Vasundara V. Varadan

Bio: Vasundara V. Varadan is an academic researcher from University of Arkansas. The author has contributed to research in topics: Metamaterial & Dielectric. The author has an hindex of 26, co-authored 114 publications receiving 2236 citations.

A review and critique of theories for piezoelectric laminates

Abstract: A review and critique of different laminate theories used for the modeling and analysis of laminated composite beams or plate structures is presented. Many finite-element models use classical laminate theory (CLT), also known as first-order shear deformation theory (FSDT), for the numerical simulation of active structures. The basic assumptions of this model have evolved from those proposed for composite laminate models and are based on thin-plate theory with resulting approximations for the elastic displacement, stress and strain components. In the case of piezoelectric laminates, the approximations spill over into the electric potential and electric field components. No studies and simulations have been documented for the dynamical electromechanical field variations through the thickness of the laminate structure at the resonant frequencies of the structure. This is essential to the understanding of the validity and range of applicability of thin-plate assumptions for active vibration control of structures. On the one hand, thin-plate models result in a computationally tractable model for smart structures, but they should not compromise on the electromechanical coupling effect, which is at the basis of active control. This paper first presents a three-dimensional (3D) complete field solution for active laminates based on a modal, Fourier series solution approach that is used to compute all the through-thickness electromechanical fields near the dominant resonance frequency of a beam plate with two piezoelectric (sensor and actuator) and one structural layers. Then a detailed review of the extant laminate models used for piezoelectric laminates, emphasizing the underlying assumptions in each case, is presented. The non-zero, through-thickness field components are computed under these assumptions. The results of the 3D model and FSDT model are compared for two aspect ratios ((ARs) - thickness-to-width of the layers). An AR of 20 is at the limit of the FSDT and an AR of 50 well within the assumptions of the FSDT. It is concluded that for moderate ARs, several of the approximations of the FSDT are questionable at resonance frequencies. A detailed set of pertinent and general references to papers dealing with piezoelectric laminates is also included. It is hoped that this study will be a reference source for those who want to use FSDT and for those want to understand the dynamical behavior of the internal fields in a smart laminate.

Unique Retrieval of Complex Permittivity and Permeability of Dispersive Materials From Reflection and Transmitted Fields by Enforcing Causality

Abstract: The electromagnetic properties of general classes of materials can be obtained by inverting the measured or numerically simulated reflection ( S 11) and transmission ( S 21) coefficients through a known thickness of a planar slab of the material. The major difficulty is the uncertainty in the change of phase of the transmitted field, if the phase change exceeds 2mpi, m=0,1,2,.... This happens for thick samples as well as for highly dispersive materials. An infinite number of solutions are generated for the imaginary part of the complex wavenumber gamma = alpha + jbeta for different choices of m. The choice of m can be made unique by noting that for a causal medium, gamma is an analytic function of frequency and this results in a Kramers-Kronig-type relation between alpha and beta. Since alpha is independent of the choice of m and, hence, uniquely determined, a Kramers-Kronig reconstruction of beta using alpha will provide a guideline for the correct choice of m. This is a "foolproof" approach even for totally unknown materials since no initial guess is required. Indeed, this approach will work in optics and ultrasonics, and should also be effective for determining the effective refractive index of photonic-bandgap structures that are also highly dispersive.

A multiple scattering theory for elastic wave propagation in discrete random media

Abstract: A multiple scattering theory for elastic wave propagation in a discrete random medium is presented. A self‐consistent multiple scattering formalism using the T matrix of a single scatterer in conjunction with the quasicrystalline approximation (QCA) and a self‐consistent pair correlation function is employed to study the phase velocity and coherent attenuation of elastic waves by a random distribution of cavities and elastic inclusions embedded in an elastic matrix. Both uniform and Gaussian size distributions are assumed. The theoretical results obtained in this study are shown to be in excellent agreement with experimental observations.

Tuning the effective properties of metamaterials by changing the substrate properties

Abstract: Tunable properties of materials are highly desirable in many applications. Metamaterials with negative properties (permittivity, permeability, or both) can have many applications if such properties can be made tunable or can be switched alternatively between positive and negative property behavior. This paper is a numerical study of the effect of substrate properties on the effective properties of a metamaterial slab. We present both simulation results and measurement data for a specific split-ring resonator structure for two different substrate thicknesses and demonstrate very good agreement. Then, using finite element simulation, varying the permittivity of the substrate from 1 to 14 while keeping its physical thickness fixed, we show that the resonance frequency drops from ∼16to∼6GHz. Alternately, when the physical thickness of the substrate is varied from 0.05to2mm, keeping its permittivity fixed, the resonance frequency decreases from ∼13.2to∼9.2GHz. In each case, the effective refractive index is re...

Measurement of the electromagnetic properties of chiral composite materials in the 8-40 GHz range

Abstract: Materials described by the constitutive equations D = eE + βe ∇ × E and B = μH + βμ ∇ × H lack inversion symmetry due to chirality or handedness in their microstructure. In this paper, we describe the first direct measurements of the material properties e, μ, and β for microwave chiral composite materials prepared in our laboratory in the frequency range of 8–40 GHz. We have used both reflection and transmission measurements for normally incident, linearly polarized plane waves in a specially designed free-space facility using spot focusing antennas. Different concentrations of the chiral inclusions in the form of miniature metallic springs that are left-handed only, right-handed only or equally mixed (racemic) have been studied. It is shown that e and μ are comparable for all three samples at a given concentration, but β has equal but opposite values for the left- and right-handed samples, whereas it is nearly zero for the equichiral sample. The values of β thus obtained are compared to estimated values for suspensions of naturally occurring chiral molecules. The accuracy of the measurements is assessed by using the experimental procedure and inversion algorithm for standard materials like quartz. A new technique involving time domain repines has been used to remove the ambiguity that is usually encountered in the inversion of measured S parameters.

I and i

Abstract: There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality. Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

Structural control: past, present, and future

Abstract: This tutorial/survey paper: (1) provides a concise point of departure for researchers and practitioners alike wishing to assess the current state of the art in the control and monitoring of civil engineering structures; and (2) provides a link between structural control and other fields of control theory, pointing out both differences and similarities, and points out where future research and application efforts are likely to prove fruitful. The paper consists of the following sections: section 1 is an introduction; section 2 deals with passive energy dissipation; section 3 deals with active control; section 4 deals with hybrid and semiactive control systems; section 5 discusses sensors for structural control; section 6 deals with smart material systems; section 7 deals with health monitoring and damage detection; and section 8 deals with research needs. An extensive list of references is provided in the references section.

T-Matrix Computations of Light Scattering by Nonspherical Particles: A Review

Abstract: We review the current status of Waterman's T-matrix approach which is one of the most powerful and widely used tools for accurately computing light scattering by nonspherical particles, both single and composite, based on directly solving Maxwell's equations. Specifically, we discuss the analytical method for computing orientationally-averaged light-scattering characteristics for ensembles of nonspherical particles, the methods for overcoming the numerical instability in calculating the T matrix for single nonspherical particles with large size parameters and/or extreme geometries, and the superposition approach for computing light scattering by composite/aggregated particles. Our discussion is accompanied by multiple numerical examples demonstrating the capabilities of the T-matrix approach and showing effects of nonsphericity of simple convex particles (spheroids) on light scattering.