Nonlinear Analysis of a Tapered Impact Damper using the Method of Harmonic Balance.
Abstract not provided.
Ganci, Claire↗
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Stability analysis of nonlinear two-grid method for multigroup neutron diffusion problems
We present theoretical analysis of a nonlinear acceleration method for solving multigroup neutron diffusion problems. This method is formulated with two energy grids that are defined by (i) fine-energy groups structure and (ii) coarse grid with just a single energy group. The coarse-grid equations are derived by averaging of the multigroup diffusion equations over energy. The method uses a nonlinear prolongation operator. We perform stability analysis of iteration algorithms for inhomogeneous (fixed-source) and eigenvalue neutron diffusion problems. To apply Fourier analysis the equations of the method are linearized about solutions of infinite-medium problems. The developed analysis enables us to predict convergence properties of this two-grid method in different types of problems. Numerical results of problems in 2D Cartesian geometry are presented to confirm theoretical predictions.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Automated Model Updating Effect on the Linear and Nonlinear Dynamic Responses of Historical Masonry Structures
Finite element models supply the simulation of the problems to obtain the structural behaviors under different loading conditions. The updating processes based on changing the uncertain parameters such as material properties, boundary conditions, meshing size etc. are made to create actual finite element models in order to represent the real conditions of the problems. This procedure can be made using two methods, namely manual model updating and global/local automatic model updating. The global/local automatic model updating procedures are very popular owing to the applicability to all kind of engineering structures, minimizing the differences nearly to zero, availability of damage localization and structural health monitoring. In this paper a historical masonry armory building selected as an application and its finite element analyses, experimental measurements and automated model updating processes are carried out. The finite element model of the structures was developed with ANSYS software and first three natural frequencies are attained. The experimental dynamic characteristics such as natural frequencies, damping ratios and mode shapes are obtained using ambient vibration method. The differences between experimental and numerical frequencies are minimized up to the range of 0–1%, by using local updating procedure. The linear and nonlinear seismic analyses of the building are conducted on initial and updated models. At the end of the analyses, maximum displacements, principal stresses and strains are given with detail. In addition, crack distributions diagrams are attained to validate the stresses accumulation points. It can be seen that there is an increasing trend in the displacement, stress and strain values after finite element model updating both linear and nonlinear analysis. In addition, linear and nonlinear analysis results are compared with each other to evaluate the nonlinear analysis effect. It is concluded that the displacement and strain values are increased after nonlinear analysis. But, there is not any agreement in stress values.
42 ENGINEERING↗
Approach for Selection of Rayleigh Damping Parameters Used for Time History Analysis
Nonlinearities, whether geometric or material, need to be addressed in seismic analysis. One good analysis method that can address these nonlinearities is direct time integration with Rayleigh damping. Modal damping is the damping typically specified in seismic analysis Codes and Standards. Modal damping is constant for all frequencies where Rayleigh damping varies with frequency. An approach is proposed here for selection of Rayleigh damping coefficients to be used in seismic analyses that is consistent with given Modal damping. The approach uses the difference between the modal damping response and the Rayleigh damping response along with effective mass properties of the model being evaluated to match overall system response levels. This paper provides a simple example problem to demonstrate the approach. It also provides results for a finite element model representing an existing piping system. Displacement, acceleration, and stress results are compared from model runs using modal damping and model runs using Rayleigh damping with coefficients selected using the proposed method.
42 ENGINEERING↗
Approximate entropy analysis for nonlinear beam dynamics
In this paper, we applied an approximate entropy (ApEn) analysis to nonlinear beam dynamics. Due to the presence of strong nonlinear magnets, the degree of chaos in beam motion gradually increases proportionally with its amplitude. Such chaos can be quantitatively characterized with ApEn of beam turn-by-turn readings. ApEn analysis is a technique used to quantify the amount of regularity and the unpredictability of fluctuations with respect to time-series data. The ApEn, when applied as a chaos indicator, can then be used for nonlinear lattice optimization and analysis. The National Synchrotron Light Source II (NSLS-II) electron storage ring lattice was used as an example of a real-world application of our technique. Published by the American Physical Society 2024
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Approximate Entropy Analysis for Nonlinear Beam Dynamics
In this paper, we applied an approximate entropy (ApEn) analysis to nonlinear beam dynamics. Due to the presence of strong nonlinear magnets, the degree of chaos in beam motion gradually increases proportionally with its amplitude. Such chaos can be quantitatively characterized with ApEn of beam turn-by-turn readings. ApEn analysis is a technique used to quantify the amount of regularity and the unpredictability of fluctuations with respect to time-series data. The ApEn, when applied as a chaos indicator, can then be used for nonlinear lattice optimization and analysis. The National Synchrotron Light Source II (NSLS-II) electron storage ring lattice was used as an example of a real-world application of our technique.
43 PARTICLE ACCELERATORS↗
Nonlinear dynamic analysis of solution multiplicity of buoyancy ventilation in a typical underground structure
Buoyancy ventilation is widely used in underground buildings, such as underground hydropower stations. Multiple solutions of buoyancy ventilation may exist in those underground structures. In this study, we developed a transient model comprising an ordinary differential equation system to describe buoyancy ventilation patterns in typical two-zone underground structures. Additionally, the accuracy of the model was validated. Nonlinear dynamical analysis was conducted to study multiple steady-state airflow. According to mathematical derivation, the configuration of one local heat source at the bottom corner introduces two stable solutions. The criterion to determine the stability and existence of solutions for more general scenarios was developed. Using this criterion, we obtained the multiple steady states of any two-zone underground buildings for different stack height ratios and the strength ratios of the heat sources. Furthermore, this criterion can be adopted for the design of buoyancy ventilation or natural smoke ventilation systems. Designers can change the height ratio of the stack or the heat ratio of two zones to induce the desired ventilation patterns. Finally, a case study was conducted with field measurements to demonstrate the use of the nonlinear dynamical analysis method to investigate the multiple steady states of buoyancy ventilation. Through the case study, we validated that the proposed criterion could produce the same result as the nonlinear dynamical analysis.
32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
Comparative Convergence Analysis of Nonlinear AMLI-Cycle Multigrid
The purpose of our paper is to provide a comprehensive convergence analysis of the nonlinear algebraic multilevel iteration (AMLI)-cycle multigrid (MG) method for symmetric positive definite problems. We show that the nonlinear AMLI-cycle MG method is uniformly convergent, based on classical assumptions for approximation and smoothing properties. Furthermore, under only the assumption that the smoother is convergent, we show that the nonlinear AMLI-cycle method is always better (or not worse) than the respective V-cycle MG method. Finally, numerical experiments are presented to illustrate the theoretical results.
97 MATHEMATICS AND COMPUTING↗
Multi-scale nonlinear stress analysis of Nb 3 Sn superconducting accelerator magnets
A multi-scale nonlinear procedure to analyze the stress in Nb 3 Sn superconducting accelerator magnets is presented to address one of the most challenging obstacles currently facing the successful development of high-field superconducting magnets—the issue of stress management. The study demonstrates that gaskets (special nonlinear materials) are capable of modeling the complex nonlinear deformation behavior of insulation layers within the Nb 3 Sn coil block and that Hill materials (orthotropic materials utilizing the Hill yield criterion) are suitable to enable homogenization of the filamentary regions and the resin-impregnated Nb 3 Sn Rutherford cables. With the whole magnet under preload, cool-down, and Lorentz forces, the nonlinear behavior of the Nb 3 Sn coil was simulated, in three orthongonal axes, by the combined properties of the gaskets (insulation layers) and Hill materials (resin-impreganted cable). The procedure entailes minimal material assumptions because it incorporated measured stress-strain curves in the analysis. The coil was simulated to a high level of detail consisting of the insulation layers and resin-impregnated cables. The computed compressive azimuthal stresses of the cables were used to assess the stress-induced performance degradation. Through submodeling, the area-weighted average axial strains of the strands were computed and employed to evaluate the strain-induced performance degradation. The overall performance degradation of the Nb 3 Sn coil was thus obtained, and this information was subsequently used to guide the design of the overall magnet. Besides Nb 3 Sn magnets, this procedure can also be employed in the design of LTS, HTS, and room temperature magnets or in any composite structures.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
The Weakly Nonlinear Magnetorotational Instability in a Global, Cylindrical Taylor–Couette Flow
We conduct a global, weakly nonlinear analysis of the magnetorotational instability (MRI) in a Taylor–Couette flow. This is a multiscale, perturbative treatment of the nonideal, axisymmetric MRI near threshold, subject to realistic radial boundary conditions and cylindrical geometry. We analyze both the standard MRI, initialized by a constant vertical background magnetic field, and the helical MRI, with an azimuthal background field component. This is the first weakly nonlinear analysis of the MRI in a global Taylor–Couette geometry, as well as the first weakly nonlinear analysis of the helical MRI. We find that the evolution of the amplitude of the standard MRI is described by a real Ginzburg–Landau equation (GLE), whereas the amplitude of the helical MRI takes the form of a complex GLE. This suggests that the saturated state of the helical MRI may itself be unstable on long spatial and temporal scales.
79 ASTRONOMY AND ASTROPHYSICS↗
Time-dependent, multimode interaction analysis of the gyroklystron amplifier
In this paper, a time-dependent multimode nonlinear analysis for the gyroklystron amplifier has been developed by extending the analysis of gyrotron oscillators by employing the self-consistent approach. The nonlinear analysis developed here has been validated by taking into account the reported experimental results for a 32.3 GHz, three cavity, second harmonic gyroklystron operating in the TE{sub 02} mode. The analysis has been used to estimate the temporal RF growth in the operating mode as well as the nearby competing modes. Device gain and bandwidth have been computed for different drive powers and frequencies. The effect of various beam parameters, such as beam voltage, beam current, and pitch factor, has also been studied. The computational results have estimated the gyroklystron saturated RF power ∼319 kW at 32.3 GHz with efficiency ∼23% and gain ∼26.3 dB with device bandwidth ∼0.027% (8 MHz) for a 70 kV, 20 A electron beam. The computed results are found to be in agreement with the experimental values within 10%.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Nonlinear spectral analysis of ion acoustic solitons arising from a streaming charged object using the numerical inverse scattering transform
Observations of nonlinear coherent plasma phenomena in spacecraft and terrestrial experiments often rely on visual identification of solitary modes because nonlinear coherent modes are broadband in a Fourier transform based analysis. We implement an alternative spectral decomposition known as the inverse scattering transform and demonstrate its ability to successfully isolate nonlinear modes on the homogeneous and forced Korteweg–De Vries equation which models these nonlinear modes. We also demonstrate for the first time that this decomposition is useful when forcing is applied. This is because the stable modes generated by localized forcing are similar to the homogeneous solutions where the inverse scattering transform is a rigorous decomposition. This spectral technique is then applied to simulations of ion acoustic waves generated by a 10 mm spherical debris object interacting with the ionospheric plasma orbiting at 2000 km altitude. The algorithm is found to successfully detect the resultant solitons. This demonstrates the feasibility of using this spectral technique as a real time analysis tool for screening spacecraft data for nonlinear solitary modes.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Design and simulation of a gyroklystron amplifier
In the present paper, a design methodology of the gyroklystron amplifier has been described and subsequently used for the design of a typically selected 200 kW, Ka-band, four-cavity gyroklystron amplifier. This conceptual device design has been validated through the 3D particle-in-cell (PIC) simulation and nonlinear analysis. Commercially available PIC simulation code “MAGIC” has been used for the electromagnetic study at the different location of the device RF interaction structure for the beam-absent case, i.e., eigenmode study as well as for the electron beam and RF wave interaction behaviour study in the beam present case of the gyroklystron. In addition, a practical problem of misalignment of the RF cavities with drift tubes within the tube has been also investigated and its effect on device performance studied. The analytical and simulation results confirmed the validity of the gyroklystron device design. The PIC simulation results of the present gyroklystron produced a stable RF output power of ∼218 kW for 0% velocity spread at 35 GHz, with ∼45 dB gain, 37% efficiency, and a bandwidth of 0.3% for a 70 kV, 8.2 A gyrating electron beam. The simulated values of RF output power have been found in agreement with the nonlinear analysis results within ∼5%. Further, the PIC simulation has been extended to study a practical problem of misalignment of the cavities axis and drift tube axis of the gyroklystron amplifier and found that the RF output power is more sensitive to misalignments in comparison to the device bandwidth. The present paper, gyroklystron device design, nonlinear analysis, and 3D PIC simulation using commercially available code had been systematically described would be of use to the high-power gyro-amplifier tube designers and research scientists.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Parameter sensitivity analysis of nonlinear piezoelectric probe in tapping mode atomic force microscopy for measurement improvement
The equations of motion for a piezoelectric microcantilever are derived for a nonlinear contact force. The analytical expressions for natural frequencies and mode shapes are obtained. Then, the method of multiple scales is used to analyze the analytical frequency response of the piezoelectric probe. The effects of nonlinear excitation force on the microcantilever beam's frequency and amplitude are analytically studied. The results show a frequency shift in the response resulting from the force nonlinearities. This frequency shift during contact mode is an important consideration in the modeling of AFM mechanics for generation of more accurate imaging. Also, a sensitivity analysis of the system parameters on the nonlinearity effect is performed. The results of a sensitivity analysis show that it is possible to choose parameters such that the frequency shift minimizes. Certain parameters such as tip radius, microcantilever beam dimensions, and modulus of elasticity have more influence on the nonlinearity of the system than other parameters. By changing only three parameters—tip radius, thickness, and modulus of elasticity of the microbeam—a more than 70% reduction in nonlinearity effect was achieved.
36 MATERIALS SCIENCE↗
Exponential Decay in the Sensitivity Analysis of Nonlinear Dynamic Programming
In this report, we study the sensitivity of discrete-time dynamic programs with nonlinear dynamics and objective to perturbations in the initial conditions and reference parameters. Under uniform controllability and boundedness assumptions for the problem data, we prove that the directional derivative of the optimal state and control at time $k$, $x^*_k$, and $u^*_k$, with respect to the reference signal at time $i$, $d_i$, will have exponential decay in terms of $|k-i|$ with a decay rate $\rho$ independent of the temporal horizon length. The key technical step is to prove that a version of the convexification approach proposed by Verschueren et al. can be applied to the KKT conditions and results in a convex quadratic program with uniformly bounded data. In turn, Riccati techniques can be further employed to obtain the sensitivity result, borne from the observation that the directional derivatives are solutions of quadratic programs with structure similar to the KKT conditions themselves. We validate our findings with numerical experiments on a small nonlinear, nonconvex, dynamic program.
97 MATHEMATICS AND COMPUTING↗
Confidentiality-preserving machine learning algorithms for soft-failure detection in optical communication networks
Automated fault management is at the forefront of next-generation optical communication networks. The increase in complexity of modern networks has triggered the need for programmable and software-driven architectures to support the operation of agile and self-managed systems. In these scenarios, the European Telecommunications Standards Institute zero-touch network and service management approach is imperative. The need for machine learning algorithms to process the large volume of telemetry data brings safety concerns as distributed cloud-computing solutions become the preferred approach for deploying reliable communication network automation. This paper’s contribution is twofold. First, we propose a simple yet effective method to guarantee the confidentiality of the telemetry data based on feature scrambling. The method allows the operation of third-party computational services without direct access to the full content of the collected data. Additionally, the effectiveness of four unsupervised machine learning algorithms for soft-failure detection is evaluated when applied to the scrambled telemetry data. The methods are based on factor analysis, principal component analysis, nonlinear principal component analysis, and singular value decomposition. Most dimensionality reduction algorithms have the common property that they can maintain similar levels of fault classification performance while hiding the data structure from unauthorized access. Evaluations of the proposed algorithms demonstrate this capability.
97 MATHEMATICS AND COMPUTING↗
Nonlinear Fourier analysis for discontinuous conductivities: Computational results
Two reconstruction methods of Electrical Impedance Tomography (EIT) are numerically compared for nonsmooth conductivities in the plane based on the use of complex geometrical optics (CGO) solutions to D-bar equations involving the global uniqueness proofs for Calderón problem exposed in Nachman (1996) [43] and Astala and Päivärinta (2006) [6]: the Astala–Päivärinta theory-based low-pass transport matrix method implemented in Astala et al. (2011) [3] and the shortcut method which considers ingredients of both theories. The latter method is formally similar to the Nachman theory-based regularized EIT reconstruction algorithm studied in Knudsen et al. (2009) [34] and several references from there. New numerical results are presented using parallel computation with size parameters larger than ever, leading mainly to two conclusions as follows. First, both methods can approximate piecewise constant conductivities better and better as the cutoff frequency increases, and there seems to be a Gibbs-like phenomenon producing ringing artifacts. Second, the transport matrix method loses accuracy away from a (freely chosen) pivot point located outside of the object to be studied, whereas the shortcut method produces reconstructions with more uniform quality.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Nonlinear Impedance Analysis of La 0.4 Sr 0.6 Co 0.2 Fe 0.8 O 3-δ Thin Film Oxygen Electrodes
Here, linear and nonlinear electrochemical impedance spectroscopy (EIS, NLEIS) were used to study 20 nm thin film La 0.6 Sr 0.4 Co 0.2 Fe 0.8 O 3-δ (LSCF-6428) electrodes at 600°C in oxygen environments. LSCF films were epitaxially deposited on single crystal yttria-stabilized zirconia (YSZ) with a 5 nm gadolinium-doped ceria (GDC) protective interlayer. Impedance measurements reveal an oxygen storage capacity similar to independent thermogravimetry measurements on semi-porous pellets. However, the impedance data fail to obey a homogeneous semiconductor point-defect model. Two consistent scenarios were considered: a homogeneous film with non-ideal thermodynamics (constrained by thermogravimetry measurements), or an inhomogeneous film (constrained by a semiconductor point-defect model with a Sr maldistribution). The latter interpretation suggests that gradients in Sr composition would have to extend beyond the space-charge region of the gas-electrode interface. While there is growing evidence supporting an equilibrium Sr segregation at the LSCF surface monolayer, a long-range, non-equilibrium Sr stratification caused by electrode processing conditions offers a possible explanation for the large volume of highly reducible LSCF. Additionally, all thin films exhibited fluctuations in both linear and nonlinear impedance over the hundred-hour measurement period. This behavior is inconsistent with changes solely in the surface rate coefficient and possibly caused by variations in the surface thermodynamics over exposure time.
36 MATERIALS SCIENCE↗