Analysis of Nonlinear Control Systems

Electromagnetic energy harvesting using magnetic levitation architectures: A review

Similitude theory allows engineers, through a set of tools known as similitude methods, to establish the necessary conditions to design a scaled (up or down) model of a full-scale prototype structure. In recent years, to overcome the obstacles associated with full-scale testing, such as cost and setup, research on similitude methods has grown and their application has expanded into many branches of engineering. The aim of this paper is to provide as comprehensive a review as possible about similitude methods applied to structural engineering and their limitations due to size effects, rate sensitivity phenomena, etc. After a brief historical introduction and a more in-depth analysis of the main methods, the paper focuses on similitude applications classified, first, by test article, then by engineering fields.

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A Review of Similitude Methods for Structural Engineering

Bending vibration of isolated structures has always been neglected when the vibration isolation was studied. Isolated structures have usually been treated as discrete systems. In this study, dynamics of a slightly curved beam supported by quasi-zero-stiffness systems are firstly presented. In order to achieve quasi-zero-stiffness, a nonlinear isolation system is implemented via three linear springs. A nonlinear dynamic model of the slightly curved beam with nonlinear isolations is established. It includes square nonlinearity, cubic nonlinearity, and nonlinear boundaries. Then, the mode functions and the frequencies of the curved beam with elastic boundaries are derived. The schemes of the finite difference method (FDM) and the Galerkin truncation method (GTM) are, respectively, proposed to obtain nonlinear responses of the curved beam with nonlinear boundaries. Numerical results demonstrate that both the GTM and the FDM yield accurate solutions for the nonlinear dynamics of curved structures with nonsimple boundaries. The multi-mode resonance characteristics of the curved beam affect the vibration isolation efficiency. The quasi-zero-stiffness isolators reduce the transmissibility of modal resonances and provide a promising future for isolating the bending vibration of the flexible structure. However, the initial curvature significantly increases the resonant frequency of the flexible structure, and thus the frequency range of the effective vibration isolation is narrower. Furthermore, the quadratic nonlinear terms in the curved beam make the dynamic phenomenon more complicated. Therefore, it is more challenging and necessary to investigate the isolation of the bending vibration of the initial curved structure.

Nonlinear vibration of a slightly curved beam with quasi-zero-stiffness isolators

Auxetic foams counter-intuitively expand (shrink) under stretching (compression). These foams can exhibit superior mechanical properties such as resistance to shear and indentation, improved toughness and energy absorption (EA) under several types of loadings. Their unique deformation mechanism and manufacturing process lead to special multiphysics properties such as variable permeability, synclastic curvature and shape memory. Except for traditional energy absorber stuff, the potential applications of auxetic foams have involved biomedicine, aerospace, smart sensing, etc. However, most of the potential applications are restrained in the theoretical stage due to complicated fabrication and a deficiency of stability. For removing the barrier for practical application, a series of issues remain to be resolved, though the explorations of the manufacture methodologies and potential applications are fruitful in the past decades. We present here a review article discussing the state-of-the-art for manufacturing, characterization and applications of auxetic foams. We also provide a view of the existing challenges and possible future research directions, aiming to state the perspective and inspire researchers to further develop the field of auxetic foams. 

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Manufacturing, characteristics and applications of auxetic foams: A state-of-the-art review

The analysis of nonlinear systems in the frequency domain using Nonlinear Output Frequency Response Functions

In this paper, a nonlinear auto regressive with eXegenous input (NARX) model of nonlinear systems, where the physical parameters of interest for the system design appear explicitly as coefficients in the model, is introduced. The model is referred to as the NARX model with parameters of interest for design (NARX-M-for-D). The output frequency response function (OFRF) in terms of these physical parameters is then introduced for the NARX-M-for-D, and an efficient algorithm is derived to determine the OFRF so as to facilitate the design of nonlinear systems in the frequency domain. Moreover, a general procedure for the design of the physical parameters of the NARX-M-for-D in the frequency domain is proposed, which has the potential to be applied to design a wide range of engineering systems and structures. Finally, two case studies are provided to demonstrate the new OFRF-based nonlinear system design and its significance in engineering applications.

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Design of Nonlinear Systems in the Frequency Domain: An Output Frequency Response Function-Based Approach

Similitude design plays a vital role in the analysis of vibration and shock problems encountered in large engineering equipment. Similitude design, including dimensional analysis and governing equation method, is founded on the dynamic similitude theory. This study reviews the application of similitude design methods in engineering practice and summarizes the major achievements of the dynamic similitude theory in structural vibration and shock problems in different fields, including marine structures, civil engineering structures, and large power equipment. This study also reviews the dynamic similitude design methods for thin-walled and composite material plates and shells, including the most recent work published by the authors. Structure sensitivity analysis is used to evaluate the scaling factors to attain accurate distorted scaling laws. Finally, this study discusses the existing problems and the potential of the dynamic similitude theory for the analysis of vibration and shock problems of structures.

Yunpeng Zhu

Papers

The analysis of nonlinear systems in the frequency domain using Nonlinear Output Frequency Response Functions

Design of Nonlinear Systems in the Frequency Domain: An Output Frequency Response Function-Based Approach

Similitude design for the vibration problems of plates and shells: A review

A novel data-driven model based parameter estimation of nonlinear systems

Topological characteristics and mechanical properties of uniaxially thermoformed auxetic foam