Global Nonlinear Response Research Articles

The Effect of Hydrogen on Nonlinear Flame Saturation

Abstract We investigate the effect of increasing levels of hydrogen enrichment on the nonlinear response and saturation of premixed bluff-body stabilized methane/hydrogen flames submitted to acoustic forcing. The thermal power is kept approximately constant to preserve the nozzle velocity while increasing the flame speed through hydrogen enrichment. The flame describing function (FDF) is measured for a fixed frequency and three hydrogen–methane blends ranging from 10% to 50% by power, corresponding to 25% to 75% by volume. We show that when the flame is forced at the same frequency at similar power and bulk velocities, increasing levels of hydrogen enrichment increase the saturation amplitude of the flame. To provide insight into the flame dynamics responsible for the change in the global nonlinear response and saturation amplitude, the flames were investigated using high-speed imaging in combination with OH planar laser-induced fluorescence (OH-PLIF) at a range of forcing amplitudes. At lower hydrogen concentrations, the flame is stabilized along the inner shear layer and saturation in the heat release rate (HRR) occurs at lower forcing amplitudes due to large-scale flame–vortex interactions causing flame annihilation as observed in several previous studies. At increased levels of hydrogen enrichment, distinctly different flame dynamics are observed. In these cases, the flame accelerates and propagates across to the outer shear layer, which acts to suppress large-scale flame annihilation during roll-up of both the inner and outer shear layers. This results in a coherent increase in flame surface area with forcing amplitudes significantly increasing the saturation amplitude of the flame. These results show that high levels of hydrogen increase the amplitude response to acoustic forcing leading to higher saturation amplitudes. This suggests that substituting natural gas with hydrogen in gas turbines increases the risk of much higher limit-cycle amplitudes if self-excited instabilities occur.

Wave self-interactions in continuum phononic materials with periodic contact nonlinearity

The existence of nonlinearity within materials manifests richer wave propagation compared to their linear counterpart in the form of amplitude-dependent material response and energy transfer between frequencies. While these properties have been extensively studied in the case of continuous and discrete nonlinear phononic materials (PMs), individually, the behavior of continuum PMs with discrete nonlinearities, which could open new opportunities for wave propagation control via discrete–continuum coupling, is relatively unexplored. In this article, we investigate nonlinear wave propagation through one-dimensional continuum PMs with periodic contacts. Specifically, the periodicity is in the form of pre-compressed rough contacts resulting in nonlinearly coupled linear finite thickness elastic layers. We analyze the system using full-scale time-domain finite element simulations by treating the contacts as spring-equivalent nonlinear thin elastic layers. The model considers a power-law pressure-gap relationship at the rough contacts. The evolution of propagating nonlinear waves within the weakly nonlinear regime is illustrated, emphasizing the generation of zero (DC), self-demodulated low, and second harmonic frequencies for excitation in different zones of the dispersion relation. The continuum between discrete contact nonlinearities exhibits local DC reduction and second harmonic increment, not observed in discrete PMs such as granular phononic crystals. The intertwined effects of nonlinearity, periodicity, and finiteness on nonlinear wave propagation are also explored, which results in maximum DC amplitude at the finite boundaries of the PMs and mode-based second harmonic characteristics. Finally, we demonstrate the flexibility of the proposed nonlinear PMs by characterizing the dependence of nonlinear wave propagation on different arrangements of embedded contacts. The concept of discretely embedding nonlinear interfaces, such as rough contacts, within an elastic continuum, opens opportunities to control the global nonlinear response of the PMs through local microstructural nonlinearities.

Nonlinear Material Model for Quasi-Unidirectional Woven Composite Accounting for Viscoelastic, Viscous Deformation, and Stiffness Reduction.

To clarify the individual contribution of viscoelastic and viscous deformation to the global nonlinear response of composites, multilevel cyclic loading-unloading recovery tensile tests were carried out. The experimental results show that there is a linear relationship between the viscous strain and viscoelastic strain of composites, regardless of the off-axis angle or loading stress level. On the basis of experimental results, a coupled damage-plasticity constitutive model was proposed. In this model, the plasticity theory was adopted to assess the evolution of viscous strains. The viscoelastic strain was represented as a linear function of viscous strains. Moreover, the Weibull function of the effective stress was introduced to evaluate the damage variables in terms of stiffness reduction. The tensile stress-strain curves, predicted by the proposed model, showed a good agreement with experimental results.

A Two‐Step Hybrid Approach for Modeling the Nonlinear Dynamic Response of Piezoelectric Energy Harvesters

An effective hybrid computational framework is described here in order to assess the nonlinear dynamic response of piezoelectric energy harvesting devices. The proposed strategy basically consists of two steps. First, fully coupled multiphysics finite element (FE) analyses are performed to evaluate the nonlinear static response of the device. An enhanced reduced‐order model is then derived, where the global dynamic response is formulated in the state‐space using lumped coefficients enriched with the information derived from the FE simulations. The electromechanical response of piezoelectric beams under forced vibrations is studied by means of the proposed approach, which is also validated by comparing numerical predictions with some experimental results. Such numerical and experimental investigations have been carried out with the main aim of studying the influence of material and geometrical parameters on the global nonlinear response. The advantage of the presented approach is that the overall computational and experimental efforts are significantly reduced while preserving a satisfactory accuracy in the assessment of the global behavior.

Nonlinear analysis of masonry panels strengthened with textile reinforced mortar

The paper proposes a simplified modelling approach for the analysis of the in-plane shear behavior of tuff stone masonry panels strengthened with a surface bonded composite Basalt Textile Reinforced Mortar (BTRM) system subjected to diagonal compression. The nonlinear behavior of the unreinforced and reinforced panels is reproduced by means of a macroscopic smeared crack approach. The masonry is modeled as an isotropic continuum material characterized by different nonlinear softening laws in tension and compression. The BTRM composite is modeled with two layers representing the basalt textile and the matrix with different constitutive relationships. Sensitivity numerical analyses are developed in order to investigate the influence of each parameter in the global nonlinear response of the panel. Then, representative numerical models for the unreinforced and the reinforced panel are presented. Two BTRM layouts are investigated: single-side and double-side reinforcement. The models aim to capture the main aspects of the observed experimental nonlinear response, such as stiffness, strength-deformation shear capacity and failure mechanism. The numerical results are compared with the experimental outcomes of diagonal compression tests to investigate the feasibility of the models in the description of the in-plane shear behavior of tuff stone panels strengthened with the BTRM system.

A new analysis method for structural failure evaluation

There are many possible approaches for structural failure evaluation which uses different nonlinear structural analysis methods. For computer implementation purposes, some important differences between them are the results precision, the amount of computer memory needed and computer processing time. For solving practical problems, a compromise between accuracy and computational effort is needed. In this work, a new method is presented for linear and nonlinear structural analysis. The new developed method was named Fibre Contact Element Method (FCEM). In the proposed method, structures are divided in a mesh of several small rectangular block elements (neighbour blocks do not need to be aligned). These elements are divided in several micro fibre elements. Fibres belonging to neighbour blocks are connected between contact points. Two degrees of freedom are considered per contact point and three degrees of freedom are considered for each block (in a 2D model). The elemental block stiffness matrix is obtained from the assembly of fibre stiffness matrix. A static matrix condensation is preformed to reduce the block stiffness matrix dimension. The elasticity and plasticity is concentrated on each fibre element. Global nonlinear response can result from flexural or from shear fibre cracking or yielding. In this work, comparisons between numerical and analytical results are presented. The new method seems to be accurate and fast enough for solving practical problems, namely for seismic damage assessment. Results seem to demonstrate that FCEM can be a valid option for using in structural failure evaluation.

Formulation of strain-dependent hydraulic conductivity for a fractured rock mass

By characterizing rock masses as anisotropic continua with one or multiple sets of critically oriented fractures, a methodology is developed in this paper to address the change in hydraulic conductivity resulted from engineering disturbance, material nonlinearity and anisotropy. An equivalent elastic–perfectly plastic constitutive model with non-associated flow rule and mobilized dilatancy is developed to describe the global nonlinear response of the rockmass under complex loading conditions. By separating the deformation of fractures from that of the equivalent medium, a strain-dependent hydraulic conductivity tensor is formulated. This not only considers the normal compressive deformation of the fractures, but also and more importantly, integrates the effect of material nonlinearity and post-peak shear dilatancy. Using this methodology, a closed-form solution is derived to describe the hydraulic behavior of a single fracture during combined normal and shear loading processes. The closed-form solution is validated by an existing coupled shear-flow test under wide ranges of normal and shear loads. Numerical simulations are performed to investigate the changes in hydraulic conductivities of a cubic block of fractured rock mass under triaxial compression and shear loading, as well as a circular underground excavation in a biaxial stress field at the Stripa mine, Sweden. The simulation results agree well with the in-situ experimental observations and an existing elastic strain-dependent analytical solution, respectively. The evaluation results clearly demonstrate that the proposed model is capable of predicting the changes in hydraulic properties of fractured rock masses under loading or excavation.

Nonlinear Response Surface and Mixture Experiment Methodologies Applied to the Study of Synergism

AbstractA new paradigm for the study of the joint action (synergism, additivity and antagonism) of different agents that combines nonlinear response surface modeling with mixture experiment methodologies is described. We achieve a global nonlinear response surface model using raw data modeling and hierarchical parameter modeling along with numerical and graphical evaluations. The method is applied to a very large previously‐published (Faessel et al., 1998) in vitro study of the combined effect of Trimetrexate (TMQ) and AG2034 on inhibition of cancer cell growth. The modulator Folic acid (Folate) concentration is also included as a continuous process variable. The mixture portion of the analysis is best identified as an “NLMAZ‐PV” experiment, incorporating a nonlinear mixture‐amount model with zero amounts (control observations) and the process variable. The underlying nonlinear structural model, describing the relationship between the mixture amount and the observed effect, is the four parameter Hill (1910) equation. This model for studying synergism was developed as an improvement over the flagship synergy/antagonism model of Greco et al. (1995) and other response surface synergy models. This new modeling approach allows for irregularly‐shaped isobols, complex patterns of local synergism and antagonism, a modulating agent with no effect of its own, and extensions to three or more drugs (White et al., 2003). (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)