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Vibration, Volume 2, Issue 4 (December 2019) – 4 articles

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Open AccessReview
A Brief Introduction to Nonlinear Time Series Analysis and Recurrence Plots
Vibration 2019, 2(4), 332-368; https://doi.org/10.3390/vibration2040021 - 08 Dec 2019
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Abstract
Nonlinear time series analysis gained prominence from the late 1980s on, primarily because of its ability to characterize, analyze, and predict nontrivial features in data sets that stem from a wide range of fields such as finance, music, human physiology, cognitive science, astrophysics, [...] Read more.
Nonlinear time series analysis gained prominence from the late 1980s on, primarily because of its ability to characterize, analyze, and predict nontrivial features in data sets that stem from a wide range of fields such as finance, music, human physiology, cognitive science, astrophysics, climate, and engineering. More recently, recurrence plots, initially proposed as a visual tool for the analysis of complex systems, have proven to be a powerful framework to quantify and reveal nontrivial dynamical features in time series data. This tutorial review provides a brief introduction to the fundamentals of nonlinear time series analysis, before discussing in greater detail a few (out of the many existing) approaches of recurrence plot-based analysis of time series. In particular, it focusses on recurrence plot-based measures which characterize dynamical features such as determinism, synchronization, and regime changes. The concept of surrogate-based hypothesis testing, which is crucial to drawing any inference from data analyses, is also discussed. Finally, the presented recurrence plot approaches are applied to two climatic indices related to the equatorial and North Pacific regions, and their dynamical behavior and their interrelations are investigated. Full article
(This article belongs to the Special Issue Irregular Engineering Oscillations and Signal Processing)
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Open AccessArticle
An Optimization-Based Framework for Nonlinear Model Selection and Identification
Vibration 2019, 2(4), 311-331; https://doi.org/10.3390/vibration2040020 - 03 Dec 2019
Viewed by 292
Abstract
This paper proposes an optimization-based framework to determine the type of nonlinear model present and identify its parameters. The objective in this optimization problem is to identify the parameters of a nonlinear model by minimizing the differences between the experimental and analytical responses [...] Read more.
This paper proposes an optimization-based framework to determine the type of nonlinear model present and identify its parameters. The objective in this optimization problem is to identify the parameters of a nonlinear model by minimizing the differences between the experimental and analytical responses at the measured coordinates of the nonlinear structure. The application of the method is demonstrated on a clamped beam subjected to a nonlinear electromagnetic force. In the proposed method, the assumption is that the form of nonlinear force is not known. For this reason, one may assume that any nonlinear force can be described using a Taylor series expansion. In this paper, four different possible nonlinear forms are assumed to model the electromagnetic force. The parameters of these four nonlinear models are identified from experimental data obtained from a series of stepped-sine vibration tests with constant acceleration base excitation. It is found that a nonlinear model consisting of linear damping and linear, quadratic, cubic, and fifth order stiffness provides excellent agreement between the predicted responses and the corresponding measured responses. It is also shown that adding a quadratic nonlinear damping does not lead to a significant improvement in the results. Full article
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Open AccessArticle
Field Experiments and Numerical Analysis of the Ground Vibration Isolation of Shock Wave Propagation under Explosion Shock Loading
Vibration 2019, 2(4), 300-310; https://doi.org/10.3390/vibration2040019 - 03 Nov 2019
Viewed by 411
Abstract
Because blast effects can jeopardize the safety of facilities, controlling blast hazards is critical in engineering design and construction. The attenuation and amplification effects generated by blast waves are affected by the topography and terrain of the blast area. This study examined the [...] Read more.
Because blast effects can jeopardize the safety of facilities, controlling blast hazards is critical in engineering design and construction. The attenuation and amplification effects generated by blast waves are affected by the topography and terrain of the blast area. This study examined the effects of topography on the propagation of seismic waves induced by explosions. From the perspective of explosion control, this study adopted explosion mechanics theories and conducted in situ explosion tests to verify finite element numerical simulation results. This study employed the finite element analysis program, to construct a 3D solid structural model to examine fluid–solid coupling, and the Multi-Material Arbitrary Lagrangian–Eulerian algorithm was adopted to develop a dynamic numerical analysis model. By analyzing the propagation of blast waves and ground vibration effects, this study examined the impact of topographical differences on blast effects. The study results may provide a reference for controlling vibration hazards subject to shock waves from explosions, in order to reduce vibrations. Full article
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Open AccessArticle
Friction-Induced Vibration in a Bi-Stable Compliant Mechanism
Vibration 2019, 2(4), 285-299; https://doi.org/10.3390/vibration2040018 - 09 Oct 2019
Viewed by 430
Abstract
This paper investigates friction-induced self-excited vibration in a bi-stable compliant mechanism. A single-degree-of-freedom oscillator, hanged vertically, vibrates on a belt moving horizontally with a constant velocity. The oscillator is excited through the frictional input provided by the belt. The friction coefficient is defined [...] Read more.
This paper investigates friction-induced self-excited vibration in a bi-stable compliant mechanism. A single-degree-of-freedom oscillator, hanged vertically, vibrates on a belt moving horizontally with a constant velocity. The oscillator is excited through the frictional input provided by the belt. The friction coefficient is defined as an exponentially decaying function of the sliding velocity. Due to the specific configuration of spring and damper, the normal contact force is variable. Therefore, the friction force is a function of the system states, namely, slider velocity and position. Employing eigenvalue analysis gives an overview of the local stability of the linearized system in the vicinity of each equilibrium point. It is shown that the normal force, spring pre-compression and belt velocity are bifurcation parameters. Since the system is highly nonlinear, a local analysis does not provide enough information about the steady-state response. Therefore, the oscillating system is studied numerically to attain a global qualitative picture of the steady-state response. The possibility of the mass-belt detachment and overshoot are studied. It is shown that one equilibrium point is always dominant. In addition, three main questions, i.e., possible mass-belt separation, location of stick-slip transition and overshoot are answered. It is proven that the occurrence of overshoot is impossible. Full article
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