Identification of the dynamic characteristics of nonlinear structures

Imperial Users onl

Ni/Ni3C Core-Shell Nanochains and Its Magnetic Properties: One-Step Synthesis at low temperature

One-dimensional Ni/Ni3C core-shell nanoball chains with an average diameter by around 30 nm were synthesized by means of a mild chemical solution method using a soft template of trioctylphosphineoxide (TOPO). It was revealed that the uniform Ni nanochains were capped with Ni3C thin shells by about 1 to 4 nm in thickness and each Ni core consists of polygrains. The coercivity of the core-shell nanochains is much enhanced (600 Oe at 5 K) and comparable with single Ni nanowires due to the one-dimensional shape anisotropy. Deriving from the distinctive structure of Ni core and Ni3C shell, this architecture may possess a possible bi-functionality. This unique architecture is also useful for the study on the magnetization reversal mechanism of one-dimensional magnetic nanostructure.Comment: 17 pages, 6 figur

Nonlinear structural and vibration analysis of graphene sheets

A nonlinear differential quadrature based method is developed and successfully applied to structural and vibration analyses of general multi-layered graphene sheets in the presence of geometrical nonlinearities and nonlinear van der Waal forces. Important nonlinear displacement characteristics of multi-layered graphene sheets have first been established. Due to relatively large magnitudes of van der Waal forces, different layers of graphene undergo similar deflections under external loadings and nonlinearities in van der Waal forces do not contribute much to the overall nonlinear structural behaviour. In the case of vibration analysis, two groups of modes each having its own unique characteristics have been identified and are defined as the lower classical bending modes and the higher van der Waal enhanced modes. For lower classical bending modes, the layers vibrate in phase and their natural frequencies are only affected by geometrical nonlinearities but decoupled from nonlinear van der Waal forces. For higher van der Waal enhanced modes however, the nonlinear vibration characteristics are dictated by the nonlinear van der Waal forces. These observations are valid for different boundary conditions and different layers of graphene sheets that have been investigated. Van der Waal forces and their effects are properly modelled and examined, together with effects of key physical parameters. The results presented for the first time provide accurate and wholesome studies on the nonlinear structural and vibration characteristics of graphene sheets. These results are important to structural designs of graphene sheets which are increasingly being deployed for innovative engineering applications such as nano-electro-mechanical systems (NEMS)

Commentary on “Discussion on ‘function-weighted frequency response function sensitivity method for analytical model updating’ by A. Esfandiari and M. Sanayei"

We would like to thank A. Esfandiari and M. Sanayei [1] for their interests and comments on our work “function-weighted frequency response function sensitivity method for analytical model updating” previously published in the Journal of Sound and Vibration [2]. The primary objective of our work was to explore the possibilities of further enhancing the numerical solution process associated with finite element model updating using FRF data by exploiting the known mathematical characteristics of the receptance sensitivities at each design point during the iterations. There is some obvious misunderstanding about the basic concept that we sought to convey in our paper [2], either because of the way we presented the material which somehow lacks clarity, or because of the mathematical complexity associated with the work, leading to difficulties in understanding well how the proposed method actually works. This commentary serves to address these concerns by (i) introducing simple generic mathematical examples to illustrate how the proposed method works, without getting involved with the mathematical complexities of model updating practice, (ii) further discussing the mathematical concept and deriving analytically the key receptance sensitivities and, (iii) providing additional numerical results to support and demonstrate the key characteristics of receptance sensitivities

Micro-systems mechanics VOLUME II

Including: 3 parts. TiNi thin films have attracted much attention in recent years as intelligent and functional materials because of their unique properties. TiNi thin film based micro-actuators will become the actuator of choice in many aspects in the rapidly growing field of micro-electro-mechanical systems. In this report, TiNi and TiNiCu films were successfully prepared by co-sputtering of a TiNi target and a separate Ti or Cu targets. Some critical issues and problems in the successfully development of TiNi thin films were discussed, including preparation and characterization considerations, residual stress and adhesion, frequency improvement, fatigue and stability, patterning and modeling of behavior as well as functionally graded or composite thin films. Comparison was made of TiNi SMA microactuation with other microactuation methods. Different types of MEMS applications we have done so far (such as microgrippers, micropumps, micromirror, etc.) were reported and the prospects for future advances in fabrication process and device development were discussed

Eigenvalue and eigenvector derivatives of fractional vibration systems

Dynamic characterizations of fractional vibration systems have recently attracted significant research interest. Increasingly, successful applications of fractional derivatives have been found to the modeling of mechanical damping, vibration transmissions, improved fractional vibration controls and nonlinear vibration analyses. To facilitate further development, the eigenvalue problem including its derivatives, which are the central issues of vibration analysis, have to be fully established. This paper examines how eigenvalue and eigenvector derivatives of fractional systems can be derived when system matrices become functions of physical design parameters. First, new important orthonormal constraints are proposed since the modes are no longer orthonormal to the mass matrix, in this case due to its complex and frequency dependent nature. Next, new methods of eigenvector derivatives are developed for distinct eigenvalues for the cases of complete, incomplete and single mode modal data. Realistic and practical FE models incorporating fractional derivatives in the form of viscoelastic supports are employed to demonstrate the numerical accuracy and computational efficiency of the proposed methods. However, when repeated eigenvalues are considered due to structural spatial symmetries, the eigenvector space degenerates and further differentiation of system matrices are required in order to uniquely determine the eigenvector derivatives. Consequently, a new and effective general method is developed which can be applied to compute eigenvector derivatives of repeated eigenvalues with any multiplicity m. A simplified turbine bladed disk vibration model which is known to have repeated eigenvalues due to its cyclic symmetry, is then used to demonstrate the accuracy and salient features of the proposed method

Frequency response functions and modal analysis of general nonviscously damped dynamic systems with and without repeated modes

This paper seeks to examine some important outstanding theoretical issues of general nonviscously damped vibration systems. Exact frequency response functions (FRFs) have been developed based on Cauchy's residue theorem for the case of repeated eigenvalues with arbitrary multiplicities. The new theory developed has not only extended the classical mode superposition principle, but also laid the necessary theoretical foundation for the modal analysis of nonviscously damped systems whose eigenvalues are nondistinct. Effective numerical methods for the computations of elastic and nonviscous modes are suggested. The unique feature, contribution and significance of nonviscous modes to FRFs have been examined and discussed. Since nonviscous modes are real and are hence similar in characteristics to structural rigid-body modes with zero frequency, a new and accurate method has been developed to lump their contributions to FRFs into a single artificial rigid-body mode, thereby eliminating the necessity of computing them which is numerically challenging. Traditional restrictions of symmetry have not been imposed on system matrices and neither state-space nor additional coordinates have been employed throughout theoretical development. Numerical examples are given to illustrate the new theory and methods developed in the paper

New theoretical developments on eigenvector derivatives with repeated eigenvalues

Many different methods have been developed since the pioneering works of Mills-Curran (1988) and Dailey (1989) on eigenvector derivatives with repeated eigenvalues. In spite of the increasing mathematical complexities witnessed in many of the newly emerged methods, some underlying fundamental theories governing the eigenvector derivatives have neither been much discussed, nor fully established to date. The present approach seeks to fill such an outstanding theoretical gap and to lay down the necessary theoretical foundation on which existing methods can be mathematically unified and further improved in numerical accuracy and computational efficiency. The particular solutions of eigenvector derivatives generally required have been derived in terms of modal properties, thereby avoiding the computationally expensive and potentially erroneous procedure of solving a set of algebraic equations of system dimension. The contributions of higher unavailable modes have been theoretically derived, enhancing the practical applicability of the proposed method to the general case where only partial eigensolutions are made. To avoid degeneration of eigenvector space in the case of repeated eigenvalues, a concept of global design variable is developed in which all intended multivariate design modifications are grouped into a single global variable to which eigenvector derivatives are derived, rendering real major applications of the proposed method to the predictions of structural design modifications. A discrete parameter model of a turbine bladed disk assembly, which is known to have many pairs of repeated eigenvalues due to its cyclic symmetry, as well as a finite element model of a cantilevered beam with large DOFs have been employed. Numerical results have demonstrated the accuracy and the practical applicability of the proposed new theoretical developments, as well as the proposed new method

A new method for the accurate measurement of higher-order frequency response functions of nonlinear structural systems

Higher-order frequency response functions (FRFs) are important to the analysis and identification of structural nonlinearities. Though much research effort has been devoted recently to their potential applications, practical issues concerning the difficulty and accuracy of higher-order FRF measurement have not been rigorously assessed to date. This paper presents a new method for the accurate measurement of higher-order FRFs. The method is developed based on sinusoidal input, which is ideal for exciting a nonlinear structure into desired regimes with flexible control, and the correlation technique, which is a novel signal processing method capable of extracting accurate frequency components present in general nonlinear responses. The correlation technique adopted is a major improvement over Fourier transform based existing methods since it eliminates leakage and aliasing errors altogether and proves to be extremely robust in the presence of measurement noise. Extensive numerical case studies have been carried out to critically assess the capability and accuracy of the proposed method and the results achieved are indeed very promising. Interesting nonlinear behavior such as frequency shift and jump have been observed in first-, second- and third-order FRFs, as well as solitary islands which have been identified over which higher-order FRFs virtually do not change as input force amplitude varies. Higher-order FRFs over such solitary islands are essentially their theoretical counterparts of Volterra transfer functions which can be measured with very low input force and can be profitably employed for the identification of physical parameters of structural nonlinearities. Subsequently, a nonlinear parameter identification method has also been developed using measured higher-order FRFs and results are presented and discussed.MOE (Min. of Education, S’pore

Micro-systems mechanics VOLUME I

Including: 3 parts. System integration and miniaturization have become one of the most distinct trends of modern technological development where electro-mechanical devices are highly miniaturized and integrated into micro-systems to meet various challenging industrial and commercial applications. However, as these micro-systems are increasingly miniaturized to become smaller in size and lighter in weight, new structural mechanics related issues such as structural dynamics, kinematics, tribology, acoustics, mechanical properties of materials, fluid mechanics, thermal- mechanical interactions etc. become ever more acute and need to be carefully considered in micro-system designs, fabrication and assembly to optimize system performances. Most of these mechanics issues will assume different roles in different forms as compared with those involved in conventional system designs and even new mechanics/physics phenomena will emerge as the feature size of a micro-system becomes ever increasingly small. In order to improve design capabilities and hence performance of micro-systems, it is obvious that these various mechanics issues need to be rigorously studied and thoroughly understood to enable accurate modeling, characterization and control methodologies needed to be developed for micro-system applications