Velocity Damping Research Articles

Effect of Internal Friction and the Lamé Ratio on Stoneley Wave Propagation in Viscoelastic Media of Order 1

AbstractThe present work aims to study the propagation of Stoneley wave at the common interface of two distinct homogeneous viscoelastic semi-infinite media. The closed-form expression of the velocity equation has been obtained. The real part of the velocity equation corresponds to the phase velocity of Stoneley wave, whereas the imaginary part corresponds to the damped velocity associated with the Stoneley wave. The Lame ratio associated with Lame’s first constant for the upper/lower viscoelastic semi-infinite medium and the frictional parameter associated with the shear strain for the upper/lower viscoelastic semi-infinite medium have significant effects on the phase velocity and the damped velocity of Stoneley wave associated with a longitudinal/transversal wave in the upper/lower viscoelastic semi-infinite medium. Numerical computation and graphical illustration were carried out to highlight the important peculiarities of the problem. Moreover, as a special case, it was observed that the velocity equa...

Boundary value problemfor multidimensional fractional advection-dispersion equation

In recent time there is a very great interest in the study of differential equations of fractional order, in which the unknown function is under the symbol of fractional derivative. It is due to the development of the theory of fractional integro-differential theory and application of it in different fields.The fractional integrals and derivatives of fractional integro-differential equations are widely used in modern investigations of theoretical physics, mechanics, and applied mathematics. The fractional calculus is a very powerful tool for describing physical systems, which have a memory and are non-local. Many processes in complex systems have nonlocality and long-time memory. Fractional integral operators and fractional differential operators allow describing some of these properties. The use of the fractional calculus will be helpful for obtaining the dynamical models, in which integro-differential operators describe power long-time memory by time and coordinates, and three-dimensional nonlocality for complex medium and processes.Differential equations of fractional order appear when we use fractal conception in physics of the condensed medium. The transfer, described by the operator with fractional derivatives at a long distance from the sources, leads to other behavior of relatively small concentrations as compared with classic diffusion. This fact redefines the existing ideas about safety, based on the ideas on exponential velocity of damping. Fractional calculus in the fractal theory and the systems with memory have the same importance as the classic analysis in mechanics of continuous medium.In recent years, the application of fractional derivatives for describing and studying the physical processes of stochastic transfer is very popular too. Many problems of filtration of liquids in fractal (high porous) medium lead to the need to study boundary value problems for partial differential equations in fractional order.In this paper the authors first considered the boundary value problem for stationary equation for mass transfer in super-diffusion conditions and abnormal advection. Then the solution of the problem is explicitly given. The solution is obtained by the Fourier’s method.The obtained results will be useful in liquid filtration theory in fractal medium and for modeling the temperature variations in the heated bar.

Propagation of Torsional Waves in a Fiber Composite Layer Lying over an Initially Stressed Viscoelastic Half-Space

AbstractThe present study investigates the possibility of torsional surface wave propagation in a fiber composite layer lying over an initially stressed viscoelastic half-space. The closed-form expression for the dispersion relation and damping equation has been obtained. Viscoelasticity of the lower half-space, reinforcement, wave number, and horizontal compressive/tensile initial stress acting in an initially stressed lower half-space have substantial effect on the dispersion curve. For the sake of comparative study, numerical computation and graphical demonstration have been carried out by considering some of the special cases of the problem in addition to the problem itself. A remarkable finding is that reinforcement in the superficial layer favors more the phase velocity and damped velocity of a torsional surface wave as compared with the reinforced free superficial layer. As a special case of the problem, it is found that the obtained dispersion relation is well in agreement with the classical Love ...

Discrete-time command profile for simultaneous travel and hoist maneuvers of overhead cranes

A strategy for generating optimal shaped command-profile for the reduction of residual vibrations in rest-to-rest crane maneuvers is proposed. The technique used is based on generating discrete-time shaped acceleration profile. This profile accommodates simultaneous travel and hoist maneuvers in the presence of damping. The discrete-time acceleration profile is derived analytically using finite step segments. These segments are integrated into an input matrix coupled with a response matrix through a time varying equation of motion of the system. The input acceleration matrix is then optimized to satisfy specific rest-to-rest maneuver conditions. Several parameters are incorporated in the proposed strategy including maneuver time, time step, hoisting speed, damping, and maximum travel velocity and acceleration. Unlike traditional command shapers, the proposed strategy matches the discrete command signal steps to the machine minimum time step of the control hardware used. To achieve an optimum maneuvering time, the shaped command utilizes the full system acceleration and velocity capabilities. The resulting shaped command profile is capable of eliminating travel and residual oscillations. Successful performance of the proposed command shaping strategy is validated through numerical simulations and experiments on a scaled model of an overhead crane.

Stiffness of intermediate unsaturated soil from simultaneous suction-controlled resonant column and bender element testing

Small-strain stiffness properties of unsaturated soils, particularly shear-wave velocity, shear modulus, and material damping, play a fundamental role in the analysis and design of geotechnical infrastructure resting on unsaturated ground, or made of compacted unsaturated soils, as they are subjected to static or dynamic loading. Most conventional soil testing devices, however, are not able to adequately capture this small-strain behavior and hence vastly underestimate the true soil stiffness. This paper introduces a suction-controlled, proximitor-based resonant column device also featuring an independent set of self-contained bender elements for simultaneous testing of soils using both techniques. The work is partly aimed at assessing the suitability of bender elements for soil testing under controlled suction states, as compared to more reliable and fully-standardized procedures such as resonant column or simple shear test methods. A series of resonant column and bender element tests were simultaneously conducted on statically compacted specimens of silty sand for suction states ranging from 50 to 400kPa attained via the axis-translation technique. Particular attention was devoted to the influence of suction over the frequency response curves, damped free-vibration cycles, and cyclic hysteretic stress–strain loops. Results show the critical influence of matric suction on small-strain stiffness properties of compacted silty sand, as well as reasonably good agreement between resonant column and bender element test results.

Entropy generation rate in a mechanical system subjected to a damped oscillation

In the present study, thermodynamic analysis of entropy generation rate pertinent to damping oscillation of a mechanical system is carried out. The entropy generation rate is simulated, incorporating various oscillation characteristics, to examine the effects of natural and damped natural frequencies, initial displacement and velocity on exergy destruction rate. It is found that natural and damped natural frequencies of oscillation have significant effect on the entropy generation rate. Results show that reducing damped natural frequency and increasing natural frequency of oscillation increase the entropy generation rate. Increasing the initial displacement increases the rate of entropy generation; however, decay rate of entropy generation becomes independent of the initial displacement with progressing time.

Dispersion of shear wave propagating in vertically heterogeneous double layers overlying an initially stressed isotropic half-space

The present paper investigates the propagation of horizontally polarised shear wave in distinct vertically heterogeneous double layers overlying an isotropic half-space under horizontal initial stress. The vertical heterogeneity in the uppermost layer is caused due to quadratic variation only in rigidity, whereas vertical heterogeneity in the sandwiched layer is caused due to exponential variation in rigidity and density both. The closed form of velocity equation is obtained which leads to the dispersion equation as its real part and damping equation as its imaginary part. The validation of dispersion relation with the classical case is made by using Debye asymptotic expansion which is the major highlight of this study. The significant effect of the width ratio of the layers, heterogeneity parameters of both the layers and horizontal compressive/tensile initial stress on the phase velocity and damped velocity of SH-wave have been traced out. The comparative study and some important peculiarities have been revealed by means of graphical illustrations.

ORBITAL CIRCULARIZATION OF A PLANET ACCRETING DISK GAS: THE FORMATION OF DISTANT JUPITERS IN CIRCULAR ORBITS BASED ON A CORE ACCRETION MODEL

Recently, gas giant planets in nearly circular orbits with large semimajor axes ($a \sim$ 30--1000AU) have been detected by direct imaging. We have investigated orbital evolution in a formation scenario for such planets, based on core accretion model: i) Icy cores accrete from planetesimals at $\lesssim$ 30AU, ii) they are scattered outward by an emerging nearby gas giant to acquire highly eccentric orbits, and iii) their orbits are circularized through accretion of disk gas in outer regions, where they spend most of time. We analytically derived equations to describe the orbital circularization through the gas accretion. Numerical integrations of these equations show that the eccentricity decreases by a factor of more than 5 during the planetary mass increases by a factor of 10. Because runaway gas accretion increases planetary mass by $\sim$ 10--300, the orbits are sufficiently circularized. On the other hand, $a$ is reduced at most only by a factor of 2, leaving the planets in outer regions. If the relative velocity damping by shock is considered, the circularization is slowed down, but still efficient enough. Therefore, this scenario potentially accounts for the formation of observed distant jupiters in nearly circular orbits. If the apocenter distances of the scattered cores are larger than the disk sizes, their $a$ shrink to a quarter of the disk sizes; the $a$-distribution of distant giants could reflect outer edges of the disks in a similar way that those of hot jupiters may reflect inner edges.

Hybrid viscous damper with filtered integral force feedback control

In hybrid damper systems active control devices are usually introduced to enhance the performance of otherwise passive dampers. In the present paper a hybrid damper concept is comprised of a passive viscous damper placed in series with an active actuator and a force sensor. The actuator motion is controlled by a filtered integral force feedback strategy, where the main feature is the filter, which is designed to render a damper force that in a phase-plane representation operates in front of the corresponding damper velocity. It is demonstrated that in the specific parameter regime where the damper force leads velocity the control is stable and yields a significant improvement in damping performance compared to the pure viscous damper.

Growth of Jupiter: Enhancement of core accretion by a voluminous low-mass envelope

We present calculations of the early stages of the formation of Jupiter via core nucleated accretion and gas capture. The core begins as a seed body of about 350km in radius and orbits in a swarm of planetesimals whose initial radii range from 15m to 50km. The evolution of the swarm accounts for growth and fragmentation, viscous and gravitational stirring, and for drag-assisted migration and velocity damping. During this evolution, less than 9% of the mass is in planetesimals smaller than 1km in radius; ≲25% is in planetesimals with radii between 1 and 10km; and ≲7% is in bodies with radii larger than 100km. Gas capture by the core substantially enhances the size-dependent cross-section of the planet for accretion of planetesimals. The calculation of dust opacity in the planet’s envelope accounts for coagulation and sedimentation of dust particles released as planetesimals are ablated. The calculation is carried out at an orbital semi-major axis of 5.2AU and the initial solids’ surface density is 10gcm-2 at that distance. The results give a core mass of nearly 7.3 Earth masses (M⊕) and an envelope mass of ≈0.15M⊕ after about 4×105 years, at which point the envelope growth rate surpasses that of the core. The same calculation without the envelope yields a core of only about 4.4M⊕.

Theoretical Analysis on Underwater Vibrating Compaction Technology of Scattering-Filling Rubble Stone Layer

This paper studied on the underwater vibrating compaction technology of scattering-filling rubble stone layer. At HongKong-Zhuhai-Macao bridge project, in order to satisfy the project time limit, underwater vibrating compaction technology with hydraulic hammer instead of conventional dynamic compaction technology was used to tamp scattering-filling rubble stone layer with no dead angle in a short time. Owing to the shortage of engineering example, the theoretical analysis was needed before field application. In this paper, the rubble stone layer and the vibration system were simplified to a mechanical model. Vibration system’s work on rubble stone was obtained by mathematical derivation, and effects of parameters were analyzed. The result shows that work on scattering-filling rubble stone layer increases with the increase of system quality, equivalent damping, exciting force and angular velocity and decreases with the increase of equivalent stiffness, water stiffness and buoyancy.

Fluidelastic instability study on a rotated triangular tube array subject to two-phase cross-flow. Part II: Experimental tests and comparison with theoretical results

The extension of the existing theoretical models for fluidelastic instability to two-phase flow is investigated in this paper. Experiments were conducted on a single flexible tube in a rotated triangular tube array subjected to air–water cross-flow. The flow independent damping, added mass and critical velocity for fluidelastic instability were measured. A new formulation of the added mass as a function of the void fraction is proposed. This formulation takes into consideration the reduction of the void fraction around the tubes in a rotated triangular tube array and yields better agreement with the experimental data compared to previous formulations.The quasi-steady and unsteady models were also used to compute the critical velocity for fluidelastic instability. The results of the unsteady model were in very good agreement with the experimental data and subsequently were used to assess the validity of the quasi-steady model over a wider range of mass-damping parameter. The predictions of the quasi-steady model were found to be in good agreement with the experimental data for high void fractions. The use of the time delay parameter, experimentally determined in the first part of this paper, was found to significantly improve the results, especially for high void fractions. However, the limitation of the current setup did not allow measurements at high values of the reduced flow velocity (U/fD) for low void fractions. Nevertheless, this study confirms the validity of the measured time delay parameter and validates the quasi-steady model for the range of void fraction considered (60%–90%).

Finite Element Analysis of Fluid-Elastic Instability of Heat Exchanger Array

From the viewpoint of primary theory of Finite Element Analysis, as well as practical application, the present paper sets up a model for the use of analyzing the fluid-elastic instability of heat exchanger array. In accordance with related compared velocity and mass damping parameter, the author obtains the stability diagram and analyzes the diagram of the array displacement when it reaches the critical value of flow velocity. Accordingly, the instability of heat exchanger array in critical value if flow velocity was verified.

Seismic base-isolation mechanism in liquefied sand in terms of energy

Seismic base isolation effect in a liquefied sand layer was investigated based on soil properties measured in a series of undrained cyclic triaxial tests. Transmission of seismic wave in a soil model consisting of a liquefied surface layer and an underlying nonliquefied layer was analyzed in terms of energy, considering liquefaction-induced changes in S-wave velocity and internal damping. It was found that, between two different base-isolation mechanisms, a drastic increase in wave attenuation in the liquefied layer due to shortening wave length gives a greater impact on the base isolation with increasing thickness of the liquefied layer than the change of seismic impedance between the liquefied and nonliquefied layer. Also indicated was that cyclic mobility behavior in dilative clean sand tends to decrease the seismic isolation effect to a certain extent.

Monte Carlo analysis of total damping and flutter speed of a long span bridge: Effects of structural and aerodynamic uncertainties

Monte-Carlo simulations are a well-established methodology to numerically assess the effect of variations of both mechanical and aerodynamic parameters on the aeroelastic stability of a suspended bridge. In this research paper we use this statistical approach to present a design methodology for the assessment of long span aeroelastic behavior that considers not only the flutter velocity as a unique safety index, as it is common practice, but also the trend of the total damping as a function of the wind velocity.Specifically, several significant in-service conditions are considered. Indeed, wind velocities at in-service conditions are events with a probability much higher than flutter condition, and in these cases a reliability analysis represents an added value in the design process. Therefore the statistical analysis of total damping at in-service conditions is suggested as a useful tool to judge the performance of a structure especially for those structures where the wind–structure interaction represents the capital aspect of the overall design as it happens for the very long span bridges.Given the probability distribution of the input parameters, the Monte Carlo simulations allows one to statistically investigate the aeroelastic stability of the structure, in terms of range of variation of the total damping and flutter velocity, through an eigenvalue analysis. It is also possible to state the probability of not matching the design technical specification and the probability of being in a certain prescribed variation band.The mathematical and statistical background of the design methodology are presented and a case of study is analyzed with reference to the Messina Straits Bridge. The test case was chosen to stress the methodology with a challenging design, where extreme structural and aerodynamic solutions are implemented to reach a main span length of 3300m and where the performances of the structure are deeply bounded to the reliability of the aeroelastic design.

Temperature dependency comparison of ultrasonic wave propagation between injected and sintered thermoplastics

Active touch localization based on a learning process of touch-disturbed broadband bending wave propagation in thin objects is used to transform any 3D surface into a multi-touch interface. Fast prototyping permits easy manufacturing of various 3D shapes that can be as quickly transformed into touch interfaces. The drawback is their weak mechanical stability with temperature. This paper details the temperature behavior differences between a sintered plastic such as polyamide polymer of type PA12 and raw injected Acrylonitrile-Butadiene-Styrene composite polymer (ABS), in particular how their physical parameters such as Young's modulus and Poisson's ratio are affected by temperature. Correlatively, longitudinal and transversal waves within injected and sintered plastics are investigated across a commercial temperature range of 10 °C to 70 °C. The internal grain structure in plastics obtained by laser sintering of powder makes these materials prone to stronger damping and clear non-linear temperature dependency of the shear wave velocity compared with injected plastics.

Boundary feedback stabilization of the telegraph equation: Decay rates for vanishing damping term

We study a semilinear mildly damped wave equation that contains the telegraph equation as a special case. We consider Neumann velocity boundary feedback and prove the exponential stability of the closed loop system. We show that for vanishing damping term in the partial differential equation, the decay rate of the system approaches the rate for the system governed by the wave equation without damping term. In particular, this implies that arbitrarily large decay rates can occur if the velocity damping in the partial differential equation is sufficiently small.

SH-waves in viscoelastic heterogeneous layer over half-space with self-weight

The effect of gravity, heterogeneity and internal friction on propagation of SH-waves (horizontally polarised shear waves) in viscoelastic layer over a half-space has been studied. Using the method of separation of variables, dispersion equation has been obtained and used to recover the damped velocity of SH-waves. Both the real and imaginary parts of dispersion equation are in well agreement with the classical Love wave equation. It has been observed that heterogeneity of the medium affects the velocity profile of SH-wave significantly. Some other peculiarities have been observed and discussed in our study.

Finite-Difference Simulation of Long-Period Ground Motion for the Sagami Trough Megathrust Earthquakes

We perform long-period ground motion simulations for Sagami Trough earthquakes by a three dimensional finite-difference method. The Sagami Trough has been the site of two well-known megathrust earthquakes, the 1923 Taisho- and the 1703 Genroku-type Kanto earthquakes. However, a lack of accumulated historical earthquake records prevents us fromobtaining knowledge of the source model of the next anticipated event for long-period ground motion hazard evaluation. Therefore, it is important to consider numerous possibilities for the unknown source parameters. We compare ground motions for several scenarios with different source area, and with magnitudes ranging from Mw7.9 to 8.6. Peak ground velocity (PGV) within the Kanto basin, including the Tokyo metropolitan area, differs by several times depending on the choice of the source area. The effects of the variety in fault parameters, such as rupture starting points and asperity patterns, are also studied. They can greatly vary the ground motion within the Kanto area, especially in the direction of rupture propagation, suggesting the severe impact of directivity effects. Source models with different rupture starting points produce PGV and 5% damped velocity response (Sv) that vary from each other by as much as 10-20 times. PGV and Sv vary by up to five times depending on the asperity pattern. Our simulation results show that the predicted ground motion for the earthquake scenarios strongly depends on both the source size and other fault parameters of the source models. It is suggested that the seismic hazard assessment requires statistical evaluation of ground motions from as many source models as possible in order to overcome the uncertainties of the source.

A reliability study for the Messina Bridge with respect to flutter phenomena considering uncertainties in experimental and numerical data

The First-Order Reliability Method is applied to bridge flutter instability considering uncertainties in structural damping, flutter derivatives and extreme wind velocity. The baseline is to set each flutter derivative value as a random variable for computing the failure probability by flutter. The flutter speed is obtained by solving the dynamic equilibrium equation. Hence performance function cannot be expressed explicitly. Reliability sampling methods are not considered in this paper because it would require a large computational time. A modification of Hasofer-Lind–Rackwitz-Fiessler algorithm is proposed for avoiding numerical oscillations. Finally, the methodology proposed is applied to the Messina bridge project.