Present Nonlinear Model Research Articles

A Nonlinear Approach for Dynamic Responses of a Nano-Beam Based on a Strain Gradient Nonlocal Theory

The transverse nonlinear vibration of a nanobeam fully clamped at both two ends was investigated using a strain gradient type of nonlocal continuum theory. The small scale effect was considered to the mechanical model at nanoscale. The axial elongation of the nanobeam was taken into account and the nonlinear partial differential equation governing the transverse motion was derived. Subsequently, a perturbation method was applied to the nonlinear governing equation. The dynamical responses of the nanobeam such as transverse displacement and resonant angular frequency were obtained and they were compared with those by a numerical method. The comparison indicated the validity of the present nonlinear model and the multiple-scales analysis method.

Enhancement of pure hydrogen production through the use of a membrane reactor

Pure hydrogen production is of great interest as it is an energy carrier which can be used in PEM fuel cells for power production. Methane Steam Reforming (MSR) is commonly used for hydrogen production although the produced hydrogen is not free of other components. Membrane Reactors (MR) enable a pure hydrogen product stream and allows the reaction to take place at significantly lower temperatures (lower than 550 °C) than in conventional reactors (greater than 800 °C) with comparable methane conversion. This is achieved by hydrogen removal through a permselective Pd–Ag based membrane that cause a favorable shift in chemical equilibrium towards hydrogen production. In the present study, a two-dimensional, nonlinear, and pseudo-homogeneous mathematical model of a catalytic fixed-bed membrane reactor for methane steam reforming over a nickel-based foam supported catalyst is presented. Simulated results referring to the distribution of species, methane conversion, temperature and hydrogen flowrate along the reactor for different radial positions are obtained and analyzed. The performance of structured catalyst and catalyst supported on foam configurations under the same operating conditions is also studied. Experimental results for the membrane facilitate the identification of suitable operating conditions.

Satellite Antenna Pointing Behavior with Laminated Shell Reflector Undergoing a Large Overall Motion

A dynamic modeling theory for satellite antenna is presented which is subjected to geometric nonlinearity and coupling deformation of flexible reflector undergoing a large overall motion. For the study of the characteristics of the reflector of the multilayer laminated structure, the displacement field description of a point in a three-node shell element is acquired in conjunction with the thickness, transverse bending, lateral bending, and torsional deformations. Therefore, a nonlinear dynamic model of satellite antenna is deduced based on Lagrange's equations. The complete expression of nonlinear terms of elastic deformation and coupling terms between the multilayer and large deflection are considered in the dynamic equations. Then, satellite antenna dynamics is analyzed between linear model and nonlinear model. The results show that the geometric nonlinear and coupling effects are ignored in the linear model at the initial period. However, as the rotational speed increases, the accuracy of present nonlinear model is suitable for dealing with large deformation problem with rigid-flexible coupling undergoing a large overall motion. Further, the satellite antenna pointing accuracy would be predicted based on the nonlinear model. The above conclusion would have important academic value and engineering significance.

Experimental investigation and modeling of viscoelastic behavior of concrete

The viscoelastic behavior of a concrete under dynamic and quasi-static loadings is studied. The viscoelastic behavior of the concrete under dynamic conditions is investigated by a transient wave propagation method using a pendulum impact setup, while its quasi-static behavior is investigated by a uniaxial compressive test. The results show that the concrete behaves viscoelastically under the stress wave loading, while nonlinearly elastic under the quasi-static loading. The dynamic viscoelastic moduli, i.e., the storage modulus and the loss modulus of the concrete can be divided into three portions with respect to wave frequency and the nonlinear behavior can be ignored for the stress wave propagation in the concrete. A nonlinear three-element viscoelastic model is subsequently proposed to describe the viscoelastic behavior of the concrete. The parameters of the present viscoelastic model are determined by the proposed dynamic and quasi-static test methods. The present nonlinear viscoelastic model is verified by the measured strain histories under dynamic loading and quasi-static tests, respectively. It shows that the present nonlinear viscoelastic model is capable in describing the viscoelastic behavior of the concrete with a high accuracy.

Influence of Heat Flux and Friction Coefficient on Thermal Stresses in Risers of Drum Boilers under Dynamic Conditions of Steam Demand

Boiler swing rate, which is the rate at which the boiler load is changed, has significant influence on the parameters of the boiler operating conditions such as drum water pressure and level, steam quality in the riser tubes, wall temperatures of riser tubes, and the associated thermal stresses. In this paper, the thermal stresses developed in boiler tubes due to elevated rates of heat transfer and friction are presented versus thermal stresses developed in tubes operated under normal conditions. The differential equations comprising the nonlinear model and governing the flow inside the boiler tubes were formulated to study different operational scenarios in terms of resulting dynamic response of critical variables. The experimental results and field data were obtained to validate the present nonlinear dynamic model. The calculations of the heat flux and the allowable steam quality were used to determine the maximum boiler swing rates at different conditions of riser tube of friction factor and heat flux. Diagrams for the influence of friction factor of the boiler tubes and the heat flux, that the tube is subjected to, on the maximum swing rate were examined.

Buckling and post-buckling of laminated composite plates

This paper addresses the buckling and post-buckling of laminated composite plates using higher order shear deformation theory associated with Green–Lagrange non-linear strain–displacement relationships. All higher order terms arising from nonlinear strain–displacement relations are included in the formulation. The present plate theory satisfies zero transverse shear strain conditions at the top and bottom surfaces of the plate in von Karman sense. A C0 isoparametric finite element is developed for the present nonlinear model.

Accurate large-signal equivalent circuit of surface channel diamond FETs based on the Chalmers model

The paper presents a large-signal nonlinear circuit-oriented model for polycrystalline and single-crystal H-terminated diamond MESFETs implemented within the Agilent ADS design suite. The DC characteristics of such devices suggest that the channel free charge control law may be modeled using the same strategy adopted for III-V HEMTs. For this reason, the well-known nonlinear Chalmers (Angelov) circuit model was chosen as the starting point for the development of the present non-linear diamond MESFET model. Model fitting was performed against DC and multibias small signal measurements, with good agreement. Model validations versus large-signal (power) measurements point out the accuracy of the proposed approach to simulate the behavior of H-terminated diamond MESFETs under large-signal operation.

Nonlinear spring model for adhesive bonding interface

The boundary conditions for an interface between two solids are analyzed to model second harmonic generation in a thin elastic adhesive layer. The approximate boundary condition models termed as “nonlinear spring models” are rigorously developed using an asymptotic expansion of the exact solutions in the limit of small ratio of interface layer thickness to wavelength. The applicability of such boundary conditions is analyzed by comparison with exact solutions for ultrasonic wave transmission. Numerical calculation indicate that as the acoustic nonlinearity increases, the model tends to be more accurate, meanwhile the second-harmonic amplitude increases in direct ratio. The present nonlinear spring models may provide a potential to evaluate the nonlinear mechanical behavior of bonding interface. Acknowledgment: This work is supported by the National Natural Science Foundation of China (Grant No.10834009)

Nonlinear viscoelastic medium equivalence for stress wave propagation in a jointed rock mass

Abstract A nonlinear viscoelastic equivalent medium model is proposed for longitudinal stress wave propagation in a rock mass that contains equally spaced parallel joints. The joint deformation is assumed to satisfy the nonlinear Bandis–Barton (B–B) deformational model. By the simplification of the nonlinear B–B model into piecewise linear segments, the material parameters in the equivalent medium model are analytically derived. The nonlinear viscoelastic equivalent medium model is verified by comparison with the results based on the displacement discontinuity method. It is shown that for smaller amplitude stress waves, when the rock joints deform in the linear elastic region, the nonlinear viscoelastic equivalent medium model is reduced to its linear form, whereas for larger amplitude stress waves, the present nonlinear model describes the wave amplitude-dependence of wave velocity. Two important properties, i.e., the wave transmission coefficient and the effective wave propagation velocity, are discussed in detail.

Nonclassical effects in a highly nonlinear generalized homogeneous Dicke model

An intensity dependent nonlinear coupling model of N two-level atoms (generalized Dicke model) interacting dispersively with a bimodal cavity field via two-photon transitions is investigated in a scenario where the rotating wave approximation is assumed. The model becomes homogeneous in the sense that the spin transition frequency is the same for all atoms and the coupling constants emerging from the collective interactions of the atomic system with the cavity field depend only on the particular radiation field mode. This allows us to represent the Dicke Hamiltonian entirely in terms of the total angular momentum J . It is assumed that, initially, the atomic system and the field are in a disentangled state where the field modes are in Glauber coherent states and the atomic system is a superposition of states | J M 〉 (Dicke states). The model is numerically tested against simulations of normal squeezing variance of the field, squeezing factors based on the Heisenberg uncertainty principle, along with the statistical properties of the light leading to the possible production of nonclassical effects, such as degree of second-order coherence in the modes, degree of intermode correlation, as well as violation of the Cauchy–Schwartz inequality. Analytical expression of the total density operator matrix elements at t > 0 shows the present nonlinear model to be strongly entangled, which is reflected in the time evolution of the linear entropy, where the superposition states are reduced to statistical mixtures. Thus, the present generalized Dicke model does not preserve the modulus of the Bloch vector. The computations, performed in the weak coupling and strong field limits, were conducted via second-order Dyson perturbative expansion of the time evolution operator matrix elements for the totality of the angular momentum states of the atomic system.

Large amplitude free vibration analysis of thermally post-buckled composite doubly curved panel using nonlinear FEM

In the present paper, nonlinear free vibration behaviour of single/doubly curved shell panel is addressed within the post-buckled state. Thermal post-buckling of shell panel is accounted for a uniform temperature field. A general mathematical model is developed for the curved panel by introducing the geometric nonlinearity in Green–Lagrange sense based on higher order shear deformation theory. The system governing differential equations are derived using Hamilton's principle. The derived differential equations are converted to set of algebraic equations with the help nonlinear finite element and solved numerically employing a direct iterative method. Effect of various parameters such as lamination schemes, amplitude ratios, aspect ratios, support conditions, thickness ratios, curvature ratios and the material properties on the nonlinear free vibration frequencies are analysed in detail and discussed. The obtained results are validated with those available in literature. The difference between the results necessitates the present nonlinear model for more actual prediction of nonlinear behaviour of the laminated panel type structures having severe nonlinearity when it exposed to temperature field.

A Nonlinear Van Der Waals Force Model for Multiwalled Carbon Nanotubes Modeled by a Nested System of Cylindrical Shells

In this paper, a more refined pressure distribution expression is derived to describe the van der Waals (vdW) interaction between any two tubes of a multiwalled carbon nanotube (MWCNT). Based on this new vdW force expression, a continuum cylindrical shell model is established for the buckling and post-buckling analysis of MWCNTs. The buckling and post-buckling responses are simulated for MWCNTs with various sizes to examine the consequences of ignoring the nonlinear term in the Taylor expansion of vdW force function. By comparing the results furnished by the commonly used linear vdW force model and the present nonlinear vdW force model, it is found that the buckling responses before the critical buckling strain are almost the same. Thus, the simple linear vdW force model suffices for the calculation of buckling loads. However, the post-buckling responses simulated from present nonlinear vdW force model are significantly lower than those given by the linear vdW force model. This indicates that the present nonlinear vdW force model must be used when considering the post-buckling responses.

Geometrically nonlinear bending analysis of laminated composite plate

In this work, a transverse bending of shear deformable laminated composite plates in Green–Lagrange sense accounting for the transverse shear and large rotations are presented. Governing equations are developed in the framework of higher order shear deformation theory. All higher order terms arising from nonlinear strain–displacement relations are included in the formulation. The present plate theory satisfies zero transverse shear strains conditions at the top and bottom surfaces of the plate in von-Karman sense. A C0 isoparametric finite element is developed for the present nonlinear model. Numerical results for the laminated composite plates of orthotropic materials with different system parameters and boundary conditions are found out. The results are also compared with those available in the literature. Some new results with different parameters are also presented.

Theoretical Development of Nonlinear Spring Models for the Second Harmonics on an Interface between Two Solids

Based on the exact solutions for the second-harmonic generations of the fundamental longitudinal and transverse waves propagating normally through a thin elastic layer between two solids, the approximate representations termed as ‘nonlinear spring models’ relating the stresses and displacements on both sides of the interface are rigorously developed by asymptotic expansions of the wave fields for an elastic layer in the limit of small thickness to wavelength ratio. The applicability for the so-called nonlinear spring models is numerically analyzed by comparison with exact solutions for the second harmonic wave reflections. The present nonlinear spring models lay a theoretical foundation to evaluate the interfacial properties by nonlinear acoustic waves.

Nonlinear free vibration of piezoelectric laminated composite plate

This paper addresses the nonlinear free vibration characteristic of laminated composite plate with embedded and/or surface bonded piezoelectric layer. Nonlinear governing equations are derived in Green–Lagrange sense in the framework of a higher order shear deformation theory. All higher order terms arising from nonlinear strain–displacement relations are included in mathematical formulation. The present plate theory satisfies zero transverse shear strains conditions at the top and bottom surfaces of the plate in von-Karman sense. A C 0 isoparametric finite element is proposed for the present nonlinear model. Comparisons of the present results with those obtained by exact approach show the accuracy and necessity of the model especially for the structures undergoing large deformations. Some new examples covering various features are presented to bring out the different aspects of the model. The results would be useful for the designers.

The Validity of Linear Elasticity in Analyzing Surface Texturing Effect for Elastohydrodynamic Lubrication

This paper presents a nonlinear theoretical model to study the effect of laser surface texturing on the tribological performance in soft elastohydrodynamic lubrication. Both geometrical and physical nonlinearities of the elastomer are considered by using a logarithmic strain and the Mooney–Rivlin constitutive law, respectively. The results of the present nonlinear model are compared with a previous linear one over a wide range of operating conditions. It is found that the simpler linear elasticity model predicts results that are only slightly different from these predicted by the more accurate nonlinear one. Hence, the linear elasticity model can be practically considered valid over the entire range of operating conditions.

A non-linear model for impinging jets atomization

The problem considered is predicting the characteristics of the spray produced by atomization of an attenuating liquid sheet formed by the impingement of two liquid jets of equal diameters and momenta. A second-order non-linear perturbation analysis is employed to model the evolution of harmonic instability waves that lead to sheet distortion and fragmentation. The onset of atomization occurs when the uneven surface modulations of the thinning sheet bring its upper and lower interfaces in contact. It is found that the sheet is torn into ligaments at each half wavelength. The instability of the ligaments causes their eventual disintegration into drops. The results indicate that sheet breakup length, time, and resultant drop size decrease as Weber number is increased. A higher Weber number induces a greater sheet breakup thickness. The breakup length, thickness, time, and drop size are diminished at larger impingement angles. The theoretical predictions of the present non-linear model are in good agreement with available experimental data and empirical correlations for sheet breakup length and drop size.

Active vibration control of nonlinear benchmark buildings

The present nonlinear model reduction methods unfit the nonlinear benchmark buildings as their vibration equations belong to a non-affine system. Meanwhile, the controllers designed directly by the nonlinear control strategy have a high order, and they are difficult to be applied actually. Therefore, a new active vibration control way which fits the nonlinear buildings is proposed. The idea of the proposed way is based on the model identification and structural model linearization, and exerting the control force to the built model according to the force action principle. This proposed way has a better practicability as the built model can be reduced by the balance reduction method based on the empirical Grammian matrix. A three-story benchmark structure is presented and the simulation results illustrate that the proposed method is viable for the civil engineering structures.

FORWARD-RATE VOLATILITIES AND THE SWAPTION MATRIX: WHY NEITHER TIME-HOMOGENEITY NOR TIME-DEPENDENCE ARE ENOUGH

This work presents the first systematic analysis of the whole swaption matrix by fitting a parsimonious, nonlinear, financially-inspired volatility model to market data. The study uses several years of data spanning period of major market volatility. We find that the quality of the fits is good (on average of the same magnitude as the bid-offer spread), and better when a displaced-diffusion approach is chosen, but some systematic shortcomings are observed and discussed. The analysis suggests that a two-regime Markov chain approach may be more successful and better financially motivated. More generally, the present study highlights the shortcomings of purely time-dependent or time-homogenous approaches. These findings should be applicable to other option markets as well. Finally, we find that the present (nonlinear) model vastly outperforms PCA-based approaches when in comes to predicting moves in implied volatilities.

Application of the TVD scheme to the nonlinear instability analysis of a capillary jet

In the past, when either the perturbation-type method or direct-simulation approach was used to analyse capillary jets, the governing equations, which are parabolic in time and elliptic in space, were simplified or linearized. In the present study, the convective derivative term and a full, nonlinear form of the capillary pressure term are retained in the governing equations to investigate nonlinear effects on the break-up of capillary jets. In this work, the TVD (i.e. total variation diminishing) scheme with flux-vector splitting is applied to obtain the solutions of the system of nonlinear equations in a matrix form. Numerical results show that the present nonlinear model predicts longer jet break-up lengths and slower growth rates for capillary jets than the previous linear model does. Comparing with other measurements from past literatures, the nonlinear results are consistent with the experimental data and appear more accurate than the linear analysis. In the past, the classic perturbation-type analyses assumed constant growth rates for the fundamental and all harmonic components. By contrast, the present model is able to capture the local features of growth rates, which are not spatially and temporally constant. Copyright © 2006 John Wiley & Sons, Ltd.