We use Anderson or vibration localization in coupled microcantilevers as an extremely sensitive method to detect the added mass of a target analyte. We focus on the resonance frequencies and eigenstates of two nearly identical coupled gold-foil microcantilevers. Theoretical and experimental results indicate that the relative changes in the eigenstates due to the added mass can be orders of magnitude greater than the relative changes in resonance frequencies. Moreover this sensing paradigm possesses intrinsic common mode rejection characteristics thus providing an alternate way to achieve ultrasensitive mass detection under ambient conditions.

/pdf/ultrasensitive-mass-sensing-using-mode-localization-in-y13lktqqww.pdf

Ultrasensitive mass sensing using mode localization in coupled microcantilevers

This analysis is concerned with the derivation of a “diffuse field” reciprocity relationship between the diffuse field excitation of a connection to a structural or acoustic subsystem and the radiation impedance of the connection. Such a relationship has been derived previously for connections described by a single degree of freedom. In the present work it is shown that the diffuse–field reciprocity relationship also arises when describing the ensemble average response of connections to structural or acoustic subsystems with uncertain boundaries. Furthermore, it is shown that the existing diffuse–field reciprocity relationship can be extended to encompass connections that possess an arbitrary number of degrees of freedom. The present work has application to (i) the calculation of the diffuse field response of structural–acoustic systems modeled by Finite Elements, Boundary Elements, and Infinite Elements; (ii) the general calculation of the Coupling Loss Factors employed in Statistical Energy Analysis (SEA); and (iii) the derivation of an alternative analysis method for describing the dynamic interactions of coupled subsystems with uncertain boundaries (a generalized “boundary” approach to SEA).

On the reciprocity relationship between direct field radiation and diffuse reverberant loading.

Research and applications of viscoelastic vibration damping materials: A review

Recent research advances in the dynamic behavior of shells: 1989–2000, Part 2: Homogeneous shells

An effective technique for analyzing the generation of second harmonics of Lamb modes in elastic plates is presented. The nonlinearity of the wave equation governing the wave propagation ensures that there is second-harmonic generation accompanying primary Lamb mode propagation. This nonlinearity may be treated as a second-order perturbation of the linear elastic response. Using a second-order perturbation approximation and a modal analysis approach, the complicated problems of the generation of second harmonics of Lamb modes have been investigated. The fields of the second harmonics of Lamb modes in elastic plates are considered as superpositions of the fields of a series of double-frequency Lamb modes. The solutions provide physical insight into the generation of second harmonics with a cumulative growth effect, and the corresponding second-harmonic solutions. Although Lamb modes are dispersive, the cumulative growth effect of the second harmonics does exist under some conditions. The influence of Lamb mode dispersion on second-harmonic generation is considered.

Analysis of second-harmonic generation of Lamb modes using a modal analysis approach

This text offers a clear and refreshing exposition of the dynamics of mechanical systems from an engineering perspective. Basic concepts are thoroughly covered, then applied in a systematic manner to solve problems in mechanical systems that have recognisable applications to engineering practice. All theoretical discussions are accompanied by numerous illustrative examples, and each chapter offers a wealth of homework problems. The treatment of the kinematics of particles and rigid bodies is extensive. In this new edition, the author has revised and reorganized sections to enhance understanding of physical principles, and he has modified and added examples, as well as homework problems. The new edition also contains a thorough development of computational methods for solving the differential equations of motion for constrained systems.

Advanced Engineering Dynamics

A global, single-input-multi-output (SIMO) implementation of the algorithm of mode isolation and application to analytical and experimental data

This study of the surface interaction between a submerged body and the surrounding fluid begins by developing reciprocity relations between alternative pressure and normal velocity distributions on the wetted surface. A corollary of these principles is proof of the symmetry of the matrix representing the acoustic contribution to the structural impedance, even in situations where the acoustic relation between surface pressure and normal velocity is not symmetric. The reciprocity properties lead to two eigenvalue problems, whose solution yields velocity and pressure radiation modes, each of which decouples the complex surface acoustic power. The matrices required to obtain the eigensolutions are shown to arise in the ordinary course of modeling fluid–structure interaction. Further analysis reveals that the velocity and pressure modes occur in a one‐to‐one correspondence, with a relative phase angle that decreases monotonically as the radiated power increases relative to the reactive power. Using the radiati...

Complex power, reciprocity, and radiation modes for submerged bodies

On the Relationship Between Veering of Eigenvalue Loci and Parameter Sensitivity of Eigenfunctions

As an initial step in the extension of the surface variational principle (SVP) to an assumed modes analysis of vibratory displacement and surface pressure on submerged axisymmetric structures subjected to arbitrary nonsymmetric loading, the present study considers an arbitrary harmonic excitation of an elastic plate. Two configurations, in which the supporting baffle is a thin rigid disk or an infinite plane, are considered. Fourier series expansions of the azimuthal dependence of pressure and displacement are shown to be uncoupled, with each harmonic being governed by equations that are similar in form to those for the analogous axisymmetric problem. Recursion relations using coefficients developed in the course of solving the axisymmetric problem are shown to substantially expedite the evaluation of the additional azimuthal harmonics. Results for a force located at r=a/2 when ka=3.35, where a is the radius of the plate, are presented in terms of the radial variation associated with each harmonic, as wel...

Jerry H. Ginsberg

Papers

Advanced Engineering Dynamics

A global, single-input-multi-output (SIMO) implementation of the algorithm of mode isolation and application to analytical and experimental data

Complex power, reciprocity, and radiation modes for submerged bodies

On the Relationship Between Veering of Eigenvalue Loci and Parameter Sensitivity of Eigenfunctions

Asymmetric vibration of a heavily fluid‐loaded circular plate using variational principles