Search

Dissipation alone can produce counterintuitive topological wave transport that is otherwise absent in a non-dissipative system. This work demonstrates the influence of dissipation on degeneracies that arise in the context of elastic wave transport. The conditions on the parameters necessary to observe non-Hermitian degeneracies in the Bloch spectrum are precisely derived. It will be shown—contrary to the expectation from singularity theory of a linear eigenvalue problem—that a proportionally damped system with commutative damping does not exhibit non-Hermitian degeneracies. The necessity of a non-commutative and non-proportional dissipation model to observe non-Hermitian degeneracies (or exceptional points) is emphasized. Non-proportional dissipation is used to induce a non-Hermitian degeneracy in a local resonance sub-Bragg bandgap of a linear chain, without using negative damping. While Bloch waves are chosen to illustrate the influence of dissipation, the results readily extend to waves in non-periodic media as well as other wave and vibration transport problems. [ABSTRACT FROM AUTHOR]

The manufacturing of low-density paper such as tissue and towel typically involves a key operation called creping. In this process, the wet web is continuously pressed onto the hot surface of a rotating cylinder sprayed with adhesive chemicals, dried in place, and then scraped off by a doctor blade. The scraping process produces periodic microfolds in the web, which enhance the bulk, softness, and absorbency of the final tissue products. Various parameters affect the creping process and finding the optimal combination is currently limited to costly full-scale experiments. In this paper, we apply a one-dimensional (1D) particle dynamics model to systematically study creping. The web is modeled as a series of discrete particles connected by viscoelastic elements. A mixed-mode discrete cohesive zone model (CZM) is embedded to describe the failure of the adhesive layer. Self-contact of the web is incorporated in the model using a penalty method. Our simulation results delineate three typical stages during the formation of a microfold: interfacial delamination, web buckling, and post-buckling deformation. The effects of key control parameters on creping are then studied. The creping angle and the web thickness are found to have the highest impact on creping. An analytical solution for the maximum creping force applied by the blade is derived and is found to be consistent with the simulation. The proposed model is shown to be able to capture the mechanism of crepe formation in the creping process and may provide useful insights into the manufacturing of tissue paper. [ABSTRACT FROM AUTHOR]

Sandwich panels are extensively used in constructional, naval, and aerospace structures due to the high stiffness and strength-to-weight ratios. In contrast, the sound transmission properties are adversely influenced by the low effective mass. Phase velocity matching of structural waves propagating within the panel and the incident pressure waves from the fluid medium leads to coincidence effects resulting in reduced impedance and high sound transmission. Truss-like lattice cores with porous microarchitecture and reduced inter panel connectivity offer the potential to satisfy the conflicting structural and vibroacoustic response requirements. This study combines Bloch-wave analysis and the finite element method to understand wave propagation and hence sound transmission in sandwich panels with a truss lattice core. Three dimensional coupled fluid-structure finite element simulations are conducted to compare the performance of a representative set of lattice core topologies. Potential advantages of sandwich structures with a lattice core are identified. The significance of partial band gaps is evident in the sound transmission loss characteristics of the panels studied. This work demonstrates that, even without optimization, significant enhancements in sound transmission loss performance can be achieved in truss lattice core sandwich panels compared to a traditional sandwich panel employing a honeycomb core under constant mass constraint. [ABSTRACT FROM AUTHOR]

Aneurysms are localized bulges of arteries; and they can rupture with fatal consequences. Complex mechanobiological factors preclude in vivo testing to assess the rupture risk of an aneurysm, and size based criteria are often used in clinical practice to guide surgical interventions. It is often found that tortuous and buckled aneurysms can exceed the size recommended for surgical intervention, and yet do not rupture. This study addresses why buckled aneurysms exhibit this intriguing behavior by combining in vitro inflation experiments on hyperelastic cylindrical tubes with finite element calculations. Using a biologically relevant material model for an arterial wall, we show that buckled aneurysms can grow in size without rupture under favorable arterial pre-tensions. Stretch reversal phenomenon exhibited by arteries governs whether buckling or bulging occurs first. Exponential stiffening favors the axial propagation of an aneurysm instead of radial growth or size. The choice of failure criteria based on Ogden's strain energy function, Gent's first stretch invariant, and Cauchy stress are discussed. Failure maps incorporating post-bifurcation (bulging and buckling) response are constructed to delineate the regimes of growth, buckling and rupture of an aneurysm. [ABSTRACT FROM AUTHOR]

We study the interaction among dispersion, nonlinearity, and disorder effects in the context of wave transmission through a discrete periodic structure, subjected to continuous harmonic excitation in its stop band. We consider a damped nonlinear periodic structure of finite length with disorder. Disorder is introduced throughout the structure by small changes in the stiffness parameters drawn from a uniform statistical distribution. Dispersion effects forbid wave transmission within the stop band of the linear periodic structure. However, nonlinearity leads to supratransmission phenomenon, by which enhanced wave transmission occurs within the stop band of the periodic structure when forced at an amplitude exceeding a certain threshold. The frequency components of the transmitted waves lie within the pass band of the linear structure, where disorder is known to cause Anderson localization. There is therefore a competition between dispersion, nonlinearity, and disorder in the context of supratransmission. We show that supratransmission persists in the presence of disorder. The influence of disorder decreases in general as the forcing frequency moves away from the pass band edge, reminiscent of dispersion effects subsuming disorder effects in linear periodic structures. We compute the dependence of the supratransmission force threshold on nonlinearity and strength of coupling between units. We observe that nonlinear forces are confined to the driven unit for weakly coupled systems. This observation, together with the truncation of higher-order nonlinear terms, permits us to develop closed-form expressions for the supratransmission force threshold. In sum, in the frequency range studied here, disorder does not influence the supratransmission force threshold in the ensemble-average sense, but it does reduce the average transmitted wave energy. [ABSTRACT FROM AUTHOR]

We study nonlinear transmission of wave energy in a finite dissipative periodic structure, which is harmonically driven at one end at a forcing frequency lying within its stop band. We show that there is a threshold for the driving amplitude above which there is a sudden increase in the energy transmitted across the finite structure. This generic phenomenon for discrete nonlinear periodic systems is due to a loss of stability of the periodic solutions that are initially localized to the driven end of the structure. The transmission threshold is therefore predicted analytically based on the corresponding saddle-node bifurcation. The influence of damping, strength of coupling and the type of nonlinearity (hardening or softening) are assessed. In particular, we show that damping may eliminate the transmission phenomenon within a frequency range in the stop band. Increasing the strength of coupling between the units is found to increase the minimum force required for the onset of transmission, and the type of nonlinearity determines on which side of the pass band the enhanced transmission may occur. [ABSTRACT FROM AUTHOR]

A systematic molecular dynamics simulation study is performed to assess the effects of temperature and free edges on the ultimate tensile strength and Young's modulus of a single-layer graphene sheet. It is observed that graphene sheets at higher temperatures fail at lower strains, due to the high kinetic energy of atoms. A numerical model, based on kinetic analysis, is used to predict the ultimate strength of the graphene under various temperatures and strain rates. As the width of a graphene reduces, the excess edge energy associated with free edge atoms induces an initial strain on the relaxed configuration of the sheets. This initial strain has a greater influence on the Young's modulus of the zigzag sheet compared with that of the armchair sheets. The simulations reveal that the carbon-carbon bond length and amplitude of intrinsic ripples of the graphene increases with temperature. The initial out-of-plane displacement of carbon atoms is necessary to simulate the physical behaviour of a graphene when the Nosé-Hoover or Berendsen thermostat is used. [ABSTRACT FROM AUTHOR]

Periodic composites such as acoustic metamaterials use local resonance phenomenon in designing low frequency sub-Bragg bandgaps. These bandgaps emerge from a resonant scattering interaction between a propagating wave and periodically arranged resonators. This paper develops a receptance coupling technique to combine the dynamics of the resonator with the unit cell dynamics of the background medium to analyze flexural wave transmission in a periodic structure, involving a single degree of freedom coupling between the medium and the resonator. Receptance techniques allow for a straightforward extension to higher dimensional systems with multiple degrees of freedom coupling and for easier experimental measurements. Closed-form expressions for the location and width of sub-Bragg bandgaps are obtained. Rigid body modes of the unit cell of the background medium are shown to set the bounding frequencies for local resonance bandgaps. Results from the receptance analysis compare well with Bloch wave analysis and experiments performed on a finite structural beam with periodic masses and resonators. Stronger coupling and inertia of the resonator increase the local resonance bandgap width. Two-fold periodicity widens the Bragg bandgap, narrowed by local resonators, thus expanding the design space and highlighting the advantages of hierarchical periodicity. [ABSTRACT FROM AUTHOR]

Dynamic response of a machine tool structure varies along the tool path depending on the changes in its structural configurations. The productivity of the machine tool varies as a function of its frequency response function (FRF) which determines its chatter stability and productivity. This paper presents a computationally efficient reduced order model to obtain the FRF at the tool center point of a machine tool at any desired position within its work volume. The machine tool is represented by its position invariant substructures. These substructures are assembled at the contacting inteifaces by using novel adaptations of constraint formulations. As the tool moves to a new position, these constraint equations are updated to predict the FRFs efficiently without having to use computationally costly full order finite element or modal models. To facilitate dynamic substructuring, an improved variant of standard component mode synthesis method is developed which automates reduced order determination by retaining only the important modes of the subsystems. Position-dependent dynamic behavior and chatter stability charts are successfully simulated for a virtual three axis milling machine, using the substructurally synthesized reduced order model. Stability lobes obtained using the reduced order model agree well with the corresponding full-order system. [ABSTRACT FROM AUTHOR]

This paper presents two experimental investigations of uncertainty in natural frequencies of linear structures estimated from measured frequency response function under dynamic loading. Experiments were conducted on 100 nominally identical realizations of two structures: a fixed-fixed beam and a thin plate with one edge fixed and the remaining three edges free. In the first set of experiments, on a fixed-fixed beam, 12 identical masses were placed at random spatial locations (generated by a computer) along the length of the beam. Each random arrangement of the masses constitutes one realization, and 100 such realizations were individually subjected to impulse loading to obtain frequency response functions. The total random mass is about 2% of the total mass of the beam. In the second set of experiments, 10 spring-mass oscillator units were attached to the cantilevered plate at random spatial locations determined from a computer-generated random matrix. Although the beam experiments represent parametric uncertainty in the mass matrix, the plate experiment pertain to unmodeled dynamics, which in turn results in randomness in both the mass and stiffness matrices. The results obtained from these experiments may be useful for the validation of many random eigenvalue analysis and prediction methods currently available to structural dynamicist. This paper is limited to comparisons with Monte Carlo simulation of deterministic finite elements models of the two structures. It is concluded that the method of estimation of natural frequencies from frequency response functions and the spatial location of the measurements has significant influence upon the first two moments (mean and standard deviation) of the natural frequency ensemble. Furthermore, although the Monte Carlo simulation estimates of the mean and standard deviation are in reasonable agreement with experiments at higher frequencies, the probability density function differ appreciably, within the limits of the sample size investigated in this study. [ABSTRACT FROM AUTHOR]

Rayleigh quotients in the context of linear nonconservative vibrating systems with vis- cous and nonviscous dissipative forces are studied in this paper. Of particular interest is the stationarity property of Rayleigh-like quotients for dissipative systems. Stationarity properties are examined based on the perturbation theory. It is shown that Rayleigh quotients with stationary properties exist for systems with proportional viscous and non- viscous damping forces. It is also shown that the stationarity property of Rayleigh quotients in the case of nonproportional damping (viscous and nonviscous) is conditional upon the diagonal dominance of the modal damping matrix. [ABSTRACT FROM AUTHOR]

The phenomenon of elastic boundary layers under quasistatic loading is investigated using the Floquet-Bloch formalism for two-dimensional, isotropic, periodic lattices. The elastic boundary layer is a region of localized elastic deformation, confined to the free edge of a lattice. Boundary layer phenomena in three isotropic latti...e topologies are investigated: the semiregular Kagome lattice, the regular hexagonal lattice, and the regular fully triangulated lattice. The boundary layer depth is on the order of the strut length for the hexagonal and the fully triangulated lattices. For the Kagome lattice, the depth of boundary layer scales inversely with the relative density. Thus, the boundary layer in a Kagome lattice of low relative density spans many cells. [ABSTRACT FROM AUTHOR]

Plane wave propagation in infinite two-dimensional periodic lattices is investigated using Floquet-Bloch principles. Frequency bandgaps and spatial filtering phenomena are examined in four representative planar lattice topologies: hexagonal honeycomb, Kagomé lattice, triangular honeycomb, and the square honeycomb. These topologies exhibit dramatic differences in their long-wavelength deformation properties. Long-wavelength asymptotes to the dispersion curves based on homogenization theory are in good agreement with the numerical results for each of the four lattices. The slenderness ratio of the constituent beams of the lattice (or relative density) has a significant influence on the band structure. The techniques developed in this work can be used to design lattices with a desired band structure. The observed spatial filtering effects due to anisotropy at high frequencies (short wavelengths) of wave propagation are consistent with the lattice symmetries. [ABSTRACT FROM AUTHOR]

A viscoelastic solid sheet fed from a certain height towards a rigid horizontal plane folds on itself provided that there is no slip. This phenomenon commonly occurs in the manufacturing process of textile and paper products. In this paper we apply a particle dynamics model to investigate this phenomenon. At a low feeding velocity and low viscosity, the inertial effect and the viscous dissipation within the sheet are negligible, and our model successfully reproduces the existing quasistatic results in the gravitational regime. As the feeding velocity and the viscosity of the sheet increase, the folding process changes significantly. The length of the folds decrease and the "rolling back" motion of the sheet vanishes. In the inertial regime, a scaling law between the fold length and the feeding velocity is derived by balancing the kinetic energy and the elastic bending energy involved in folding, which is verified by the simulation. It is found that above a critical feeding velocity, the folding morphology transforms from line contact into point contact with the sheet exhibiting a lemniscate-like pattern. Finally, a phase diagram for the folding morphology is constructed. The results presented in this work may offer some insights into the high-speed manufacturing of paper and fabric sheets. [ABSTRACT FROM AUTHOR]

Abstract The manufacturing of low-density tissue paper involves a key process called creping, which consists of pressing and bonding a wet web onto a drying cylinder rotating at a high speed, and scraping it off subsequently. Creping is understood as a periodic debonding and buckling process which creates a series of micro-folds in the paper. Despite the fact that fibers in the web undergo significant plastic deformation during creping, previous models treat the web as a single thin elastic layer. In this paper we apply a particle dynamics model to investigate the effects of plasticity on creping. A bilinear elastoplastic material model with associated kinematic hardening rule is used to describe the constitutive behavior of the web and a discrete cohesive zone model is implemented for the interfacial delamination. Inclusion of the plasticity of the web leads to significant decrease in creping force and wavelength. A virtual tensile test is performed to predict the stretch and stiffness of the simulated tissue paper. It is found that the stretch increases and the stiffness decreases as the ratio between the creping amplitude and the wavelength increases, thus leading to a higher softness. The simulated tensile stress-strain curve shows significant nonlinearity and qualitatively agrees with experiments. Finally, we explore the "explosive bulk" regime by modeling the web as three individual layers connected by inter-layer bonds. A phase diagram for the creping regimes is constructed. Our simulations indicate that the "explosive bulk" is more likely to occur when the interfacial fracture energy is high and the cohesion of the web is weak. [ABSTRACT FROM AUTHOR]

Fiber networks are ubiquitous. The networks of interest to this study are distinguished from the widely studied planar random fiber networks (RFN) by their low areal density (grammage), preferential orientation, and fiber curl. Oriented networks are created through a high speed manufacturing process called forming in paper making. A dilute suspension of elastic fibers in water impinges on a moving wire to create a formed network. A discrete element method (DEM) based forming model is developed that incorporates the qualitative effects of fluid shear (preferred fiber orientation) and viscous drag during drainage (fiber conformation to the wire topography). Virtual tensile tests performed on thus formed networks reveal that the tensile response is initially softer due to non-affine deformation, and anisotropic due to preferential orientation. Consequently, an orientation dependent power law with a non-unique exponent emerges for the scaling of modulus and strength with the network density. Tensile test simulations reveal the re-alignment of fibers along the loading direction, and strong strain localization resulting in a few fibers (∼ 1%) carrying the imposed strain energy. Fiber curl and orientation are observed to govern the degree of non-affine response, stiffness, and strain localization, suggesting that controlling the degree of anisotropy and fiber curl offers the possibility to design networks for specific stiffness and specific strength. • Significant degree of non-affinity in low grammage networks. • Anisotropy in tensile properties and non-affinity in oriented networks. • Bending is important in networks with curled fibers. • Strain energy distribution in fiber networks is highly skewed. • Shear-lag and affine predictions do not hold for low grammage networks. [ABSTRACT FROM AUTHOR]

Low density tissue papers are soft fiber networks with a folded internal microstructure—deliberately imparted during a widely used manufacturing process, called dry creping. The folded crepe structure enhances a tissue paper's specific volume, stretchability, and softness. The influence of the micron-scale crepe structure on nonlinear tensile response is studied using experiments and a discrete elasto-plastic model (DEM). First, 'Crepe Index (CI)' is defined to quantify the crepe structure. An optical method to obtain high resolution edge images is developed to measure the CI. The relationship between the CI and tensile failure strain and initial elastic stiffness is assessed: the failure strain is observed to be proportional to CI, while the dependence of initial stiffness on CI is unclear–presumably due to the damage induced through the de-densification of fiber layers during the manufacturing. The effect of CI on initial stiffness and failure strain is assessed using DEM by idealizing the creped paper as a segmented triangular wave—each segment governed by a bilinear elastoplastic constitutive law and a strength-based failure criterion. The model reveals that the initial stiffness of a creped sheet depends not only on the CI but also on sheet-thickness to crepe-wavelength ratio, and the stiffness of the uncreped sheet. The failure strain is found to be stretching dominated at low CI, and bending dominated at higher CI. Qualitative agreement is found between the DEM and experiments. The significance of both the material and the geometric non-linearity on the macroscale tensile response of a creped tissue paper emerges from this study. • Tissue paper is a complex architected fiber network. • Imaging method is developed to visualize folded internal structure of a tissue paper at micron scale. • Nonlinear tensile response of a tissue paper originates from the folded geometry and the fiber network. • Crepe Index is introduced to quantify crepe structure and correlate with failure strain. strain. [ABSTRACT FROM AUTHOR]

Deformation properties of venous stents based on braided design, chevron design, Z design, and diamond design are compared using in vitro experiments coupled with analytical and finite element modelling. Their suitability for deployment in different clinical contexts is assessed based on their deformation characteristics. Self-expanding stainless steel stents possess superior collapse resistance compared to Nitinol stents. Consequently, they may be more reliable to treat diseases like May-Thurner syndrome in which resistance against a concentrated (pinching) force applied on the stent is needed to prevent collapse. Braided design applies a larger radial pressure particularly for vessels of diameter smaller than 75 % of its nominal diameter, making it suitable for a long lesion with high recoil. Z design has the least foreshortening, which aids in accurate deployment. Nitinol stents are more compliant than their stainless steel counterparts, which indicates their suitability in veins. The semi-analytical method presented can aid in rapid assessment of topology governed deformation characteristics of stents and their design optimization. [ABSTRACT FROM AUTHOR]