Viscoelastic Structures Research Articles

Complex dispersion analysis of topologically protected interface states in two-dimensional viscoelastic phononic crystals

In this paper, the viscoelastic effect on the topologically protected interface states in two-dimensional (2D) solid phononic crystals (PnCs) is investigated. The valley topological interface states for the 2D in-plane and out-of-plane modes are generated on the interfaces between two PnCs with opposite topological phases. The complex band structures are calculated by the ω-k approach based on the weak formulation of the governing equations of wave motion, which is solved numerically by the finite element method. From the complex band structures, it is demonstrated that even though the material viscoelasticity is introduced into the systems, the topological interface states still exist. However, for the viscoelastic case, the topological interface states becomes the complex wave modes, which means that the interface states inevitably attenuate as they propagate in the viscoelastic PnCs. The amplitude of the elastic waves traveling along the interfaces exhibits an exponential decay, which can be analytically predicted based on the imaginary part of the wave number. Despite suffering from the attenuation due to the material loss, the topological interface states in the viscoelastic PnC structures also exhibit their robustness against the sharp bends or local disorders. In practice, the material loss is ubiquitous, and hence these results are relevant to the PnC devices based on the topological states.

Numerical modeling for viscoelastic sandwich smart structures bonded with piezoelectric materials

Regarding to viscoelastic laminated piezo smart plates and shells, electro-mechanically coupled finite element (FE) formations are derived based on zig-zag hypothesis for vibration and damping analyses. Three lamination configurations are considered in the model, where both elastic layers and viscoelastic layers are assumed to be Reissner–Mindlin plate. The quadratic element is adopted for FE modeling, each node has seven mechanical degrees of freedom (DOFs), which considers the complex shear modulus of viscoelastic materials. The analytical model is first validated by FE simulation of viscoelastic sandwich plates. Later, the effects of various parameters on the damping performance of piezo-viscoelastic laminated cylindrical structures are carried out, e.g. boundary conditions, reinforcement orientation angle, thickness of the viscoelastic core and structural curvature. The present FE modeling and analyses provide a powerful tool to accurately investigate the behaviors of viscoelastic laminated structures.

Wave Propagation Approach for Elastic Transient Responses of Transversely Isotropic Asphalt Pavement under an Impact Load: A Semianalytical Solution

The conventional transfer matrix method, adopted formerly in a semianalytical solution for layered elastic or viscoelastic asphalt pavement structures, has inherent deficiencies, such as ill-condition matrix, numerical overflow, and error accumulation, due to exponential items. This phenomenon is more evident in multilayered dynamic analysis with imperfect interfaces. Moreover, several studies revealed that pavement materials exhibit transverse isotropy in service. Consequently, a novel semianalytical solution methodology, wave propagation approach, was proposed herein to calculate the dynamic responses of asphalt pavement under an impact load considering the transversely isotropic material model and the imperfect interfaces. First, the transfer matrix was established based on matrix theory and wave propagation approach, while the relation between the state vector and wave vector in the transformed domain was constructed simultaneously. Then, combined with the boundary conditions and interface contact conditions, the solution of the wave vector in the transformed domain was derived. Finally, based on Laplace–Hankel inverse transform, the state vector in the time domain was obtained, followed by numerical computation with programming. The accuracy and efficiency of the proposed semianalytical solution, together with the influence regularities of several variables, were discussed. Results showed that due to the absence of positive exponential functions and a large-dimensional matrix, accuracy and efficiency requirements were satisfied during calculation. Moreover, the variation induced by the transversely isotropic properties and interface conditions, presented in the dynamic responses, reiterated that these factors should be considered during the design and analysis of asphalt pavement structures.

On the tri-dimensional constitutive theory identification of linearly viscoelastic solids based on Bayesian framework

Linearly viscoelastic constitutive theories are usually expressed as a Prony series involving fourth order tensors and retardation times. Obtaining the numerical values of the terms involved in such constitutive models from experiments is an ill-posed problem in the sense that many parameter sets can adequately fit experimental data. Considering that the computational time involved in the simulation of the response of viscoelastic structures scales with the number of viscoelastic coefficients, it would be of considerable interest to devise identification strategies yielding the minimum number of parameters. We propose in this work a framework based on the Bayesian inference to reach this objective. We have applied our methodology to three-dimensional experimental data and validated the obtained constitutive theory on an independent data set, for two different viscoelastic materials. Our results demonstrated the robustness and adequacy of our method.

Development of electric actuator hybrid test system and experimental study on viscoelastic damping structures

• A new hybrid test system based on electric actuator which is very simple and low-cost is developed in this study. • A hybrid test of a viscoelastic damping structure under the earthquake excitation is carried out with this new hybrid test system.

Dynamic Stability of Orthotropic Viscoelastic Rectangular Plate of an Arbitrarily Varying Thickness

The research object of this work is an orthotropic viscoelastic plate with an arbitrarily varying thickness. The plate was subjected to dynamic periodic load. Within the Kirchhoff–Love hypothesis framework, a mathematical model was built in a geometrically nonlinear formulation, taking into account the tangential forces of inertia. The Bubnov–Galerkin method, based on a polynomial approximation of the deflection and displacement, was used. The problem was reduced to solving systems of nonlinear integrodifferential equations. The solution of the system was obtained for an arbitrarily varying thickness of the plate. With a weakly singular Koltunov–Rzhanitsyn kernel with variable coefficients, the resulting system was solved by a numerical method based on quadrature formulas. The computational algorithm was developed and implemented in the Delphi algorithmic language. The plate’s dynamic stability was investigated depending on the plate’s geometric parameters and viscoelastic and inhomogeneous material properties. It was found that the results of the viscoelastic problem obtained using the exponential relaxation kernel almost coincide with the results of the elastic problem. Using the Koltunov–Rzhanitsyn kernel, the differences between elastic and viscoelastic problems are significant and amount to more than 40%. The proposed method can be used for various viscoelastic thin-walled structures such as plates, panels, and shells of variable thickness.

Vibration and damping characteristics of CNTR viscoelastic skewed shell structures under the influence of hygrothermal conditions

The vibration and damping characteristics of carbon nanotubes reinforced (CNTR) skewed shell structure under a hygrothermal environment have been investigated using the finite element method. CNT as reinforcing phase and polymer as matrix phase are considered for the nanocomposites (NCs) based viscoelastic skewed shell structure. Dynamic mechanical analysis is used to conduct the creep test for NCs samples which were fabricated, as per ASTM-D4065 standard, and obtained the viscoelastic properties in the frequency domain under different hygrothermal conditions. The shell geometry is defined by considering an arbitrary coordinate system for the skewed shell structure. Finite element modelling has been done with Serendipity element with five degrees of freedom in all eight nodes. The present formulation is based on Koiter’s shell theory and first-order shear deformation theory is considered to incorporate the transverse shear effect based on Mindlin’s hypothesis. The frequency dependant viscoelastic properties are directly used to obtain the frequency responses of the skewed shell panel using fast Fourier transform (FFT) whereas the transient responses are determined using inverse fast Fourier transform (IFFT). An in-house MATLAB code is developed for the numerical simulation and the accuracy of the proposed formulation is validated with available results in literatures and using ANSYS software. A parametric study has been carried out for the skewing angle and CNT volume fraction on the vibration behaviour of different thin and thick NC skewed shell structures under various hygrothermal conditions.

Modal parameter calculation for viscoelastic composite structures from reduced order models

The moduli and loss factors of viscoelastic materials are frequency-dependent, which brings difficulty to solve the eigenvalue problems. In this note, an estimation method for resonance frequencies and loss factors of viscoelastic composite structures from reduced order models is presented. The reduced order model could be constructed from calculated or measured forced vibration data, and there is no need to know the specific structural matrices or to solve the eigenvalue problem of the vibration system directly. Thus, the difficulties caused by frequency-dependent behaviors of moduli and loss factors of viscoelastic materials are avoided. Numerical examples are presented to illustrate and validate the method.

Time-space characteristics of viscoelastic post-seismic deformations corresponding to different rheology models

On a long time (> 1 a) scale, the viscoelastic properties of mantle media significantly affect post-seismic deformation. The stress field disturbance in viscoelastic medium caused by fault slip gradually relax, and the relaxation process and its temporal-spatial characteristics are determined by the viscoelastic model. In this paper, we assume that the mantle media are types of common linear rheological models, i.e., the Burgers body, the standard linear solid, and the Maxell body, and we calculate the dislocation Love number and Green function for a spherically symmetric, non-rotating, viscoelastic, and isotropic (SNRVEI) Earth model. The characteristics of the post-seismic relaxation deformations corresponding to the different models are compared. Our results show that for a short time period, the Burgers body and standard linear solid are similar; while for the long time period, the Burgers body and Maxwell body are similar. This suggests that the observations of post-seismic deformation on the surface have a great potential for the inversion of underground viscoelastic structures. However, the potential of using surface displacement to distinguish different rheological models is limited when the observation period is not long enough.

Effect of Potato Protein on Thermal and Rheological Characteristics of Maize Starches with Different Amylose Contents

AbstractThe aim of this study is to evaluate the effect of potato protein (PP) on thermal and rheological characteristics of maize starches with different amylose contents. Samples are prepared by substituting 0, 1, 2, or 3 parts by weight of PP for 10 parts by weight of high amylose (HA), common (CM), or waxy (WM) maize starch. The PP has a different influence on the gelatinization characteristics of starch. Gelatinization enthalpy of the CM and WM starches increases from 12.08 to 21.76 J g–1 and from 16.95 to 25.62 J g–1, respectively, when the highest amount of the PP is used. Pasting temperature of the HA and CM starches decrease by 0.3–1.56 °C and 0.43–3.60 °C, respectively, while that of WM starch remains unchanged. The HA starch–PP pastes show higher final viscosity (736 × 10–3–2123 × 10–3 Pa s) than the starch‐only paste (580 × 10–3 Pa s). The starch‐protein pastes exhibit a shear‐thinning flow and a phenomenon of thixotropy. Substitution of the part of the HA or CM starch with the PP result in weakened viscoelastic structures of the produced gels, while the WM starch gel structure is strengthened. Results of the study may be useful in designing maize starch‐based foods supplemented with potato protein.

The biofilm matrix scaffold of Pseudomonas aeruginosa contains G-quadruplex extracellular DNA structures

Extracellular DNA, or eDNA, is recognised as a critical biofilm component; however, it is not understood how it forms networked matrix structures. Here, we isolate eDNA from static-culture Pseudomonas aeruginosa biofilms using ionic liquids to preserve its biophysical signatures of fluid viscoelasticity and the temperature dependency of DNA transitions. We describe a loss of eDNA network structure as resulting from a change in nucleic acid conformation, and propose that its ability to form viscoelastic structures is key to its role in building biofilm matrices. Solid-state analysis of isolated eDNA, as a proxy for eDNA structure in biofilms, reveals non-canonical Hoogsteen base pairs, triads or tetrads involving thymine or uracil, and guanine, suggesting that the eDNA forms G-quadruplex structures. These are less abundant in chromosomal DNA and disappear when eDNA undergoes conformation transition. We verify the occurrence of G-quadruplex structures in the extracellular matrix of intact static and flow-cell biofilms of P. aeruginosa, as displayed by the matrix to G-quadruplex-specific antibody binding, and validate the loss of G-quadruplex structures in vivo to occur coincident with the disappearance of eDNA fibres. Given their stability, understanding how extracellular G-quadruplex structures form will elucidate how P. aeruginosa eDNA builds viscoelastic networks, which are a foundational biofilm property.

Development of hybrid test system for three-dimensional viscoelastic damping frame structures based on Matlab-OpenSees combined programming

Most of hybrid test researches utilizing OpenSees are based on the hybrid test system framework software OpenFresco. Such software is convenient but can only be connected to specific test control systems, which limits the widespread application of hybrid test. In this paper, a new hybrid test system based on Matlab-OpenSees combined programming is developed, and the details of hybrid test system including core architecture, test facilities and Matlab-OpenSees system are described. Then, the performance verification of test facilities and Matlab-OpenSees system is conducted. Next, the mechanical properties of viscoelastic damper are tested under different amplitudes, frequencies and temperatures. Finally, the hybrid tests of three-dimensional viscoelastic damping structures are implemented by the developed hybrid test system for the first time. The feasibility and accuracy of hybrid test system based on Matlab-OpenSees combined programming are verified by the seismic response comparison of viscoelastic damping structures obtained by the hybrid test and the finite element numerical simulation. A good damping effect of viscoelastic dampers on the structures under earthquake excitation is demonstrated by comparing the results of the damped and undamped structure.

Self-assembly of multi-component mitochondrial nucleoids via phase separation.

Mitochondria contain an autonomous and spatially segregated genome. The organizational unit of their genome is the nucleoid, which consists of mitochondrial DNA (mtDNA) and associated architectural proteins. Here, we show that phase separation is the primary physical mechanism for assembly and size control of the mitochondrial nucleoid (mt-nucleoid). The major mtDNA-binding protein TFAM spontaneously phase separates in vitro via weak, multivalent interactions into droplets with slow internal dynamics. TFAM and mtDNA form heterogenous, viscoelastic structures in vitro, which recapitulate the dynamics and behavior of mt-nucleoids in vivo. Mt-nucleoids coalesce into larger droplets in response to various forms of cellular stress, as evidenced by the enlarged and transcriptionally active nucleoids in mitochondria from patients with the premature aging disorder Hutchinson-Gilford Progeria Syndrome (HGPS). Our results point to phase separation as an evolutionarily conserved mechanism of genome organization.

Dynamic analyses of viscoelastic three-dimensional structures with advanced one-dimensional finite elements

This paper presents mechanical responses of viscoelastic structures with complicated geometries. The structures are discretized with finite beam elements, whose kinematic theories are derived according to the Carrera Unified Formulation. The governing equations are solved in the Laplace domain to avoid the computation of the convolution integral, which mathematically simulates the viscoelastic constitutive law. The three-dimensional displacement, strain, and stress fields are transformed in the time domain through a numerical inversion algorithm. The numerical simulations are performed on a beam with a hole at the center of its cross-section and on a thick-walled cylindrical shell subjected to various loading and boundary conditions. The comparisons between the present results, analytical predictions, and three-dimensional finite element solutions demonstrate the accuracy of the formulation.

Spectra of Gurtin-Pipkin type of integro-differential equations and applications to waves in graded viscoelastic structures

In this paper, we study spectral properties and spectral enclosures for the Gurtin-Pipkin type of integro-differential equations in several dimensions. The analysis is based on an operator function and we consider the relation between the studied operator function and other formulations of the spectral problem. The theory is applied to wave equations with Boltzmann damping.

Modeling and characterization of viscoelastic origami structures using a temperature variation-based model

The use of origami cores in sandwich structures is attracting increasing attention in many engineering applications due to origami cores’ good compromise between weight and strength and their ability to dissipate energy. Modeling is one of the best tools for estimating design parameters for high performance. The primary outcome of this investigation is a general platform for modeling polymeric origami cores that takes into account the viscoelastic properties of the base material at elevated temperatures and periodic boundary conditions. The model considers a single origami unit cell as a representative unit element, which consists of repeating elements of the origami structure. Periodic boundary conditions were applied in the shared edges of the repeated unit cells. Furthermore, the work shows the results of multi-unit cell origami panel using the viscoelastic model.

NEWMARK ALGORITHM FOR DYNAMIC ANALYSIS WITH MAXWELL CHAIN MODEL

This paper investigates a time-stepping procedure of the Newmark type for dynamic analyses of viscoelastic structures characterized by a generalized Maxwell model. We depart from a scheme developed for a three-parameter model by Hatada et al. [1], which we extend to a generic Maxwell chain and demonstrate that the resulting algorithm can be derived from a suitably discretized Hamilton variational principle. This variational structure manifests itself in an excellent stability and a low artificial damping of the integrator, as we confirm with a mass-spring-dashpot example. After a straightforward generalization to distributed systems, the integrator may find use in, e.g., fracture simulations of laminated glass units, once combined with variationally-based fracture models.

Decay rate for systems of $ m $-nonlinear wave equations with new viscoelastic structures

<abstract> The article discusses the effect of weak and strong damping terms on decay rate for systems of nonlinear $ m $- wave equations with new viscoelastic structures. The factors that allowed system (1.1) to coexist for a long time are the strong nonlinearities in the sources. We showed, under a novel condition on the kernel function in (2.4), a new scenario for energy decay in (3.7) by using an appropriate energy estimates. This result extend the results in ^{[<xref ref-type="bibr" rid="b18">18</xref>,<xref ref-type="bibr" rid="b27">27</xref>]} for system of $ m $-equations inspired from the paper ^{[<xref ref-type="bibr" rid="b1">1</xref>]}. </abstract>

Control of damping of structural vibrations by using different mechanisms of energy dissipation

In current paper an influence of adding piezoelectric elements and connection of their electrodes to external resistive electric circuits on coefficients of vibration damping of piecewise-homogeneous viscoelastic structures was demonstrated on the example of a cantilever plate. The calculations were carried for two options of location of piezoelectric elements in relation to the plate (in the middle of the plate and nearby the clamped edge) and two options of mutual arrangement of a piezoelectric element and a viscoelastic layer (at one side of the plate and at opposite sides). One was demonstrated that damping coefficients for the first two the most energy-intensive vibration modes can be increased in different degree by using different mechanisms of energy dissipation. In this case the most preferable configuration for reaching the highest value of vibration damping coefficients is the option when piezoelectric element and viscoelastic layer located at opposite sides of the plate.

Nonlinear free and forced vibrations of fractional modeled viscoelastic FGM micro-beam

In this paper, nonlinear vibrations of fractional viscoelastic functionally graded micro-beam are studied based on the fractional calculus. The Modified Couple Stress Theory (MCST) is utilized for considering the effect of the micro-scale. The micro-beam is modeled based on the Euler-Bernoulli theory and the Von Karman’s nonlinear strain relations. The viscoelastic part of the micro-beam is considered using the fractional Kelvin-Voigt viscoelastic model. Functionally graded properties vary along the thickness based on a power-law function. The small-scale effects of the micro-beam are modeled using the MCST. Hamiltons principle is used to derive the governing equation of motion. For the solution, the Finite Difference Method (FDM) and the Finite Element Method (FEM) are employed. The FDM is used for discretizing the time domain, and the FEM is used for discretizing the space domain. Effects of the fractional-order, microstructure parameters, and Functionally Graded Material (FGM) properties on the time response of the viscoelastic micro-beam are analyzed numerically. Numerical results show that the fractional-order modeling of the viscoelastic micro-beam can change the behavior of the structure, and increasing the fractional-order, can increase the damping of the system. Numerical simulations also suggest that the effect of the fractional derivative order on the responses of free and forced vibrations is different because there is an important correlation between the fractional-order derivative and the excitation frequency. The results of this paper can be used for modeling the damping of the viscoelastic structures.