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Charge pump phase locked loops (CPPLLs) are nonlinear systems as a result of the nonlinear behavior of voltage-controlled oscillators (VCO). This paper aims to specify jitter generation of voltage controlled oscillator phase noise in CPPLLs, by considering approximated practical model for VCO.

CPPLL, in practice, shows nonlinear behavior, and usually in LC-VCOs, it follows second-degree polynomial function behavior. Therefore, the nonlinear differential equation of the system is obtained which shows the CPPLLs are a nonlinear system with memory, and that Volterra series expansion is useful for such systems.

In this paper, by considering approximated practical model for VCO, jitter generation of voltage controlled oscillator phase noise in CPPLLs is specified. Behavioral simulation is used to validate the analytical results. The results show a suitable agreement between analytical equations and simulation results.

The proposed method in this paper has two advantages over the conventional design and analysis methods. First, in contrast to an ideal CPPLL, in which the characteristic of the VCO’s output frequency based on the control voltage is linear, in the present paper, a nonlinear behavior was considered for this characteristic in accordance with the real situations. Besides, regarding the simulations in this paper, a behavior similar to the second-degree polynomial was considered, which caused the dependence of the produced jitter’s characteristic corner frequency on the jitter’s amplitude. Second, some new nonlinear differential equations were proposed for the system, which ensured the calculation of the produced jitter of the VCO phase noise in CPPLLs. The presented method is general enough to be used for designing the CPPLL.

The purpose of this paper is to propose the generalized integral transform technique (GITT) to the solution of convection-diffusion problems with nonlinear boundary conditions by employing the corresponding nonlinear eigenvalue problem in the construction of the expansion basis.

The original nonlinear boundary condition coefficients in the problem formulation are all incorporated into the adopted eigenvalue problem, which may be itself integral transformed through a representative linear auxiliary problem, yielding a nonlinear algebraic eigenvalue problem for the associated eigenvalues and eigenvectors, to be solved along with the transformed ordinary differential system. The nonlinear eigenvalues computation may also be accomplished by rewriting the corresponding transcendental equation as an ordinary differential system for the eigenvalues, which is then simultaneously solved with the transformed potentials.

An application on one-dimensional transient diffusion with nonlinear boundary condition coefficients is selected for illustrating some important computational aspects and the convergence behavior of the proposed eigenfunction expansions. For comparison purposes, an alternative solution with a linear eigenvalue problem basis is also presented and implemented.

This novel approach can be further extended to various classes of nonlinear convection-diffusion problems, either already solved by the GITT with a linear coefficients basis, or new challenging applications with more involved nonlinearities.

This paper aims to present an approach for calibrating the numerical models of dynamical systems that have spatially localized nonlinear components. The approach implements the extended constitutive relation error (ECRE) method using multi-harmonic coefficients and is conceived to separate the errors in the representation of the global, linear and local, nonlinear components of the dynamical system through a two-step process.

The first step focuses on the system’s predominantly linear dynamic response under a low magnitude periodic excitation. In this step, the discrepancy between measured and predicted multi-harmonic coefficients is calculated in terms of residual energy. This residual energy is in turn used to spatially locate errors in the model, through which one can identify the erroneous model inputs which govern the linear behavior that need to be calibrated. The second step involves measuring the system’s nonlinear dynamic response under a high magnitude periodic excitation. In this step, the response measurements under both low and high magnitude excitation are used to iteratively calibrate the identified linear and nonlinear input parameters.

When model error is present in both linear and nonlinear components, the proposed iterative combined multi-harmonic balance method (MHB)-ECRE calibration approach has shown superiority to the conventional MHB-ECRE method, while providing more reliable calibration results of the nonlinear parameter with less dependency on a priori knowledge of the associated linear system.

This two-step process is advantageous as it reduces the confounding effects of the uncertain model parameters associated with the linear and locally nonlinear components of the system.

The purpose of this study is to present a finite element (FE) implementation of phenomenological three-dimensional viscoelastic and viscoplastic constitutive models for long term behaviour prediction of polymers.

The method is based on the small strain assumption but is extended to large deformation for materials in which the stress-strain relation is nonlinear and the concept of incompressibility is governing. An empirical approach is used for determining material parameters in the constitutive equations, based on measured material properties. The modelling process uses a spring and dash-pot and a power-law approximation function method for viscoelastic and viscoplastic nonlinear behaviour, respectively. The model improvement for long term behaviour prediction is done by modifying the material parameters in such a way that they account for the current test time. The determination of material properties is based on the non-separable type of relations for nonlinear materials in which the material properties change with stress coupled with time.

The proposed viscoelastic and viscoplastic models are implemented in a user material algorithm of the FE general-purpose program ABAQUS and the validity of the models is assessed by comparisons with experimental observations from tests on high-density polyethylene samples in one-dimensional tensile loading. Comparisons show that the proposed constitutive model can satisfactorily represent the time-dependent mechanical behaviour of polymers even for long term predictions.

The study provides a new approach in long term investigation of material behaviour using FE analysis.

In this paper, the important aspects of vibration analysis of carbon nanotubes (CNTs) as nano-resonators are studied. This study has covered the important nonlinear phenomena such as jump super-harmonic and chaotic behavior. CNT is modeled by using the modified nonlocal theory (MNT).

In previous research studies, the effects of CNT’s rotary inertia, stiffness and shear modulus of the medium were neglected. So by considering these terms in MNT, a comprehensive model of vibrational behavior of carbon nanotube as a nanosensor is presented. The nanotube is modeled as a nonlocal nonlinear beam. The first eigenmode of an undamped simply supported beam is used to extract the nonlinear equation of CNT. Harmonic balance method is used to solve the equation, while to study its super-harmonic behavior, higher-order harmonic terms were used.

In light of frequency response equation, jump phenomenon and chaotic behavior of the nanotube with respect to the amplitude of excitation are investigated. Also in each section of the study, the effects of elastic medium and nonlocal parameters on the vibration behavior of nanotube are investigated. Furthermore, parts of the results in linear and nonlinear cases were compared with results of other references.

The present modification of the nonlocal theory is so important and useful for accurate investigation of the vibrational behavior of nano structures such as a nano-resonator.

Stiffened plates have been widely used in civil, marine, aerospace engineering. As a kind of thin-walled structure operating in complex environment, stiffened plates mostly undergo a variety of dynamic loads, which may sometimes result in large-amplitude vibration. Additionally, initial stresses and geometric imperfections are widespread in this type of structure. Furthermore, it is universally known that initial stresses and geometric imperfections may affect mechanical behavior of structures severely, particularly in dynamic analysis. Thus, the purpose of this paper is to study the stress variation rule of a stiffened plate during large-amplitude vibration considering initial stresses and geometric imperfections.

The initial stresses are represented in the form of initial bending moments applying to the stiffened plate, while the initial geometric imperfections are considered by means of trigonometric series, and they are assumed existing in the plate along the z-direction exclusively. Then, the dynamic equilibrium equations of the stiffened plate are established using Lagrange’s equation as well as aforementioned conditions. The nonlinear differential equations of motion are simplified as a two-degree-of-freedom system by considering 1:2 and 1:3 internal resonances, respectively, and the multiscale method is applied to solve the equations.

The influence of initial stresses on the plate, stresses during internal resonance is remarkable, while that is moderate for initial geometric imperfections. (Upon considering the existence of initial stresses or geometric imperfections, the stresses of motivated modes are less than the primary mode for both and internal resonances). The influence of bidirectional initial stresses on the plate’s stresses during internal resonance is more remarkable than that of unidirectional initial stresses. The coupled vibration in 1%3A2 internal resonance is fiercer than that in internal resonance.

Stiffened plates are widely used in engineering structures. However, as a type of thin-walled structure, stiffened plates vibrate with large amplitude in most cases owning to their complicated operation circumstance. In addition, stiffened plates usually contain initial stresses and geometric imperfections, which may result in the variation of their mechanical behavior, especially dynamical behavior. Based on the above consideration, this paper studies the nonlinear dynamical behavior of stiffened plates with initial stresses and geometrical imperfections under different internal resonances, which is the originality of this work. Furthermore, the research findings can provide references for engineering design and application.

This study aims to present comprehensive nonlinear material modelling techniques and simulations of reinforced concrete (RC) beams subjected to short-term monotonic static load using the robust and reliable general-purpose finite element (FE) software ANSYS. A parametric study is carried out to analyse the flexural and ductility behaviour of RC beams under various influencing parameters.

To develop and validate the numerical FE models, a total of four experimentally tested simply supported RC beams are taken from the available literature and two beams are selected from each author. The concrete, steel reinforcements, bond-slip mechanism, loading and supporting plates are modelled using SOLID65, LINK180, COMBIN39 and SOLID185 elements, respectively. The validated models are then used to conduct parametric FE analysis to investigate the effect of concrete compressive strength, percentage of tensile reinforcement, compression reinforcement ratio, transverse shear reinforcement, bond-slip mechanism, concrete compressive stress-strain constitutive models, beam symmetry and varying overall depth of beam on the ultimate load-carrying capacity and ductility behaviour of RC beams.

The developed three-dimensional FE models can able to capture the load and midspan deflections at critical points, the accurate yield point of steel reinforcements, the formation of initial and progressive concrete crack patterns and the complete load-deflection curves of RC beams up to ultimate failure. From the numerical results, it can be concluded that the FE model considering the bond-slip effect with Thorenfeldt’s concrete compressive stress-strain model exhibits a better correlation with the experimental data.

The ultimate load and deflection results of validated FE models show a maximum deviation of less than 10% and 15%, respectively, as compared to the experimental results. The developed model is also capable of capturing concrete failure modes accurately. Overall, the FE analysis results were found quite acceptable and compared well with the experimental data at all loading stages. It is suggested that the proposed FE model is a practical and reliable tool for analyzing the flexural behaviour of RC members and can be used for performing parametric studies.

The purpose of this paper is to propose an efficient and accurate numerical model that employs isogeometric analysis (IGA) for the geometrically nonlinear analysis of functionally graded plates (FGPs). This model is utilized to investigate the effects of boundary conditions, gradient index, and geometric shape on the nonlinear responses of FGPs.

A geometrically nonlinear analysis of thin and moderately thick functionally graded ceramic-metal plates based on IGA in conjunction with first-order shear deformation theory and von Kármán strains is presented. The displacement fields and geometric description are approximated with nonuniform rational B-splines (NURBS) basis functions. The Newton-Raphson iterative scheme is employed to solve the nonlinear equation system. Material properties are assumed to vary along the thickness direction with a power law distribution of the volume fraction of the constituents.

The present model for analysis of the geometrically nonlinear behavior of thin and moderately thick FGPs exhibited high accuracy. The shear locking phenomenon is avoided without extra numerical efforts when cubic or high-order NURBS basis functions are utilized.

This paper shows that IGA is particularly well suited for the geometrically nonlinear analysis of plates because of its exact geometrical modelling and high-order continuity.

The recent unprecedented levels reached by financial ratios have led to a re‐examination of their time‐series properties, with evidence of long memory and nonlinearity reported. The purpose of this paper is to re‐examine the nature of these series in the light of potential time‐variation in the unconditional mean.

The paper uses econometric techniques designed to capture fractional integration, nonlinearity and time‐variation in the unconditional mean level of a series.

Reported results support such time‐variation, with cyclical behaviour evident in the unconditional mean of each ratio. Evidence of nonlinearity is still apparent in the mean‐adjusted series.

A key result that arises is that accounting for this time‐variation appears to provide improved long horizon returns predictability.

The paper demonstrates that a nonlinear model incorporating a time‐varying mean improves returns predictability. This is of interest to market participants.

The purpose is to detect the nonlinearity wholesale rice price formation process in Italy in the 1995–2017 period.

A nonlinear smooth transition autoregressive (STAR)-type dynamics model is used.

Wholesale rice prices are significantly affected by variations in the international price of rice as well as variations in Arborio price.

The limitations include policy recommendations for the production and commercialization of rice in Italy.

Understanding rice pricing dynamics and nonlinearity behavior is pivotal for the survival of the entire European and Italian rice supply chain.

In the extant literature, no evidence exists on non-linearity of rice prices in Italy.