Analog methods of nonlinear vibration analysis

This thesis presents methods by which electrical analogies can be obtained for nonlinear systems. The accuracy of these methods is investigated and several specific types of nonlinear equations are studied in detail.

In Part I a general method is given for obtaining electrical analogs of nonlinear systems with one degree of freedom. Loop and node methods are compared and the stability of the loop analogy is briefly considered.

Parts II and III give a description of the equipment and a discussion of its accuracy. Comparisons are made between experimental and analytic solutions of linear systems.

Part IV is concerned with systems having a nonlinear restoring force. In particular, solutions of Duffing's equation are obtained, both by using the electrical analogy and also by approximate analytical methods.

Systems with nonlinear damping are considered in Part V. Two specific examples are chosen: (1) forced oscillations and (2) self-excited oscillations (van der Pol’s equation). Comparisons are made with approximate analytic solutions.

Part VI gives experimental data for a system obeying Mathieu's equation. Regions of stability are obtained. Examples of subharmonic, ultraharmonic, and ultrasubharmonic oscillat1ons are shown.

Randomized nonlinear component analysis

Copyright © (2014) by the International Machine Learning Society (IMLS) All rights reserved. Classical methods such as Principal Component Analysis (PCA) and Canonical Correlation Analysis (CCA) are ubiquitous in statistics. However, these techniques are only able to reveal linear re-lationships in data. Although nonlinear variants of PCA and CCA have been proposed, these are computationally prohibitive in the large scale. In a separate strand of recent research, randomized methods have been proposed to construct features that help reveal nonlinear patterns in data. For basic tasks such as regression or classification, random features exhibit little or no loss in performance, while achieving drastic savings in computational requirements. In this paper we leverage randomness to design scalable new variants of nonlinear PCA and CCA; our ideas extend to key multivariate analysis tools such as spectral clustering or LDA. We demonstrate our algorithms through experiments on real- world data, on which we compare against the state-of-the-art. A simple R implementation of the presented algorithms is provided.

Comparison of finite element and finite volume methods application in geometrically nonlinear stress analysis

A novel three-dimensional finite volume (FV) procedure is described in detail for the analysis of geometrically nonlinear problems. The FV procedure is compared with the conventional finite element (FE) Galerkin approach. FV can be considered to be a particular case of the weighted residual method with a unit weighting function, where in the FE Galerkin method we use the shape function as weighting function. A Fortran code has been developed based on the finite volume cell vertex formulation. The formulation is tested on a number of geometrically nonlinear problems. In comparison with FE, the results reveal that FV can reach the FE results in a higher mesh density.

Simplified Procedure for the Nonlinear Seismic Analysis of Bridges

The severe accidents suffered by bridges during recent earthquake show that more careful analysis are needed to guarantee their behaviour. In particular simplified non-linear analysis could be useful to bridge the gap between theoretical research and practical applications. This paper presents one of those simplified methods that can be applied for first designs or to retrofitting of groups of bridges.

Design of array processor software for nonlinear structural analysis /

"Dec. 1983."

Nonlinear speech analysis algorithms mapped to a standard metric achieve clinically useful quantification of average Parkinson's disease symptom severity

The standard reference clinical score quantifying average Parkinson's disease (PD) symptom severity is the Unified Parkinson's Disease Rating Scale (UPDRS). At present, UPDRS is determined by the subjective clinical evaluation of the patient's ability to adequately cope with a range of tasks. In this study, we extend recent findings that UPDRS can be objectively assessed to clinically useful accuracy using simple, self-administered speech tests, without requiring the patient's physical presence in the clinic. We apply a wide range of known speech signal processing algorithms to a large database (approx. 6000 recordings from 42 PD patients, recruited to a six-month, multi-centre trial) and propose a number of novel, nonlinear signal processing algorithms which reveal pathological characteristics in PD more accurately than existing approaches. Robust feature selection algorithms select the optimal subset of these algorithms, which is fed into non-parametric regression and classification algorithms, mapping the signal processing algorithm outputs to UPDRS. We demonstrate rapid, accurate replication of the UPDRS assessment with clinically useful accuracy (about 2 UPDRS points difference from the clinicians' estimates, p < 0.001). This study supports the viability of frequent, remote, cost-effective, objective, accurate UPDRS telemonitoring based on self-administered speech tests. This technology could facilitate large-scale clinical trials into novel PD treatments.

Study of a beam-column joint of a precast system by nonlinear numerical analysis

The present work consists of a detailed numerical analysis of a 4-way joint made of a precast column and two partially precast beams. The structure has been previously built and experimentally analyzed through a series of cyclic loads at the Laboratory of Tests on Structures (Laboratorio di Prove su Strutture, La. P. S.) of the University of Bologna. The aim of this work is to design a 3D model of the joint and then apply the techniques of nonlinear finite element analysis (FEA) to computationally reproduce the behavior of the structure under cyclic loads. Once the model has been calibrated to correctly emulate the joint, it is possible to obtain new insights useful to understand and explain the physical phenomena observed in the laboratory and to describe the properties of the structure, such as the cracking patterns, the force-displacement and the moment-curvature relations, as well as the deformations and displacements of the various elements composing the joint.

种子汽泡传热原理与实验研究

两相流动不稳定性是在各种水力学直径通道内所遇到的复杂现象，这些不稳定性对热能系统可能造成有害影响。本文以丙酮为工质，在受热微通道入口处设置微汽泡发生器，采用脉冲电压激励产生可控微汽泡，并以微汽泡为种子尝试对热微通道内沸腾不稳定性及传热的控制。实验研究表明低频种子汽泡热控能够减轻各参数的脉动幅度；高频种子汽泡热控能彻底抑制沸腾不稳定性；种子汽泡技术的优点是能够在各发泡频率下抑制沸腾不稳定性，强化换热。本研究结果为解决微通道内沸腾不稳定性提供了一种崭新有效的手段，大大延长了待冷却芯片的使用寿命。

Nonlinear analysis of a thin pre-twisted and delaminated anisotropic strip

The present work is aimed at the development of an efficient mathematical model to assess the degradation in the stiffness properties of an anisotropic strip due to delamination. In particular, the motive is to capture those nonlinear effects in a strip that arise due to the geometry of the structure, in the presence of delamination. The variational asymptotic method (VAM) is used as a mathematical tool to simplify the original 3D problem to a 1D problem. Further simplification is achieved by modeling the delaminated structure by a sublaminate approach. By VAM, a 2D nonlinear sectional analysis is carried out to determine compact expression for the stiffness terms. The stiffness terms, both linear and nonlinear, are derived as functions of delamination length and location in closed form. In general, the results from the analysis include fully coupled nonlinear 1D stiffness coefficients, 3D strain field, 3D stress field, and in-plane and warping fields. In this work, the utility of the model is demonstrated for a static case, and its capability to capture the trapeze effect in the presence of delamination is investigated and compared with results available in the literature.

A low-order model investigation of the analysis of gravity waves in the ensemble Kalman filter.

The behavior of the ensemble Kalman filter (EnKF) is examined in the context of a model that exhibits a nonlinear chaotic (slow) vortical mode coupled to a linear (fast) gravity wave of a given amplitude and frequency. It is shown that accurate recovery of both modes is enhanced when covariances between fast and slow normal-mode variables (which reflect the slaving relations inherent in balanced dynamics) are modeled correctly. More ensemble members are needed to recover the fast, linear gravity wave than the slow, vortical motion. Although the EnKF tends to diverge in the analysis of the gravity wave, the filter divergence is stable and does not lead to a great loss of accuracy. Consequently, provided the ensemble is large enough and observations are made that reflect both time scales, the EnKF is able to recover both time scales more accurately than optimal interpolation (OI), which uses a static error covariance matrix. For OI it is also found to be problematic to observe the state at a frequency that is a subharmonic of the gravity wave frequency, a problem that is in part overcome by the EnKF.However, error in themodeled gravity wave parameters can be detrimental to the performance of the EnKF and remove its implied advantages, suggesting that a modified algorithm or a method for accounting for model error is needed.

A nonlinear analysis of laying a floating pipeline on the seabed

In this article, a model for the determination of displacements, strains, and stresses of a submarine pipeline during its construction is presented. Typically, polyethylene outfall pipelines are the ones treated by this model. The process is carried out from an initial floating situation to the final laying position on the seabed. The following control variables are considered in the laying process: the axial load in the pipe, the flooded inner length, and the distance of the control barge from the coast. External loads such as self-weight, dead loads, and forces due to currents and small waves are also taken into account.This paper describes both the conceptual framework for the proposed model and its practical application in a real engineering situation. The authors also consider how the model might be used as a tool to study how sensitive the behavior of the pipeline is to small changes in the values of the control variables. A detailed description of the actions is considered, especially the ones related to the marine environment such as buoyancy, current, and sea waves. The structural behavior of the pipeline is simulated in the framework of a geometrically nonlinear dynamic analysis. The pipeline is assumed to be a two-dimensional Navier_Bernoulli beam. In the nonlinear analysis an updated Lagrangian formulation is used, and special care is taken regarding the numerical aspects of sea bed contact, follower forces due to external water pressures, and dynamic actions. The paper concludes by describing the implementation of the proposed techniques, using the ANSYS computer program with a number of subroutines developed by the authors. This implementation permits simulation of the two-dimensional structural pipe behavior of the whole construction process. A sensitivity analysis of the bending moments, axial forces, and stresses for different values of the control variables is carried out. Using the techniques described, the engineer may optimize the construction steps in the pipe laying process