scholarly journals Development of an improved mathematical model for the dynamic response of a sphere located at a viscoelastic medium interface

2021 ◽  
Author(s):  
Hasan Koruk
Keyword(s):  
Mathematical Model ◽  
Dynamic Response ◽  
Elastic Medium ◽  
Young’S Modulus ◽  
Viscoelastic Medium ◽  
Young's Modulus ◽  
Radiation Damping ◽  
Dynamic Responses ◽  
Static Displacement ◽  
Medium Interface

Abstract A comprehensive investigation on the static and dynamic responses of a sphere located at elastic and viscoelastic medium interfaces is performed in this study. First, the mathematical models commonly used for predicting the static displacement of a sphere located at an elastic medium interface are presented and their performances are compared. After that, based on the finite element analyses, an accurate mathematical model to predict the static displacement of a sphere located at an elastic medium interface valid for different Poisson’s ratios of the medium and small and large sphere displacements is proposed. Then, an improved mathematical model for the dynamic response of a sphere located at a viscoelastic medium interface is developed. In addition to the Young’s modulus of the medium and the radius of the sphere, the model takes into account the density, Poisson’s ratio and viscosity of the medium, the mass of the sphere and the radiation damping. The effects of the radiation damping, the Young’s modulus, density and viscosity of the medium and the density of the sphere on the dynamic response of the sphere located at a viscoelastic medium interface are explored. The developed model can be used to understand the dynamic responses of spherical objects located at viscoelastic medium interfaces in practical applications. Furthermore, the proposed model is a significant tool for graduate students and researchers in the fields of engineering, materials science and physics to gain insight into the dynamic responses of spheres located at viscoelastic medium interfaces.

Longitudinal vibration wave in the composite elastic metamaterials containing Bragg structure and local resonator

2020 ◽  
Vol 34 (26) ◽  
pp. 2050232
Author(s):  
Xiaofei Lei ◽  
Peng Chen ◽  
Heping Hou ◽  
Shanhui Liu ◽  
Peng Liu
Keyword(s):  
Mathematical Model ◽  
Young’S Modulus ◽  
Transmission Spectrum ◽  
Strain Energy ◽  
Young's Modulus ◽  
Dynamic Properties ◽  
Longitudinal Vibration ◽  
Total Width ◽  
Bragg Structure ◽  
Vibration Wave

In this paper, a novel composite acoustical hyperstructure of Bragg structure with local resonator is investigated theoretically for discussing the scattering performance of longitudinal vibration wave, its bandgaps are calculated using the established mathematical model. For confirming the veritable existence of bandgap and verifying the correctness of established mathematical model, the transmission spectrum of composite acoustical hyperstructure is also studied using finite-element method, and comparing the vibration transmission spectrum with bandgaps, the results indicate that the established theoretical model can correctly predict longitudinal wave bandgaps. Moreover, the bandgaps and modes shapes are calculated and compared with an unalloyed Bragg structure for probing the dispersion mechanics of composite acoustical hyperstructure, it turned out that local resonator can add one bandgap at the base of Bragg structure and the total bandgaps can be broadened. Further, for discussing the effect of spring of local resonator on bandgaps, bandgap of local resonator with different spring is calculated, the results showed that the total width of BG is larger when Young’s modulus is 1E and 16E, the total width are 772.48 and 774.30 Hz, respectively; as Young’s modulus is 0.5E and 2E, the width of BG are lower, 753.79 and 754.23 Hz, respectively. In view of longitudinal vibration wave inducing structural distortion and vibration energy conversion, the dynamic properties of composite acoustical hyperstructure are studied via strain energy density, the results indicate that reaction formation of local resonator can dissipate strain energy, when the local resonator is not activated (or waveless along with Bragg structure), un-dissipation strain energy.

Dynamic Responses of Plates With Viscoelastic Free Layer Damping Treatment

1996 ◽  
Vol 118 (3) ◽  
pp. 362-367 ◽  
Author(s):  
Sung Yi ◽  
M. Fouad Ahmad ◽  
H. H. Hilton
Keyword(s):  
Young’S Modulus ◽  
Layer Thickness ◽  
Young's Modulus ◽  
Dynamic Responses ◽  
Viscoelastic Damping ◽  
Free Layer ◽  
Modulus Ratio ◽  
Transient Responses ◽  
Damping Materials

Dynamic transient responses of plates with viscoelastic free damping layers are studied in order to evaluate free layer damping treatment performances. The effects of forcing frequencies and temperatures on free-layer viscoelastic damping treatment of plates are investigated analytically. Young’s modulus ratio of structures to viscoelastic damping materials and the damping layer thickness effects on the damping ability are also explored.

scholarly journals Dynamic Response of Railway Bogie Due to Change in Vertical Primary Suspension Stiffness Parameters

2011 ◽  
Vol 5 (1) ◽  
pp. 19
Author(s):  
Karim H. Ali Abood ◽  
R. A. Khan
Keyword(s):  
Mathematical Model ◽  
Dynamic Response ◽  
Lateral Displacement ◽  
Single Point ◽  
Vertical Displacement ◽  
Roll Angle ◽  
Dynamic Responses ◽  
Model Combination ◽  
Suspension Stiffness ◽  
Yaw Angle

A mathematical model of a railway carriage moving on tangent tracks is constructed by deriving the equations of motion concerning the model in which single-point and two-point wheel-rail contact is considered. The presented railway carriage model comprises of carbody and front and rear simple conventional bogie with two leading and trailing wheelets attached to each bogie. The railway carriage is modeled by 31 degrees of freedom which govern vertical displacement, lateral displacement, roll angle and yaw angle dynamic response of wheelset whereas vertical displacement, lateral displacement, roll angle, pitch angle and yaw angle dynamic response of carbody and each of the two bogies. Linear stiffness and damping parameters of longitudinal, lateral and vertical primary and secondary suspensions are provided to the railway carriage model. Combination of linear Kalker's theory and nonlinear Heuristic model is adopted to calculate the creep forces in which introduced at wheel and rail contact patch area. Computer aided-simulation is constructed to solve the governing differential equations of the mathematical model using Runge-Kutta fourth order method. Principle of limit cycle and phase plane approach is applied to realize the stability and to evaluate the concerning critical hunting velocity at which railway carriage starts to hunt. Numerical simulation model is used to study the dynamic responses of a railway carriage bogie subjected to specific parameters of wheel conicity and primary suspension characteristics. A comparison to study the sensitivity of railway carriage bogie to dynamic responses is also presented at different vertical primary suspension stiffness parameters.

Dynamic response of insurance systems with delayed profit/loss sharing feedback to isolated unpredicted claims

1980 ◽  
Vol 107 (4) ◽  
pp. 513-528 ◽  
Author(s):  
L. A. Balzer ◽  
S. Benjamin
Keyword(s):  
Mathematical Model ◽  
Dynamic Response ◽  
Cash Flow ◽  
Dynamic Behaviour ◽  
Feedback Mechanism ◽  
Dynamic Responses ◽  
Insurance System

SummaryA mathematical model of the dynamic behaviour of an insurance system with delayed profit/loss sharing feedback is developed. The model is then subjected to a disturbance input consisting of an isolated group of unpredicted claims and the dynamic responses of cash flow and accumulated cash flow determined. Increasing delays are seen to lead first to undesirable oscillatory responses and eventually to instability. where the responses become unbounded. Such behaviour is noted to be independent of the type of business and to be a property of the feedback mechanism and not related to the type of disturbance input.

scholarly journals Modelling of the Dynamic Young’s Modulus of a Sedimentary Rock Subjected to Nonstationary Loading

Energies ◽  
2020 ◽  
Vol 13 (23) ◽  
pp. 6461
Author(s):  
Mikhail Guzev ◽  
Evgenii Riabokon ◽  
Mikhail Turbakov ◽  
Evgenii Kozhevnikov ◽  
Vladimir Poplygin
Keyword(s):  
Mathematical Model ◽  
Young’S Modulus ◽  
Sedimentary Rock ◽  
Rock Sample ◽  
Young's Modulus ◽  
Point Location ◽  
Load Frequency ◽  
Dynamic Young’S Modulus ◽  
Dynamic Young's Modulus ◽  
The Mathematical Model

This paper presents a mathematical model that reflects the nature of the dynamic Young’s modulus of a dry sedimentary rock during nonstationary uniaxial loading. The model is based on an idealized model of a system suggested by Jaeger J.C. A rock sample is considered as a spring with stiffness, the bottom point of which is fixed, while the upper point carries a mass. A sample experiences dynamic load and the rock matrix response. Displacement of the mass from the equilibrium state sets the variation of the sample’s length. Displacement of all the sample’s points goes according to the same law regardless of the point location. The response of a rock to a disturbing nonstationary load is selected based on the combination of conditions of each experiment, such as the load frequency and amplitude and the mass, length, and diameter of a sample. The mathematical model is consistent with experimental data, according to which an increase in load frequency leads to an increase in the dynamic Young’s modulus for each value of the load. The accuracy of the models is evaluated. The relations underlying the model can be used as a basis to describe the Young’s modulus dispersion of sedimentary rocks under the influence of nonstationary loads.

The Effect of Temperature and Pulling Rate on Young's Modulus of Steel FAS390Q

2011 ◽  
Vol 299-300 ◽  
pp. 337-340
Author(s):  
Bing Yu Liu ◽  
Jing Yuan Yu
Keyword(s):  
Mathematical Model ◽  
Statistical Analysis ◽  
Young’S Modulus ◽  
Power Index ◽  
Young's Modulus ◽  
Heating Temperature ◽  
Absolute Temperature ◽  
Effect Of Temperature ◽  
The Mathematical Model ◽  
The Relationship

The effect of heating temperature and pulling rate on Young's modulus of steel FAS390Q was studied. The results show that the relationship between Young's modulus and reciprocal of absolute temperature follows exponent change, and Young's modulus and pulling rate follows power function relation (power index for 0.189). Crystal vacancy is one of the most important reasons for elasticity phenomenon of steels, which results in the fact that the Young's modulus is affected by pulling rate. Based on the statistical analysis, the mathematical model between Young's modulus of high temperature and pulling rate is established.

scholarly journals Dynamic Responses of a Multilayered Transversely Isotropic Poroelastic Seabed Subjected to Ocean Waves and Currents

2022 ◽  
Vol 10 (1) ◽  
pp. 73
Author(s):  
Xi Chen ◽  
Qi Zhang ◽  
Xiang Yuan Zheng ◽  
Yu Lei
Keyword(s):  
Young’S Modulus ◽  
Young's Modulus ◽  
Dynamic Stiffness ◽  
Transversely Isotropic ◽  
Ocean Waves ◽  
Offshore Structures ◽  
Dynamic Responses ◽  
Vertical Shear ◽  
Waves And Currents ◽  
Poroelastic Seabed

In this study, a semi-analytical solution to the dynamic responses of a multilayered transversely isotropic poroelastic seabed under combined wave and current loadings is proposed based on the dynamic stiffness matrix method. This solution is first analytically validated with a single-layered and a two-layered isotropic seabed and then verified against previous experimental results. After that, parametric studies are carried out to probe the effects of the soil’s anisotropic characteristics and the effects of ocean waves and currents on the dynamic responses and the maximum liquefaction depth. The results show that the dynamic responses of a transversely isotropic seabed are more sensitive to the ratio of the soil’s vertical Young’s modulus to horizontal Young’s modulus (Ev/Eh) and the ratio of the vertical shear modulus to Ev (Gv/Ev) than to the vertical-to-horizontal ratio of the permeability coefficient (Kv/Kh). A lower degree of quasi-saturation, higher porosity, a shorter wave period, and a following current all result in a greater maximum liquefaction depth. Moreover, it is revealed that the maximum liquefaction depth of a transversely isotropic seabed would be underestimated under the isotropic assumption. Furthermore, unlike the behavior of an isotropic seabed, the transversely isotropic seabed tends to liquefy when fully saturated in nonlinear waves. This result supplements and reinforces the conclusions determined in previous studies. This work affirms that it is necessary for offshore engineering to consider the transversely isotropic characteristics of the seabed for bottom-fixed and subsea offshore structures.

Dynamic Responses of Plates With Viscoelastic Damping Treatment

1993 ◽  
Author(s):  
Sung Yi ◽  
M. Fouad Ahmad ◽  
Harry H. Hilton
Keyword(s):  
Young’S Modulus ◽  
Layer Thickness ◽  
Young's Modulus ◽  
Dynamic Responses ◽  
Viscoelastic Damping ◽  
Free Layer ◽  
Modulus Ratio ◽  
Transient Responses ◽  
Damping Materials

Abstract Dynamic transient responses of plates with free damping layers are studied in order to evaluate free layer damping treatment performances. The effects of forcing frequencies and temperatures on free-layer viscoelastic damping treatment of plates are investigated analytically. Young’s modulus ratio of structures to viscoelastic damping materials and the damping layer thickness effects on the damping ability are also explored.

Ultrasonic characterization of the complex Young’s modulus of polymer parts fabricated with microstereolithography

2018 ◽  
Vol 24 (7) ◽  
pp. 1193-1202 ◽  
Author(s):  
Clinton B. Morris ◽  
John M. Cormack ◽  
Mark F. Hamilton ◽  
Michael R. Haberman ◽  
Carolyn C. Seepersad
Keyword(s):  
Dynamic Response ◽  
Young’S Modulus ◽  
Material Properties ◽  
Dynamic Modulus ◽  
Young's Modulus ◽  
Ultrasonic Waves ◽  
Frequency Dependent ◽  
Content Type ◽  
Material Parameters ◽  
Complex Young’S Modulus

Purpose Microstereolithography is capable of producing millimeter-scale polymer parts having micron-scale features. Material properties of the cured polymers can vary depending on build parameters such as exposure. Current techniques for determining the material properties of these polymers are limited to static measurements via micro/nanoindentation, leaving the dynamic response undetermined. The purpose of this paper is to demonstrate a method to measure the dynamic response of additively manufactured parts to infer the dynamic modulus of the material in the ultrasonic range. Design/methodology/approach Frequency-dependent material parameters, such as the complex Young’s modulus, have been determined for other relaxing materials by measuring the wave speed and attenuation of an ultrasonic pulse traveling through the materials. This work uses laser Doppler velocimetry to measure propagating ultrasonic waves in a solid cylindrical waveguide produced using microstereolithography to determine the frequency-dependent material parameters of the polymer. Because the ultrasonic wavelength is comparable with the part size, a model that accounts for both geometric and viscoelastic dispersive effects is used to determine the material properties using experimental data. Findings The dynamic modulus in the ultrasonic range of 0.4-1.3 MHz was determined for a microstereolithography part. Results were corroborated by using the same experimental method for an acrylic part with known properties and by evaluating the natural frequency and storage modulus of the same microstereolithography part with a shaker table experiment. Originality/value The paper demonstrates a method for determining the dynamic modulus of additively manufactured parts, including relatively small parts fabricated with microstereolithography.

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