initially healthy nonlinear systems. Conclusions are drawn based on these investigations, highlighting the strengths and weaknesses of the two model updating approaches

An improved version of conditioned time and frequency domain reverse path methods for nonlinear parameter estimation of MDOF systems

The nonlinearities present in engineering structures are generally local in nature. Hence for system identification, it is required first to identify the spatial location and then the nonlinearities are characterized. Once the nonlinearity is characterized, the system identification involves identifying coefficient of nonlinear terms. In the present work, an improved version of traditional conditioned time and frequency domain reverse path method for nonlinear parameter estimation of multiple-degree-of-freedom structures is presented. Both numerical and experimental studies have been carried out to investigate the effectiveness of the proposed improved time and frequency domain parameter estimation techniques over the traditional ones. The comparisons between the time and frequency domain reverse path approaches are also carried out to highlight the strengths and weaknesses of each of these approaches. Numerical and experimental investigations reveal that both the time and frequency domain approaches proposed in this paper overcomes the major limitations of their traditional counterparts and are capable of estimating the nonlinear coefficients of multiple nonlinear attachments either grounded or attached between the masses.