Development of an electrical analogue for modeling natural vibrations of a viscoelastic structure with piezoelectric element

This paper focuses on the development of an equivalent electrical model with lumped parameters capable of describing the natural vibrations of an electromechanical system comprising a viscoelastic structure with a piezoelectric element attached to its surface. The important advantage of the model is that it takes into account the energy losses associated with the viscoelastic properties of the material of the main structure. Two versions of the equivalent electric analogue of the initial electro-viscoelastic system in the form of electric circuits, the elements of which are described by the real or complex quantities, are considered. The approaches to the formulation of the problem of natural vibrations in the developed electric analogue are based on Kirchhoff’s laws for electric circuits and Ohm’s law for alternating current. Special attention is paid to the identification of model parameters. A procedure for determining the parameters for the equivalent electrical model is based on the results gained from the solution of a coupled problem of natural vibrations of the initial electromechanical system; problem formulation is also given here. The effectiveness and reliability of the developed equivalent electric models with lumped parameters for the determination of complex eigenfrequencies of the electromechanical system containing energy dissipation elements are demonstrated by analyzing the behavior of structures in the form of a rectangular plate and a semi-cylindrical shell.

Effect of Prebiotic Polysaccharides on the Rheological Properties of Reduced Sugar Potato Starch Based Desserts

The aim of the study was to assess the possibility of using polysaccharides: inulin and polydextrose in combination with steviol glycosides as sucrose substitutes in starch-based desserts with reduced sugar content and to determine their influence on the rheological properties of these desserts. The samples (starch-milk desserts) were prepared from native potato starch, milk, dye, flavouring agent, and sucrose. The sucrose was partially or completely substituted with steviol glycosides and inulin or polydextrose. The rheological evaluation of the desserts was performed by determining pasting characteristics, viscosity curves, creep and recovery curves and mechanical spectra. Substitution of sucrose with prebiotic polysaccharides modified the rheological characteristics of the starch-milk desserts to a degree depending on the type and level of the substituting agent. Inulin reduced the peak viscosity of starch-milk paste, while it had no effect on the final viscosity of the product, contrary to polydextrose, which increased value of the latter parameter. The desserts exhibited a non-Newtonian, shear-thinning flow behaviour. The use of inulin, in both the highest and the lowest concentrations, significantly changed the consistency coefficient and the flow index values, while such a phenomenon was not observed in the case of polydextrose. The desserts with inulin showed increased values of the storage modulus and reduced susceptibility to stress, manifesting strengthened viscoelastic structure. The results indicate that the both prebiotic polysaccharides can serve as substitutes for sucrose in desserts with reduced sugar contents.

Predicting delayed instabilities in viscoelastic solids

Determining the stability of a viscoelastic structure is a difficult task. Seemingly stable conformations of viscoelastic structures may gradually creep until their stability is lost, while a discernible creeping in viscoelastic solids does not necessarily lead to instability. In lieu of theoretical predictive tools for viscoelastic instabilities, we are presently limited to numerical simulation to predict future stability. In this work, we describe viscoelastic solids through a temporally evolving instantaneous reference metric with respect to which elastic strains are measured. We show that for incompressible viscoelastic solids, this transparent and intuitive description allows to reduce the question of future stability to static calculations. We demonstrate the predictive power of the approach by elucidating the subtle mechanism of delayed instability in thin elastomeric shells, showing quantitative agreement with experiments.

Coseismic and post-seismic gravity disturbance induced by seismic sources using a 2.5-D spectral element method

SUMMARY I present a prescription for computing free-air coseismic and post-seismic gravity changes induced by seismic sources in a viscoelastic earth model. I assume a spherical earth geometry and a 2.5-D calculation, that is, 3-D motions that satisfy the equations of quasi-static equilibrium on a 2-D viscoelastic structure. The prescription permits application to regional gravity computations where a 2-D structure adequately represents the structural heterogeneity. I use a hybrid approach where deformation is computed on a discretized domain and the resulting density perturbations are expanded with spherical harmonics to produce the free-air gravity field. Starting with a solution to the equations of quasi-static displacements in the Laplace transform domain for a given dislocation source, I solve Poisson’s equation using Lagrangian interpolation on spectral element nodes to compute the required deformation quantities that contribute to free-air gravity. A numerical inverse Laplace transform then yields time domain results. This methodology is tested with analytic solutions on a spherically stratified viscoelastic structure, then applied to evaluate the effect of a descending slab of relatively high viscosity on post-seismic gravity in a megathrust faulting setting.

Age-related changes of the vitreous body

Innovative advances in recent years in the study of pathological changes of the posterior segment of the eye including the use of optical coherence tomography which is considered the gold standard for diagnosing vitreoretinal interface pathology, not only significantly expanded the idea of the most prevalent lesions of the structure of posterior eye segment but also discovered absolutely new aspects of their pathology. The review emphasizes the spreading understanding of vitreous body, its age-related changes in the pathology of the posterior eye segment. Two main interrelated processes occurring in the vitreous body - synchysis and syneresis, gradually increasing with age, are considered. Synchysis process begins at the early age and by the age of 70 reaches 50% of the volume of the vitreous body in 70% of the population. Parallelly, syneresis provides strength and plasticity of the entire vitreous volume due to collagen involved in formation of fibrillar frame. An important role in maintaining a stable and viscoelastic structure of the vitreous body, belonging to hyaluronic acid, is discussed, the level of which remains relatively stable at any age due to its constant synthesis. The accumulated data on the structure of age-related and pathological biodegradation of the vitreous body demonstrates inevitable progression of this process leading to age-related posterior vitreous detachment, which is a detachment of the posterior cortical layers of the vitreous body from subjacent retina. Posterior detachment under the influence of age-related changes in the vitreous body has certain stages - from incomplete juxtafoveolar detachment to complete posterior vitreous detachment with clinical retinal changes corresponding to each stage (idiopathic macular holes, lamellar macular tears, macular fibrosis, vitreomacular traction syndrome, myopic foveoschisis). Complete posterior vitreous detachment usually does not cause anatomical retinal disorders and any clinical forms of its diseases, thus, it can be considered as a natural favorable outcome.

Free vibration of frame structures made of Zener type viscoelastic material

A method for determining the dynamic characteristics of structures made of viscoelastic material is presented. The fractional Zener model is used to the describe the rheological properties of materials. All of the elements of a structure must be built of material with identical rheological properties. The solution to the linear eigenvalue problem for some elastic structure and the solution to a single nonlinear algebraic equation are needed to obtain the dynamic characteristics of a viscoelastic structure. Moreover, the frequency response functions are determined in a very efficient way. The results of a representative calculation are presented and briefly discussed.