Frequency-dependent Material Properties Research Articles

Prediction of the sound pressure response in an enclosed cavity with sound absorbent walls using the CMA and AMA methods

The sound pressure response in an enclosed cavity with sound absorbent walls is predicted using the classical modal analysis (CMA) method and the asymptotic modal analysis (AMA) method. The sound absorbing material is represented as an equivalent fluid with frequency dependent bulk material properties. The equivalent fluid properties can be obtained from either impedance tube test data or based on micro-scale Biot material properties. In the low frequency range, the CMA method is implemented to include the frequency dependent material properties. In the medium and high frequency ranges, when modal density is high, the frequency dependence effects become cumbersome using CMA. The AMA method has been developed as an asymptotic extension of the CMA method for the mid- and high-frequency ranges and is extended here to incorporate the frequency dependence of an equivalent fluid properties of the sound absorbing materials. An enclosed rectangular box subjected to loudspeaker excitation is used to evaluate the effect of absorption materials using the CMA method for the low-frequency range and the AMA method for the mid- and high-frequency ranges. Test data have also been obtained for comparisons of the CMA method in the low frequency range. Using these procedures, the CMA and AMA methods can be applied to represent absorbent materials over a wide frequency range for enclosure architectural design.

Systematic design of 2D and 3D vibroacoustic fluidic cavity sensors using topology optimization

In this research we investigate a novel sensor concept, which utilizes a standing acoustic wave inside a liquid-filled cavity to probe volumetric properties of a fluid analyte. However, realizing a high-Q cavity resonator is a challenge because of low acoustic impedance contrast between liquids and solids. In our previous studies, we surround the cavity resonator with phononic crystal layers that provide a strong cavity resonance within the phononic band gap. The quality factor drastically depends on the geometry of the metamaterial lattice. Therefore, the main aim of this study is to find an optimal material layout of the solid domain around the cavity by employing topology optimization. We formulate the optimization problem as maximization of the Q-factor of the cavity resonance. We consider the sensor as a fully coupled vibroacoustic system, taking into account material losses and frequency-dependent material properties. Since resonance problems are very sensitive to minor variations in geometry, we apply a gray scale suppression constraint to minimize the influence of geometrical uncertainties and make the optimized designs suitable for additive manufacturing

Measurements and estimation of frequency-dependent multi-scale viscoelastic damping properties of materials

The state-of-art viscoelastic property measurement and estimation methods at different frequencies/length scales inherently couple structural effects or sometimes lose accuracy for relevant parameters at smaller length scales in the material. We report a unified approach to measuring and estimating the frequency-dependent viscoelastic damping properties across different frequency scales independently of the specimen size effect and boundary conditions. The Dynamic Mechanical Analysis (DMA) method with three-point bending configuration is extended to higher-fidelity modeling in terms of time–frequency scales and material micro-mechanical scales together. The methodology demonstrates ways to identify the possible sources of undesired dynamics in the measurement process and eliminate those effects. It includes exciter tip contact dynamics in three-point bending configuration, anharmonic energy transfer to different frequencies (fractal bifurcation), and unmodelled artifacts or noise. Critically reviewing the standard DMA procedure with normal mode synthesis, this paper proposes a time–frequency Fourier spectral method that resolves a broader frequency range that extends to even acoustic/ultrasonic wave regimes of viscoelastic damping. An algorithm proposed in this paper with the advanced viscoelastic model with multi-parameters (standard linear solid model) estimates the fundamental material parameters at small length scales, which is more insightful to obtain a frequency-dependent correlation of material response to general dynamic loading. Stiffness and damping properties are estimated from measured data and validated for self-consistencies via different controls regarding static preload, specimen resonance, filtered noise, and model fidelity across the frequency range, and certain consistency and convergence properties of a series solution. The unified approach with a single test will be helpful in the design and evaluation of a wide variety of materials and their applications in vibration and acoustic problems. The proposed technique further demonstrates a novel way to extend low-frequency measurement to high-frequency response modeling.

An Analytical Approach to Locate Short Circuit Fault in a Cable Using Sweep Frequency Response Analysis

In this paper, analytical methods are proposed for the location of a short circuit fault in a power cable using sweep frequency response analysis (SFRA). The impedance spectroscopy is estimated using classical transmission line (TL) theory whereas the driving point impedance function (DPIF) of the cable is proposed to be constructed either by using experimental SFRA data or analytically from the knowledge of the frequency-dependent parameters, material properties, and dimensions of the cable. Finally, an analytical formula is proposed for the estimation of the location of a short-circuit fault using the location of poles and zeros of the impedance function before and after the fault. The formulae are validated using FEM software simulations as well as experimentally on a test cable.

In-situ study of phase changes in glass by impedance spectroscopy and scaling

Transformation in “evolving glass” in ion-conducting silicate glasses, glass ceramics or ceramics containing an intergranular glass is studied by in-situ impedance spectroscopy and scaling laws. Approaches are developed to scale frequency-dependent electrical conductivity and dielectric properties of multiphase ion-conducting materials to derive temperature-independent information on bulk phases and interfaces in presence. A material's scaled electric conductivity provides a unique response over a range of temperature, if the material remains unaltered, but changes, once modifications in the material occur. Therefore, impedance spectroscopy in combination with scaling can be used for tracking modifications in structure, organization, chemistry and microstructure in “evolving (ion-conducting) glass”.In a first part of this work, our approach is validated through application to stable silicate glasses and glass ceramics. Then “evolving glass” is studied in bulk glasses and ceramics with intergranular glass. Examples include ceramming of glass under formation of a glass ceramic, glass-glass phase separation, modification of intergranular glass in ceramics as result of chemical reactions or melt corrosion.Our approach allows to determine onset of phase separation, nucleation or reaction with high precision. It further reveals that nucleation in our exemplary lithium aluminum silicate glass starts with formation of interfaces (phase separation) prior to forming a well-organized crystal lattice. During phase separation in glass, early capacitive contributions in the impedance spectra indicate that the formation of glass-glass interface precedes the compositional changes in the bulk glass.Impedance of refractories is monitored during thermal treatments or corrosion in glass melt at temperatures up to 1600 °C, and glass characteristics of refractories with glass content as low as 3% are extracted. Conductivity and/or level and/or interconnectivity of the refractory's glass are shown to change during thermal treatments due to reactions between glass and crystalline refractory phases, due to phase transformation or, in case of melt corrosion, due to melt infiltration and ion exchange with the melt.In-situ tracking of impedance and application of scaling laws is shown to be able to reveal changes in bulk glass and intergranular glass.

Automatic model order reduction for systems with frequency-dependent material properties

The frequency response of vibro-acoustic systems can be improved by using various forms of damping materials. Their material properties are typically varying with the excitation frequency and are introduced by one or multiple complex-valued functions. Numerical models of such systems are typically large and require efficient solving strategies. In this contribution, a workflow to reduce the numerical complexity of systems containing frequency-dependent damping materials is presented. The functions modeling the material’s frequency-dependent behavior are approximated in rational form and the resulting transfer function is used in a Krylov based moment matching method. The approximation is performed automatically using the adaptive Antoulas–Anderson algorithm. As robust and efficient automatic reduction algorithms are vital for an efficient design process of vibro-acoustic structures, we also show an adaptive procedure to automatically find a reasonably sized reduced model for a given system under a certain tolerance. The algorithms are tested for two forms of damping materials common in vibro-acoustic systems: poroelastic materials following the Biot theory and a constrained layer damping material.

Nonlinear eigenvalue topology optimization for structures with frequency-dependent material properties

Eigenvalue topology optimization problem has been a hot topic in recent years for its wide applications in many engineering areas. In the previous studies, the applied materials are usually assumed as elastic, and the resulting structural eigenfrequencies are obtained by solving a linear eigenvalue problem. However, many engineering materials, such as viscoelastic materials, have frequency-dependent modulus, which results in a more complicated nonlinear eigenvalue problem. This paper presents a systematic study on the nonlinear eigenvalue topology optimization problem with frequency-dependent material properties. The nonlinear eigenvalue problem is solved by a continuous asymptotic numerical method based on the homotopy algorithm and perturbation expansion technique, which involves higher-order differentiation of the nonlinear term and shows a fast convergence. Several schemes are proposed to improve the computational accuracy, applicability, and robustness of the method for the application in topology optimization, including Faà di Bruno's theorem, bisection method, and inverse iteration based eigenvector modification method. Three optimization problems are solved to demonstrate the effectiveness of the developed methods, including the maximization of the fundamental frequency, the eigenfrequency separation interval between two adjacent eigenfrequencies of given orders, and the eigenfrequency separation interval at a given frequency. Numerical examples show the large influence of the frequency-dependent material properties on the optimized results and validate the effectiveness of the developed method.

Optical tweezer measurements of asymptotic nonlinearities in complex fluids.

This article presents micro-medium-amplitude oscillatory shear (μMAOS), a method to measure the frequency-dependent micromechanical properties of soft materials in the asymptotically nonlinear regime using optical tweezers. We have developed a theoretical framework to extract these nonlinear mechanical properties of the material from experimental measurements and also proposed a physical interpretation of the third-order nonlinearities measured in single-tone oscillatory tests. We validate the method using a well-characterized surfactant solution of wormlike micelles, and subsequently employ this technique to demonstrate that the cytoplasm of a living cell undergoes strain softening and shear thinning when locally subjected to weakly nonlinear oscillatory deformations.

Measurement of frequency-dependent shear properties of highly compliant materials using Kibble’s method

We present a method to determine the frequency-dependent properties of highly-compliant materials by measuring the response of rod-like specimens subjected to an applied torque. Kibble’s method, which utilizes a velocity measurement and two electrical measurements, is used to calculate the applied torque on the specimen as a function of frequency. Shear modulus and loss factor in shear are determined by fitting mechanical models to transfer functions between the applied torque and torsional response of the sample. We demonstrate this technique on a prototype apparatus using different polymer materials and specimen geometry. Estimates of the shear modulus and loss factor in shear are determined over a range of frequencies that include the first six torsional resonant modes. These material properties are compared with data obtained using a commercial Dynamic Material Analyzer wherein the samples are excited in a bending mode.

Multiphysics Investigation of an UltrathinVehicular Wireless Power Transfer Module for Electric Vehicles

The functional and spatial integration of a wireless power transfer system (WPTS) into electric vehicles is a challenging task, due to complex multiphysical interactions and strict constraints such as installation space limitations or shielding requirements. This paper presents an electromagnetic–thermal investigation of a novel design approach for an ultrathin onboard receiver unit for a WPTS, comprising the spatial and functional integration of the receiver coil, ferromagnetic sheet and metal mesh wire into a vehicular underbody cover. To supplement the complex design process, two-way coupled electromagnetic–thermal simulation models were developed. This included the systematic and consecutive modelling, as well as experimental validation of the temperature- and frequency-dependent material properties at the component, module and system level. The proposed integral design combined with external power electronics resulted in a module height of only 15mm. The module achieved a power of up to 7.2 kW at a transmission frequency of f0=85kHz with a maximum efficiency of 92% over a transmission distance of 110mm to 160mm. The proposed simulations showed very good consistency with the experimental validation on all levels. Thus, the performed studies provide a significant contribution to coupled electromagnetic and thermal design wireless power transfer systems.

Dynamic-mechanical-thermal analysis of hybrid continuous–discontinuous sheet molding compounds

Sheet molding compounds (SMC) are very promising for the production of lightweight structural components, due to the specific mechanical properties combined with the suitability for a large-scale manufacturing process. Automotive industry already implements SMC materials for structural components in their vehicle concepts. Polymeric materials, hence also fiber reinforced polymers, show a viscoelastic behavior and dynamic-mechanical-thermal analysis (DMTA) is an important method of determining the influence of temperature and loading speed of this material class. In this work, SMC which based on a novel hybrid resin system were examined under bending loads using a electric-dynamic test system to realize high-force dynamic-mechanical-thermal analysis. The examined SMC materials were either discontinuously (Dico) or continuously (Co) reinforced. In addition a hybrid continuous–discontinuous reinforcement was realized by stacking different SMC materials. The mechanical characterization aimed to investigate the influence of the reinforcement architecture and the effect of hybridization on the temperature- and frequency-dependent material properties. Glass transition temperature of the hybrid SMC was comparable to glass transition temperature of the discontinuous glass fiber reinforced component. Compared to the continuous carbon fiber SMC, the decrease of storage modulus of the hybrid SMC could be shifted to higher temperatures and damping was also significantly increased due to hybridization.

Experimental methodology to assess the dynamic equivalent stiffness properties of elliptical orthotropic plates

This paper deals with the dynamic characterisation of plate structures with elliptical orthotropic stiffness properties, using an equivalent thin plate theory using a wave fitting approach. The method consists in projecting the experimentally determined transverse displacement field of a plate on an analytical Green’s function of an elliptical orthotropic plate based on Hankel’s functions. The error between the projected and measured fields is then minimized, varying the characteristics of the function until an optimal fit is reached. The thus obtained characteristics are the two flexural rigidities defining the elliptical orthotropy of the plate, and the orthotropy angle. This fitting procedure is applied at each frequency, enabling the determination of frequency dependent dynamic material properties. The method is applied to a honeycomb sandwich panel to validate the proposed fitting approach. The identified flexural rigidities are compared to the estimations obtained by means of an analytical model and the IWC (Inhomogeneous Wave Correlation) method assuming three different type of plate characteristics (anisotropic, orthotropic and elliptical orthotropic). For the elliptical orthotropic assumption, consistent results are observed between the methods and the model over a large frequency range (from 1 to 50 kHz).

Rheometer enabled study of cartilage frequency-dependent properties

Despite the well-established dependence of cartilage mechanical properties on the frequency of the applied load, most research in the field is carried out in either load-free or constant load conditions because of the complexity of the equipment required for the determination of time-dependent properties. These simpler analyses provide a limited representation of cartilage properties thus greatly reducing the impact of the information gathered hindering the understanding of the mechanisms involved in this tissue replacement, development and pathology. More complex techniques could represent better investigative methods, but their uptake in cartilage research is limited by the highly specialised training required and cost of the equipment. There is, therefore, a clear need for alternative experimental approaches to cartilage testing to be deployed in research and clinical settings using more user-friendly and financial accessible devices. Frequency dependent material properties can be determined through rheometry that is an easy to use requiring a relatively inexpensive device; we present how a commercial rheometer can be adapted to determine the viscoelastic properties of articular cartilage. Frequency-sweep tests were run at various applied normal loads on immature, mature and trypsinased (as model of osteoarthritis) cartilage samples to determine the dynamic shear moduli (G*, G′ G″) of the tissues. Moduli increased with increasing frequency and applied load; mature cartilage had generally the highest moduli and GAG depleted samples the lowest. Hydraulic permeability (KH) was estimated from the rheological data and decreased with applied load; GAG depleted cartilage exhibited higher hydraulic permeability than either immature or mature tissues. The rheometer-based methodology developed was validated by the close comparison of the rheometer-obtained cartilage characteristics (G*, G′, G″, KH) with results obtained with more complex testing techniques available in literature. Rheometry is relatively simpler and does not require highly capital intensive machinery and staff training is more accessible; thus the use of a rheometer would represent a cost-effective approach for the determination of frequency-dependent properties of cartilage for more comprehensive and impactful results for both healthcare professional and R&D.

Development of high frequency equivalent electric circuits for capacitors and chokes taking into account frequency-dependent dielectric and magnetic permittivity properties of dielectric and magnetic materials

Switching of power semiconductor devices in secondary power supplies is the main source of electromagnetic interference. The level of conductive interference must be lowered to meet standards of electromagnetic compatibility. This lowering can be achieved by various methods, including radio interference filters, that are built mainly from inductor coils (chokes) and capacitors. Chokes and capacitors are key elements to design radio interference filters and knowledge of their accurate high-frequency models is required for a wide range of frequencies up to 100 MHz and higher. The article is devoted to development of high-frequency models of capacitors and chokes based on equivalent electric circuits, which parameters are expressed either through electrical-physical values, or through frequency-dependent dielectric permittivity of the dielectric material and magnetic permittivity of the core. Results of modelling are confirmed by impedance measurements of a capacitor with ferroelectric and pyroelectric material used as capacitor’s dielectric and a choke with a core made of nanocrystalline alloy based on GM414 iron. An example of radio interference filter for attenuation of balanced and unbalanced conductive interference is used to consider the negative impact of «spray inductance» of capacitors and «spray capacitance» of chokes.

Dielectric Loss Tangent Extraction Using Modal Measurements and 2-D Cross-Sectional Analysis for Multilayer PCBs

Frequency-dependent electrical properties of dielectric materials are one of the most important factors for high-speed signal integrity design. To accurately characterize material's dielectric loss tangent (tanδ) after multilayer printed circuit board fabrication a novel method was proposed recently to extract tanδ using coupled striplines' measured S-parameters and cross-section geometry. By relating modal attenuation factors to the ratio between the differential and common mode per-unit-length resistances, the surface roughness contribution is eliminated and the contributions of dielectric and conductor loss are separated. Here, we specifically decided to avoid using any physical dielectric model in the extraction algorithm in order to eliminate a need for any a priori information about dielectric behavior. Further analysis and improvement of the tanδ extraction approach is presented in this article. To evaluate the accuracy of the extraction, the impact of errors due to de-embedding, vector network analyzer measurement, and two-dimensional solver's calculation are taken into account by a statistical error model. A confidence interval of extracted tanδ is provided. To describe the frequency dependence of tanδ, a two-term Djordjevic model is proposed to fit the extracted tanδ curve, which guarantees causality and gives better agreement with measured insertion loss compared to the traditional Djordjevic model.

Adaptable boronate ester hydrogels with tunable viscoelastic spectra to probe timescale dependent mechanotransduction

Cells are capable of sensing the differences in elastic and viscous properties (i.e., the ‘viscoelasticity’) of their tissue microenvironment and responding accordingly by changing their transcriptional activity and modifying their behaviors. When designing viscoelastic materials to mimic the mechanical properties of native tissue niches, it is important to consider the timescales over which cells probe their microenvironment, as the response of a viscoelastic material to an imposed stress or strain is timescale dependent. Although the timescale of cellular mechano-sensing is currently unknown, hydrogel substrates with tunable viscoelastic spectra can allow one to probe the cellular response to timescale dependent mechanical properties. Here, we report on a cytocompatible and viscoelastic hydrogel culture system with reversible boronate ester cross-links, formed from pendant boronic acid and vicinal diol moieties, where the equilibrium kinetics of esterification were leveraged to tune the viscoelastic spectrum. We found that viscoelasticity increased as a function of the boronic acid and vicinal diol concentration, and also increased with decreasing cross-linker concentration, where the maximal loss tangent achieved with this system was 0.55 at 0.1 rad s−1. Additionally, we found that the cis-vicinal diols configuration altered the viscoelastic spectra, where a tan δ peak occurred at ~1 rad s−1 for hydrogels functionalized with boronic acid, while an additional peak formed at ≥10 rad s−1 for hydrogels functionalized with both boronic acid and cis-vic-diols. In experiments with NIH-3T3 fibroblasts cultured on these hydrogels, the projected cell area and nuclear area, focal adhesion tension, and subcellular localization of YAP/TAZ were all found to be lower for cells cultured on the viscoelastic hydrogels compared to elastic hydrogels with a similar storage modulus. Despite these differences, there was not a statistically significant relationship between the frequency dependent viscoelastic material properties characterized in this study and cellular morphologies, focal adhesion tension, or the subcellular localization of YAP. While these results demonstrate that mechanotransduction pathways are affected by viscoelasticity, they also suggest that these mechanotransduction pathways are not particularly sensitive to the frequency dependent viscoelastic material properties from 0.1 to 10 rad s−1.

Transient response of sandwich plate with transversely flexible and viscoelastic frequency-dependent material core based on a three-layered theory

In this paper, the dynamic response of a simply supported sandwich plate with viscoelastic transversely flexible core is investigated, analytically using three-layered sandwich plate theory. Hamilton’s principle is employed to obtain governing equations of motion. Also, GHM (Golla–Hughes–McTavish) method is used to model the Frequency-Dependent Material properties of viscoelastic core. Modal superposition method is used to convert partial differential equations of motion to ordinary differential equations with time varying coefficients. Newmark approach is applied to solve the ordinary differential equations, numerically. Results of dynamic analysis in the present model are validated by the results published in the literatures. The natural frequencies and modal loss factors of the sandwich plate are extracted at 30°C and 90°C and effects of geometrical parameters are discussed. The advantages of the GHM model over the classical models such as Kelvin–Voigt are illustrated. The obtained results show that GHM model presents a more accurate description of transient response of the sandwich plate with viscoelastic core by considering the frequency dependency behavior of viscoelastic material. Core flexibility causes a difference between deflection of lower and upper surfaces, so that the three-layered sandwich theory will lead to more exact results with a remarkable deviation from the high-order single-layered theory.

Frequency-dependent material properties of copper and aluminum alloys

In this paper, the dynamic behavior of copper and aluminum alloys as used in electric drive units is investigated. Isothermal frequency sweeps are performed from 0.1 up to 50 Hz at temperatures of up to 400 °C. An evaluation of the test results at a constant frequency of 1 Hz shows a decrease in the storage modulus and an increase in the material damping. Considering all frequencies, a supplementary frequency dependency related to the material composition is detected. The lower the volume fraction of the alloying elements, the higher the impact of temperature and frequency on the material properties. The variations of the material parameters allow applying the time temperature superposition principle to estimate the dynamic behavior beyond the limited tested frequency range and temperatures by fitting the Williams–Landel–Ferry equation. Additional thermal aging of CU-ETP specimens does not affect the storage modulus, but diminishes the material damping. The findings show that each material has to be tested with regard to its respective application, material composition and manufacturing process. Furthermore, they demonstrate the relevance of considering the frequency-dependent material properties of low-alloyed copper and aluminum, especially in case of temperatures above 100 °C.

Parameter determination for the Mini-Oscillator Model of the Viscoelastic Material

The viscoelastic composite structure is widely used in the vibration and noise suppression of thin-walled components. The vibration analysis of viscoelastic composite structures must involve the constitutive equation of viscoelastic materials. The form of the constitutive equation of viscoelastic material has a decisive influence on the dynamic analysis process of viscoelastic composite structures. Since the constitutive relation of the viscoelastic material changes with time, frequency and temperature, the analysis of the dynamic characteristics of the viscoelastic composite structure is greatly complicated. The mini-oscillator model considers the frequency-dependent properties of viscoelastic materials. Therefore, it is widely used in the dynamic analysis of composite structures. Aims at the need of viscoelastic material passive vibration control for viscoelastic composite structures, a method for determining the parameters of mini-oscillator model is proposed. The method obtains the viscoelastic material mini-oscillator model parameters by parameter fitting by the measured viscoelastic material complex modulus data in the frequency domain or other viscoelastic material damping model expressions obtained from experimental data. The results are compared with fractional derivative model. The results show that the mini-oscillator model can correctly describe stress-strain relationship of viscoelastic material and the parameter fitting method proposed in this paper is accurate and effective.

A viscoelastic nonlinear compressible material model of lung parenchyma – Experiments and numerical identification

Characterizing material properties of lung parenchyma is essential in order to describe and predict the mechanical behavior of the lung in health and disease. Hence, we aim to identify the viscoelastic constitutive behavior of viable lung parenchyma with a particular focus on the nonlinear, compressible, and frequency-dependent material properties. To quantify the viscoelastic material behavior of rat lung parenchyma experimentally, we performed uniaxial tension tests with different frequencies, including the whole range of physiological frequencies, in combination with full-field displacement measurements (a total of 120 tests on 30 samples of 5 rats). By means of these experimental measurements, we identified the material parameters of two viscoelastic material models applicable to large three-dimensional deformations, i.e., the standard linear solid model and the model of fractional viscoelasticity. Our aim is to identify one set of material parameters that describes the whole range of physiological frequencies; therefore, we utilized a coupled inverse analysis, which equally incorporates all different tensile tests performed on one sample. The model most suitable for the description of the viscoelastic, nonlinear, and compressible material behavior of viable rat lung parenchyma is the strain energy function Ψ=356.7Pa(I1−3)+331.7Pa(I3−1.075−1)+71.05Pa(J−23I1−3)3+5.766Pa(I313−1)6 in combination with the model of fractional viscoelasticity (τ=0.06454s,α=0.5378, and β=1.856). This material model was validated to describe the complex nonlinear and compressible viscoelastic material behavior of lung parenchyma and can be utilized in finite element simulations of the whole range of physiological frequencies. Based on this model, it will be possible to quantify the stresses and strains of lung tissue during spontaneous and artificial breathing more reliable in the future.