Various Sources Of Nonlinearities Research Articles

Modelling nonlinear behavior of [formula omitted] frames using the Force Analogy Method

The nonlinear dynamic analysis of civil engineering structures is a topic of high significance for civil engineering community. In recent years, the linear dynamic analysis, in which no damage is taken into account, was improved to consider various sources of nonlinearity. Many commercial software packages were developed to consider both the material and geometrical nonlinearity. A new technique, entitled the Force Analogy Method, was introduced recently. In this technique, the material nonlinearity is addressed by considering a constant stiffness matrix throughout the entire dynamic analysis. Based on the principle of superposition, the displacement vector is decomposed into an elastic and inelastic component. The inelastic component of the displacement will cause perturbation forces once this term is moved to the right hand side of the equation of motion. However, although this intriguing technique has proved to be both accurate and numerical efficient over the years, no paper has addressed the 3D models case yet. In this paper, the authors develop the fundamental approach to generalize FAM for modeling the nonlinear response of three dimensional frame structures. The numerical results obtained are compared and validated using a well established commercial software.

Experimental realization of an active non-reciprocal metamaterial using an eigen-structure assignment control strategy.

This paper presents a class of active non-reciprocal metamaterials (ANMMs) in an attempt to control the flow of acoustic waves along a one-dimensional acoustic duct. The proposed method distinguishes itself from the available approaches where the non-reciprocities are generated either actively or passively by various sources of nonlinearities, circulators and gyroscopic/gyrator components, and/or spatiotemporal modulation. The proposed method relies in its operation on a controller that is designed by simultaneous allocation of both the eigenvalues and eigenvectors. In other words, the entire eigen-structure of the closed-loop system is assigned as deemed necessary. Conventionally, the placement of the eigenvalues has been employed to enhance both the damping and response of the system. However, in this study, the focus is placed on adjusting the eigenvectors in a way that enables the spatial control and redistribution of the wave propagation along the acoustic duct in order to produce any desirable non-reciprocal behavior. During this entire process, the system continues to behave in a linear fashion. The theory governing the operation of this proposed approach is introduced, and a comprehensive experimental validation effort is presented to demonstrate the basic features, non-reciprocal behavior, and control characteristics. Generalization of the presented strategies to two-dimensional acoustic systems is a natural extension of the present work.

Nonlinear dynamic response of open and breathing cracked functionally graded beam under single and multi-frequency excitation

The present work investigates a time domain nonlinear modeling and response analysis of cracked functionally graded Timoshenko beam. Response of the system influenced by various sources of nonlinearity is studied in detail. Properties of functionally graded material (FGM) are assumed to vary nonlinearly in thickness direction by an exponential gradation relation. Initially, an open crack model is considered and subsequently, methodology is extended for breathing cracks assuming periodic variation in the stiffness of beam on opening and closing of cracks. It is to be highlighted that hardly any work has been carried out to model and analyze breathing crack in continuous or discrete multi degree of freedom (MDOF) models for FGM beams. In addition, present methodology seems to be computationally easier and can effectively solve dynamic problems with coupled nonlinearity, one arises from time dependent stiffness (nonlinearity due to crack) and another due to geometric aspect (nonlinear strain-displacement), for isotropic as well as nonlinear material property variation of beam models, leading to wide ranges of applications. Nonlinear differential equations of motion are derived using Lagrange’s equation. These equations are solved using an implicit direct time integration method, known as Newmark-β method, in conjunction with an iterative technique. Accuracy of the solution is confirmed by comparing some of the results with that of available results. Subsequently, an exhaustive parametric study on effects of cracks, material properties, multi frequency excitation, influence of super harmonics on periodic as well as quasi periodic nonlinear dynamic response of thick and thin beams are performed.

Learning to Communicate and Energize: Modulation, Coding, and Multiple Access Designs for Wireless Information-Power Transmission

The explosion of the number of low-power devices in the next decades calls for a re-thinking of wireless network design, namely, unifying wireless transmission of information and power so as to make the best use of the RF spectrum, radiation, and infrastructure for the dual purpose of communicating and energizing. This article provides a novel learning-based approach towards such wireless network design. To that end, a parametric model of a practical energy harvester, accounting for various sources of nonlinearities, is proposed using a nonlinear regression algorithm applied over collected real data. Relying on the proposed model, the learning problem of modulation design for Simultaneous Wireless Information-Power Transmission (SWIPT) over a point-to-point link is studied. Joint optimization of the transmitter and the receiver is implemented using Neural Network (NN)-based autoencoders. The results reveal that by increasing the receiver power demand, the baseband transmit modulation constellation converges to an On-Off keying signalling. Utilizing the observations obtained via learning, an algorithmic SWIPT modulation design is proposed. It is observed via numerical results that the performance loss of the proposed modulations are negligible compared to the ones obtained from learning. Extension of the studied problem to learning modulation design for multi-user SWIPT scenarios and coded modulation design for point-to-point SWIPT are considered. The major conclusion of this work is to utilize learning-based results to design non learning-based algorithms, which perform as well. In particular, inspired by the results obtained via learning, an algorithmic approach for coded modulation design is proposed, which performs very close to its learning counterparts, and is significantly superior due to its high real-time adaptability to new system design parameters.

Dosage effects in morphogenetic gradients of transcription factors: insights from a simple mathematical model

The classical Hill equation is the simplest way to model sharp transcriptional responses (TR) to changing concentrations of a regulator. Such steep sigmoidal transitions of the TR are often involved in the creation of boundaries or domains during development. Here, I use the Hill function to explore the response of a promoter to a gradient of a transcription factor (TF). Specifically, I examine how various sources of nonlinearity (such as that imposed by the number of TF-binding sites) and the nonlinearity of the gradient itself influence TR and modulate its robustness to variations in the dosage of morphogen. This qualitative analysis underscores how nonlinearities can modulate the robustness of TR and is a convenient way to convey concepts in a teaching setting.

Modelling nonlinearity of guided ultrasonic waves in fatigued materials using a nonlinear local interaction simulation approach and a spring model

Modelling and numerical simulation – based on the framework of the Local Interaction Simulation Approach – was developed to have more insight into nonlinear attributes of guided ultrasonic waves propagating in fatigued metallic materials. Various sources of nonlinearity were considered in this modelling work, with particular emphases on higher-order harmonic generation and accumulation of nonlinearity along wave propagation. The material hyper-elasticity was considered in the model using an energy density approach based on the Landau–Lifshitz formulation; and the “breathing” motion pattern of a fatigue crack in the material was interrogated using a spring model. Upon the successful validation with the model prepared in the commercial software based on the Finite Element Methods, two scenarios were comparatively investigated, i.e. the lower and higher frequency regime. In the first case propagation of a basic symmetric mode pair was simulated using the model to observe a cumulative characteristic of the second harmonic mode with nonlinear hyper-elastic material definition upon appropriate selection of excitation frequency. In the second case, the higher-order symmetric mode pair was excited according to the “internal resonance” conditions, revealing a strong dependence of manifested nonlinearity on numerical parameters. Moreover, it was shown that with the use of the wave from the low frequency regime it was easier to differentiate later stages of the crack development, being in contrary to waves in the high frequency regime, which allowed to clearly observe early stages of the crack expansion. Such outcome lays the foundation to develop the damage detection and monitoring scheme in the field of Structural Health Monitoring based on utilising the nonlinear features of guided ultrasonic waves.

Nonlinearity, fuzziness and incommensurability in indicator-based assessments of vulnerability to climate change: A new mathematical framework

The earth’s climate system is highly nonlinear and the vulnerability of a community to a climate hazard is no exception. While this fact is widely accepted, indicator-based vulnerability assessments (IBVA) hardly ever take such nonlinearities into account. This is mainly due to the fact that the majority of assessment studies use methods based on Multiple Attribute Utility Theory (MAUT) (e.g. simple additive weight or multiplicative aggregation) to aggregate indicators. These methods convert all indicators into a global utility function and produce only a linear, threshold-free scaling of the effects of an indicator on vulnerability. In a previous paper, we showed that outranking procedures developed in decision-making science offer a more theoretically-sound approach to aggregation because they allow the analyst to incorporate the incommensurability, fuzziness and uncertainty associated with indicators. In this paper, we develop a new mathematical framework for vulnerability in order to clearly identify various sources of nonlinearity and incommensurability in vulnerability assessments. We then propose a new outranking formulation which can accommodate both and can be used to conduct assessments at different scales. We do so by introducing the concept of harm criterion as a mediator between an indicator and the vulnerability it represents. The new assessment approach can aggregate a mix of indicators with various degrees of subjectivity and non-linearity, without converting them into a single utility function and without requiring them to be mutually compensating.We illustrate the proposed approach by applying it to a simplified model of urban vulnerability to heat, focusing on the non-linear relationship between mortality and temperature above a ‘comfort temperature’, long evidenced in the epidemiological literature. We compare vulnerability rankings yielded by linear and non-linear characterizations of the relationship between temperature and mortality and find that the incorporation of non-linearity can have a significant impact on the rankings.

A computational compensation method for fabric panels of tensioned membrane structures using a shape optimization method based on gradientless algorithms

Tensioned fabric membrane structures, in which a coated fabric material is used as both cladding and supporting structure, are classified as unconventional structures and demand a dedicated design method. In this paper, we propose a method to combine different stages in design and analysis of these structures within the shape optimization framework. The proposed method facilitates the incorporation of various sources of nonlinearities in the analysis of tensioned membrane structures. Especially, the amount of fabric panels compensation when using simple material model for the coated fabric, i.e., linear orthotropic elasticity, as is widely used in practice, is presented. The novelty of the proposed method lies on the postulation of a stress-free 3-D intermediate configuration, which is built from flat fabric panels. The goal is to find an optimum shape of this 3-D intermediate configuration such that the stress distribution in the resulting structure, which is formed by deforming the 3-D intermediate configuration, remains at desired levels. A nonlinear finite element analysis is employed to identify these stress fields in the resulting structures. In this analysis, material and geometrical nonlinearities are taken into account. Moreover, the nonlinear kinematical interaction between the boundary cables and the membrane is also considered. Hence the stress fields on the resulting structures are expected to be reliable and close to the physical ones. In this work, different gradientless optimization algorithms, viz., genetic algorithm, pattern search, and Bayesian, are considered. The obtained results show that the stress levels in the resulting structures obtained from the proposed method are close to the desired ones, and the Bayesian optimization algorithm has the best performance among the considered algorithms.

Reliability Assessment Framework of the Long-Span Cable-Stayed Bridge and Traffic System Subjected to Cable Breakage Events

As important load bearing members of cable-stayed bridges, stay cables may experience corrosion, fatigue, and accidental or intentional actions that may lead to possible breakage failure. The current bridge design guidelines require that a cable-stayed bridge be designed against single-cable breakage. A holistic reliability assessment framework is developed for a long-span cable-stayed bridge and traffic system subjected to breakage of stay cables considering service load conditions from both traffic and wind. In addition to the bridge structural ultimate limit state, a new bridge serviceability limit state is also introduced by focusing on the overall traffic safety performance of all vehicles of the traffic flow on the bridge following cable breakage incidents. Random variables are defined by considering uncertainties related to structural material properties, sectional properties, traffic, wind condition, and cable breakage parameters. The Latin hypercube sampling technique is adopted to sample the random variables and establish the simulation models by considering various uncertainties of parameters. Nonlinear dynamic analysis is conducted in each experiment to simulate the breakage of stay cables, during which various sources of nonlinearities and dynamic coupling effects from traffic and wind are incorporated. Fragility analyses of the bridge subjected to cable breakage events in terms of the ultimate limit state and the serviceability limit state are finally conducted.

Nonlinear dynamics of MEMS/NEMS resonators: analytical solution by the homotopy analysis method

Due to various sources of nonlinearities, micro/nano-electro-mechanical-system (MEMS/NEMS) resonators present highly nonlinear behaviors including softening- or hardening-type frequency responses, bistability, chaos, etc. The general Duffing equation with quadratic and cubic nonlinearities serves as a characterizing model for a wide class of MEMS/NEMS resonators as well as lots of other engineering and physical systems. In this paper, after brief reviewing of various sources of nonlinearities in micro/nano-resonators and discussing how they contribute to the Duffing-type nonlinearities, we propose a Homotopy Analysis Method (HAM) approach for derivation of analytical solutions for the frequency response of the resonators. Toward this aim, we first apply the HAM to the proposed Duffing equation, and through this procedure, we derive the first-order and second-order HAM-based analytical solutions for the frequency response of the resonator. As the main novelty, we show that the second-order solution benefits from a tunable parameter, known as the convergence-control parameter, which is a distinguishing aspect of the HAM and plays a key role in enhancing the accuracy of the obtained analytical expressions in strongly nonlinear problems. We use the obtained analytical solutions for the study of nonlinear dynamics in two types of electrostatically actuated MEMS resonators proposing hardening, softening or mixed behaviors near their primary resonance frequency. Numerical simulations are performed to validate the analytical results.

Placement-Based Nonlinearity Reduction Technique for Differential Current-Steering DAC

This paper presents a switching scheme-based placement method to reduce the effect of various sources of nonlinearity arising due to layout routing parasitic in a current-steering digital-to-analog converter (DAC), thereby providing excellent static and dynamic performance. The proposed technique reduces both the individual and the cumulative effect of different nonidealities. Improvement in both the static and the dynamic performance is observed when compared with that provided by conventional common centroid placement. A 10-bit 500-MHz differential current-steering DAC has been designed and evaluated in 65-nm CMOS process as a case study, which provides a $\sim 72$ -dB spurious-free dynamic range at a 122-Ms/s input frequency.

On the force density method for slack cable nets

The design of cable nets and light tenso-structures requires a non conventional mechanical analysis, due either to the various sources of non linearity (large displacements, unilateral behaviour of the cables, non conservative loads) and to the fact that the initial configuration of the cable net is not known, depending on the prestress applied and, in general, on the dead load acting on it. As a consequence, the first problem that the engineer has to face is to determine the initial state of the structure under its own weight compatible with a set of fixed supports (the so called zero state). This problem is known as form finding.The paper examines the force density method for form finding, and it is presented a generalization that uses the exact expressions of the equilibrium derived from the equation of the catenary. The method allows to obtain an exact configuration that may be used as a starting point for subsequent incremental non linear analyses.In the paper it is shown that the use of the exact equilibrium conditions leads to a form finding method that is very similar to the FDM, but yields significant differences in the initial form when the weight of the cables is not negligible. A dimensionless parameter is introduced as degree of freedom of the form.

Overload Behavior of Composite Steel-Concrete Bridges

This study is concerned with the overload behavior of composite steel-concrete highway girder bridges. The post-elastic behavior is investigated, and the effect of some design parameters on bridge response is studied. This paper describes a nonlinear finite element analysis procedure permitting the determination of the state of stress and deformation under given levels of overload. The nonlinear behavior of the structure due to the various sources of nonlinearity: crack propagation, concrete yielding and crushing, and yielding of the reinforcing steel and girder steel is reproduced through the use of appropriate constitutive laws. A shear retention factor is introduced to account for aggregate interlock and dowel action. An analysis of the effects of discretization and of some material properties on bridge response in the post-cracking range is included, and numerical examples are presented to confirm the validity of the developed numerical solution procedure.