Strategic Damping Placement in Viscoelastic Bandgap Structures: Dissecting the Metadamping Phenomenon in Multiresonator Metamaterials

Energy dissipation in polymeric composite metamaterials requires special mathematical models owing to the viscoelastic nature of their constituents, namely, the polymeric matrix, bonding agent, and local resonators. Unlike traditional composites, viscoelastic metamaterials possess a unique ability to exhibit strong wave attenuation while retaining high stiffness as a result of the “metadamping” phenomenon attributed to local resonances. The objective of this work is to investigate viscoelastic metadamping in one-dimensional multibandgap metamaterials by combining the linear hereditary theory of viscoelasticity with the Floquet-Bloch theory of wave propagation in infinite elastic media. Important distinctions between metamaterial and phononic unit cell models are explained based on the free wave approach with wavenumber-eliminated damping-frequency band structures. The developed model enables viscoelastic metadamping to be investigated by varying two independent relaxation parameters describing the viscoelasticity level in the host structure and the integrated resonators. The dispersion mechanics within high damping regimes and the effects of boundary conditions on the damped response are detailed. The results reveal that in a multiresonator cell, strategic damping placement in the individual resonators plays a profound role in shaping intermediate dispersion branches and dictating the primary and secondary frequency regions of interest, within which attenuation is most required.

Numerical Modeling of pipes conveying gas-liquid two-phase flow

Results of studies of the oscillations of pipelines conveying a two-phase slug flow are presented in the paper. A viscoelastic model of the theory of beams and the Winkler base model are used in the study of pipeline oscillations with a gas-containing slug flowing inside. The Boltzmann-Volterra hereditary theory of the viscoelasticity is used to describe the viscoelastic properties of the pipeline material and earth bases. The effect of gas and liquid phases flow rates, influence of tensile forces in the longitudinal direction of the pipeline, parameters of Winkler bases, parameters of singularity in the heredity kernels and geometric parameters of the pipeline on the oscillations of structures with viscoelastic properties are numerically studied. It is revealed that an increase in the length of the gas bubble zone leads to a decrease in the amplitude and oscillation frequency of the pipeline. The critical rates for a two-phase slug flow are determined. It is revealed that an increase in the soil density of the bases leads to an increase in the critical rate of gas flow. It is shown that an account of viscoelastic properties of structure material and earth bases leads to a decrease in the critical flow rate.

Calculation of structural-inhomogeneous multiply connected shell structures with viscoelastic elements

Using the basic relationships of the hereditary theory of viscoelasticity and asymptotic methods, the problem of natural oscillations of structural-inhomogeneous, multiply connected, axisymmetric shell structures is reduced to an effectively solvable mathematical problem of complex eigenvalues, in which approximate engineering methods are proposed.

An account of the foundation in assessment of earth structure dynamics

An assessment of the dynamic behavior of a plane earth structure with account of its foundation is considered in the paper. A structure with a foundation is considered as an inhomogeneous system, the material of its certain parts is considered elastic or viscoelastic. To assess the effect of the foundation on dynamic behavior of the structure, a finite domain is cut from the foundation and conditions are set at the boundary of this domain that provide energy entrainment from the structure to infinity in the form of the Rayleigh wave. To describe the internal dissipation in material, a linearly hereditary theory of viscoelasticity with the Rzhanitsin kernel is used. A mathematical model, method and algorithm have been developed to assess the dynamic behavior of the structure-finite foundation system. To ensure the adequacy of the mathematical model and to assess the accuracy of the calculation, model problems have been solved when describing the process under consideration. Dynamic behavior of inhomogeneous viscoelastic system of earth dam-foundation with non-reflecting boundary conditions on the boundary of the final domain of the foundation is investigated. In the process of studying the dynamic behavior of inhomogeneous viscoelastic “structure-foundation” systems, a number of mechanical effects.

Computational Experiments to Evaluate the Approaches to the Modeling of Viscoelastic Plates Motion Based on Various Theories

Mathematical and computer modeling of the flutter of elements and units of the aircraft design is an actual scientific problem; its study is stimulated by the failure of aircraft elements, parts of space and jet engines. In view of the complexity of the flutter phenomenon of aircraft elements, simplifying assumptions are used in many studies. However, these assumptions, as a rule, turn out to be so restrictive that the mathematical model ceases to reflect the real conditions with sufficient accuracy. Therefore, results of theoretical and experimental studies are in bad agreement.At present, the problem of panel flutter is very relevant. Improvement of characteristics of military and civil aircraft inevitably requires reducing their weight, and consequently, the rigidity of paneling, which increases the possibility of a panel flutter. The concept of creating the aircraft with a variable shape, which would inevitably lead to a reduction in paneling thickness are actively discussed. Finally, the use of new materials and, in particular, composites, changes physical properties of the panels and can also lead to a flutter.The above-mentioned scientific problem gives grounds to assert that the development of adequate mathematical models, numerical methods and algorithms for solving nonlinear integral-differential equations of dynamic problems of the hereditary theory of viscoelasticity is actual.In connection with this, the development of mathematical models of individual elements of aircraft made of composite material is becoming very important.Generalized mathematical models of non-linear problems of the flutter of viscoelastic isotropic plates, streamlined by a supersonic gas flow, are constructed in the paper on the basis of integral models. To study oscillation processes in plates, a numerical algorithm is proposed for solving nonlinear integro-differential equations with singular kernels. Based on the developed computational algorithm, a package of applied programs is created. The effect of the singularity parameter in heredity kernels on the vibrations of structures with viscoelastic properties is numerically investigated. In a wide range of changes in plate parameters, critical flutter velocities are determined. Numerical solutions of the problem of viscoelastic plate flutter are compared for different models. It is shown that the most adequate theory for investigating a wide class of problems of the hereditary theory of viscoelasticity is the geometric nonlinear Kirchhoff-Love theory with consideration of elastic waves propagation. It is established that an account of viscoelastic properties of plate material leads to 40-60% decrease in the critical flutter velocity.

The legacy of our ancestors' lifestyle: Special Feature

Recent scientific developments are revolutionizing our perception of heredity. These advancements, arising from independent research groups including ours, are reviving the hereditary theory put forth in 1809 by the French evolutionist Jean-Baptiste Lamarck, who postulated that acquired traits could be transmitted to the next generation. With ‘Lamarckian’ inheritance, as a giraffe stretches its neck to reach the leaves of tall trees, neck length becomes longer with subsequent generations. This astounding theory, proposed more than 200 years ago, implies that our health is determined by the chosen lifestyle of our ancestors, long before our own existence.