Nonlinear Mathematical Models of Metamaterials Defined as “Mass-in-Mass” and “Damper-in-Mass” Chains

To describe dynamic processes in an acoustic (mechanical) metamaterial, there are proposed models that are a one-dimensional chain containing the same masses connected by linearly elastic (or nonlinearly elastic) elements (springs) with the same stiffness. In this case, it is assumed that each mass contains inside itself a series connection of another mass and an elastic element or viscous element (damper).

Viscoelastoplastic Displacement Solution for Deep Buried Circular Tunnel Based on a Fractional Derivative Creep Model

Time-dependent deformation of surrounding rock is a common phenomenon for tunnels situated in soft rock stratum or hard rock stratum with high geo-stress. To describe this phenomenon, a creep model combining the Abel dashpot and a non-Newton viscous element was adopted, and the analytical solution about the viscoelastoplastic deformation for circular tunnel was obtained based on this creep model. Then, the auxiliary tunnel of Jinping II hydropower station was taken as an example to reveal the influence of creep parameters on the creep deformation. The research shows that (1) the creep model can well describe the whole creep stage of rocks, that is, the decay, constant, and accelerated creep stages, (2) the creep deformation has a positive relation with the value of fractional order of Abel dashpot and the order of the non-Newton viscous element, and (3) the creep curves between test results and analytical solutions are well consistent with each other, which demonstrate the validity of the analytical solution.

Modeling the Bending and Recovery Behaviour of Woven Fabrics

On the basis of viscoelastic theory of textile material, the viscoelastic solid model consisting of a spring element and viscous element either in series or parallel is one of the most useful research models to study the mechanical behaviour of fabrics. This paper presents a method to study the bending behaviour of wool/polyester fabrics using a model consisting of the three-element model in parallel with a sliding element on the assumption that the internal frictional moment is a constant during the bending processes. From the needs of practical study, a testing method has been presented to study the bending behaviour of wool/polyester fabrics using a KES-FB3 compression tester. A comparison and analysis of the experimental results and theoretical predictions indicate that the agreement between them is satisfactory.

Viscoelastic properties of tablets from Osborne fractions, pentosans, flour and bread evaluated by creep tests

Little attention has been given to the influence of non-gluten components on the viscoelastic properties of wheat flour dough, bread making process and their products. The aim of this study was to evaluate by creep tests the viscoelastic properties of tablets manufactured from Osborne solubility fractions (globulins, gliadins, glutenins, albumins and residue), pentosans, flour and bread. Hard and soft wheat cultivars were used to prepare the reconstituted tablets. Sintered tablets (except flour and bread) showed similar values to those obtained from the sum of the regression coefficients of the fractions. Gliadins and albumins accounted for about 54% of the total elasticity. Gliadins contributed with almost half of the total viscosity (45.7%), and showed the highest value for the viscosity coefficient of the viscous element. When the effect of dilution was evaluated, the residue showed the highest instantaneous elastic modulus (788.2 MPa). Retardation times of the first element (λ1~ 3.5 s) were about 10 times lower than the second element (λ2~ 39.3 s). The analysis of compliance of data corrected by protein content in flour showed that the residue fraction presented the highest values. An important contribution of non-gluten components (starch, albumins and globulins) on the viscoelastic performance of sintered tablets from Osborne fractions, flour and bread was found.

Viscoelastically Supported Viscous Mass Damper Incorporated into a Seismic Isolation System

This work discusses the application of a two-node apparent mass device, designated as an inerter, which generates inertial resistance forces proportional to relative accelerations between its two nodes, to seismic isolated civil structures. This study employs a viscous mass damper (VMD) consisting of an inerter and a viscous element in parallel arrangement. Although the use of a VMD is effective in reducing relative responses, previous studies have experienced excessive floor response accelerations because the inerter directly transmits ground accelerations to the superstructure. This work examines the acceleration reduction effect of a viscoelastic element arranged in series to the VMD for filtering out the higher frequency components of the ground motion accelerations.

A NEW LINEAR MUSCLE FIBER MODEL FOR NEURAL CONTROL OF SACCADES

A comprehensive model for the control of horizontal saccades is presented using a new muscle fiber model for the lateral and medial rectus muscles. The importance of this model is that each muscle fiber has a separate neural input. This model is robust and accounts for the neural activity for both large and small saccades. The muscle fiber model consists of serial sequences of muscle fibers in parallel with other serial sequences of muscle fibers. Each muscle fiber is described by a parallel combination of a linear length tension element, viscous element and active state tension generator.

Bearing Damping: A Simple, Inexpensive Experiment in System Dynamics

Bearings commonly are modeled as a linear viscous element. This behavior is easily confirmed with a simple, inexpensive experiment using only a wristwatch and a bicycle equipped with a speedometer. With the bicycle inverted so that its rear wheel is free to spin, this experiment involves observing and recording the variation of the angular velocity of the rear wheel as it decelerates from some initial speed. This experiment is a group activity, requiring teamwork to record the data by hand. From the data recorded and an estimate of the moment of inertia of the wheel, students determine the time constant of the system, the degree to which first-order response is exhibited by the system, and the equivalent damping coefficient for the bearings that support the rear wheel. Because of the familiarity of the components of the system being examined, the simplicity of the experiment, the teamwork required in the experiment, and the high degree of agreement between the analytical predictions and the experimental results, this experiment is an excellent experiment in system dynamics.

Viscoelastic properties of the contracting detrusor. II. Experimental approach

Mechanical properties of detrusor muscle were studied with small-amplitude oscillatory volume perturbations in isometrically contracting bladders of anesthetized dogs. Contractions were studied at oscillatory frequencies (f) of 2 and 4 Hz and at bladder volumes (Vbl) ranging from 30 to 110 ml. The magnitude of bladder hydrodynamic stiffness (magnitude of G) increased linearly with mean detrusor pressure (Pdet) while the phase angle remained relatively constant during contraction. The slope (mG) of magnitude of G-Pdet relations had a positive dependence on f and a negative dependence on Vbl. Analysis of oscillatory data, described in the companion paper, was performed using incremental lumped-parameter models consisting of a spring with incremental constant (S = dF/dL), a viscous element with incremental viscosity (b = dF/du), and a mass (m). Only the model where elastic and viscous elements were placed in series with each other and in parallel with mass was compatible with the experimental data. Both S and b increased linearly with effective force (F), defined as Pdet times the cross-sectional area of the intravesical cavity. Slopes of the S-F and b-F relationships (ms and mb) were independent of Vbl and varied only slightly with f. The importance of this finding stems from recognizing that ms and mb correspond to the exponential coefficients of nonlinear series elastic and internal viscosity elements. These parameters, when normalized by resting muscle length, represent fundamental muscle properties independent of muscle cross-sectional area, stretch, or level of activation and compare well with parameters derived from other muscle systems using techniques such as quick releases and isotonic contractions.

Dynamic stiffness profiles in the left ventricle

Diastolic pressure-volume (P-V) curves were calculated on a beat-to-beat basis in the open-chest, pentobarbital-anesthetized dog, using the technique of direct transmitral flow measurement previously described. P-V curves were constructed and the slope (dP/dV) was plotted vs. pressure and time. dP/dV was used as an index of stiffness in each heart and its instantaneous changes with time were followed throughout the diastolic period. The end-diastolic P-V relation based on points from successive cycles during volume loading was found to be exponential. In contrast, the instantaneous P-V relation during any one diastolic period was not exponential. That is, the dynamic dP/dV vs. pressure plot was nonlinear. In the normal heart, stiffness was characterized in early diastole by a negative dP/dV as the ventricle continued to relax, and then frequently decreased prior to a second stiffness rise with atrial augmentation. These findings can be explained by a model containing an element whose deformation is rate dependent, i.e., a parallel viscous element. Stiffness profiles in mitral stenosis where dynamic effects are minimized substantiate this conclusion.