scholarly journals Deformation of elastic-viscous beams by explosive load in water

2021 ◽  
pp. 56-63
Author(s):  
Геннадий Тимофеевич Володин ◽  
Денис Сергеевич Кочергин
Keyword(s):  
Separation Of Variables ◽  
Viscosity Coefficient ◽  
Equation Of Motion ◽  
Analytical Relationship ◽  
Strain Rates ◽  
Explosive Load ◽  
Condensed Explosive ◽  
Elastic Line ◽  
Deformation Work ◽  
Minimum Deformation

Представлено аналитическое решение задачи о деформировании взрывом сосредоточенного заряда конденсированного взрывчатого вещества (ВВ) балки, материал которой чувствителен к скорости деформации. Влияние внешней среды (воды) на процесс и результаты деформирования учитывается введением присоединенной массы. Коэффициент вязкости и модуль упругости в фиксированных интервалах скоростей деформирования определяются из экспериментов. Для этих параметров, характеризующих материал балки при импульсном деформировании, получена аналитическая взаимосвязь и нижняя граница значений для коэффициента вязкости. Решение задачи найдено методом разделения переменных в определяющем уравнении движения. При этом форма упругой линии балки для каждого момента времени выбрана, исходя из требования выполнения граничных условий и принципа минимума работы деформирования. An analytical solution to the problem of deformation by an explosion of a concentrated charge of a condensed explosive (HE) of a beam, the material of which is sensitive to the rate of deformation, is presented. The influence of the external environment (water) on the process and the results of deformation is taken into account by introducing the added mass.The viscosity coefficient and the modulus of elasticity in fixed intervals of strain rates are determined from experiments. For these parameters, which characterize the material of the beam under impulse deformation, an analytical relationship and a lower limit of values for the viscosity coefficient are obtained. The solution to the problem is found by the method of separation of variables in the governing equation of motion. In this case, the shape of the elastic line of the beam for each moment of time is selected based on the requirement to fulfill the boundary conditions and the principle of minimum deformation work.

The Effect of Penetration Rate on the Strength of Remolded Clay and Sand Samples

1975 ◽  
Vol 12 (3) ◽  
pp. 336-348 ◽  
Author(s):  
Umesh Dayal ◽  
John H. Allen
Keyword(s):  
Penetration Rate ◽  
Velocity Ratio ◽  
Viscosity Coefficient ◽  
Analytical Relationship ◽  
Granular Soils ◽  
Cohesive Soils ◽  
Static Tests ◽  
Proportionality Constant ◽  
Penetration Tests ◽  
Penetration Velocity

The penetration rate effect on the strength of clay and sand was studied by constant velocity penetration tests performed with various velocities up to 2.662 f.p.s. (81.14 cm/s). The clay and sand targets were of various strengths and moisture contents. The construction of the penetrometer is similar to that used in static tests, and in each test the cone resistance, sleeve friction, and penetration velocity were recorded.Experimental results indicated that for granular soils the effects of penetration velocity on cone and sleeve friction resistances are insignificant, whereas, for cohesive soils, the increase in penetration velocity causes an increase in the cone and friction resistances. It is found that for the cohesive soils the ratio of dynamic to static strength is directly proportional to the logarithm of the penetration velocity ratio. The proportionality constant of this relationship defined as soil viscosity coefficient depends on the physical properties of the soil and the soil strength and its value increases as the strength of the soil decreases. For the tested soils various values of the soil viscosity coefficient are proposed for different strength ranges. The validity of the analytical relationship is established for penetration velocities ranging from 0.0044 f.p.s. (0.13 cm/s) to 18 f.p.s. (550 cm/s).

scholarly journals Multistable Slip of a One-degree-of-freedom Spring-slider Model in the Presence of Thermal-pressurized Slip-weakening Friction and Viscosity

2017 ◽  
Author(s):  
Jeen-Hwa Wang
Keyword(s):  
Numerical Simulations ◽  
Fixed Points ◽  
Time Variation ◽  
Maximum Velocity ◽  
Viscosity Coefficient ◽  
Equation Of Motion ◽  
Degree Of Freedom ◽  
Model Parameters ◽  
Maximum Displacement ◽  
The One

Abstract. This study is focused on multistable slip of earthquakes based on a one-degree-of-freedom slider-slider model in the presence of thermal-pressurized slip-weakening friction and viscosity by using the normalized equation of motion of the model. The major model parameters are the normalized characteristic displacement, Uc, of the friction law and the normalized viscosity coefficient, η, between the slider and background plate. Analytic results at small slip suggest that there is a solution regime for η and γ (= 1 / Uc) to make the slider slip steadily. Numerical simulations exhibit that the time variation in normalized velocity, V / Vmax (Vmax is the maximum velocity), obviously depends on Uc and η. The effect on the amplitude is stronger due to η than due to Uc. In the phase portrait of V / Vmax versus the normalized displacement, U / Umax (Umax is the maximum displacement), there are two fixed points. The one at large V / Vmax and large U / Umax is not an attractor; while that at small V / Vmax and small U / Umax can be an attractor for some values of η and Uc. When Uc 

MOLECULAR DYNAMIC STUDY OF A SINGLE DISLOCATION IN A TWO-DIMENSIONAL LENNARD–JONES SYSTEM

2003 ◽  
Vol 14 (04) ◽  
pp. 407-421 ◽  
Author(s):  
MIGUEL ROBLES ◽  
VILLE MUSTONEN ◽  
KIMMO KASKI
Keyword(s):  
Constant Strain Rate ◽  
Equation Of Motion ◽  
Dislocation Motion ◽  
Strain Rates ◽  
Interactive Simulation ◽  
Two Dimensional ◽  
Single Dislocation ◽  
Lennard Jones ◽  
Quasi Static Process ◽  
Dynamics Method

In this work the motion of a single dislocation in a two-dimensional triangular lattice is studied by using classical Molecular Dynamics method with the Lennard–Jones inter-atomic potential. The dislocation motion is investigated with an interactive simulation program developed to track automatically the movement of lattice defects. Constant strain and constant strain-rate deformations were applied to the system. From constant strain simulations a curve of shear stress versus dislocation velocity is obtained, showing a nonlinear power law relation. An equation of motion for the dislocation is proposed and found to be applicable when the movement of dislocation follows a quasi-static process. Numerical simulations at different strain rates show an elastic-to-plastic transition that modifies the dynamics of the dislocation motion.

scholarly journals Multistable slip of a one-degree-of-freedom spring-slider model in the presence of thermal-pressurized slip-weakening friction and viscosity

2017 ◽  
Vol 24 (3) ◽  
pp. 467-480 ◽  
Author(s):  
Jeen-Hwa Wang
Keyword(s):  
Maximum Velocity ◽  
Nonlinear Behavior ◽  
Viscosity Coefficient ◽  
Equation Of Motion ◽  
Degree Of Freedom ◽  
Model Parameters ◽  
Maximum Displacement ◽  
Linear Behavior ◽  
Fourier Spectra ◽  
The One

Abstract. This study is focused on multistable slip of earthquakes based on a one-degree-of-freedom spring-slider model in the presence of thermal-pressurized slip-weakening friction and viscosity by using the normalized equation of motion of the model. The major model parameters are the normalized characteristic displacement, Uc, of the friction law and the normalized viscosity coefficient, η, between the slider and background plate. Analytic results at small slip suggest that there is a solution regime for η and γ ( = 1∕Uc) to make the slider slip steadily. Numerical simulations exhibit that the time variation in normalized velocity, V∕Vmax (Vmax is the maximum velocity), obviously depends on Uc and η. The effect on the amplitude is stronger due to η than due to Uc. In the phase portrait of V∕Vmax versus the normalized displacement, U∕Umax (Umax is the maximum displacement), there are two fixed points. The one at large V∕Vmax and large U∕Umax is not an attractor, while that at small V∕Vmax and small U∕Umax can be an attractor for some values of η and Uc. When Uc<0. 55, unstable slip does not exist. When Uc ≥ 0. 55, Uc and η divide the solution domain into three regimes: stable, intermittent, and unstable (or chaotic) regimes. For a certain Uc, the three regimes are controlled by a lower bound, ηl, and an upper bound, ηu, of η. The values of ηl, ηu, and ηu − ηl all decrease with increasing Uc, thus suggesting that it is easier to yield unstable slip for larger Uc than for smaller Uc or for larger η than for smaller η. When Uc<1, the Fourier spectra calculated from simulation velocity waveforms exhibit several peaks, thus suggesting the existence of nonlinear behavior of the system. When Uc>1, the related Fourier spectra show only one peak, thus suggesting linear behavior of the system.

Expansion of source equation of elastic line

Robotica ◽  
2008 ◽  
Vol 26 (6) ◽  
pp. 739-751 ◽  
Author(s):  
Mirjana Filipovic ◽  
Miomir Vukobratovic
Keyword(s):  
Bending Moment ◽  
Equation Of Motion ◽  
Robotic Systems ◽  
Lumped Mass ◽  
Elastic Line ◽  
Force Dynamics ◽  
Long Time ◽  
The Difference ◽  
Direct Outcome ◽  
The Relationship

SUMMARYThe paper is concerned with the relationship between the equation of elastic line motion, the “Euler-Bernoulli approach” (EBA), and equation of motion at the point of elastic line tip, the “Lumped-mass approach” (LMA). The Euler–Bernoulli equations (which have for a long time been used in the literature) should be expanded according to the requirements of the motion complexity of elastic robotic systems. The Euler–Bernoulli equation (based on the known laws of dynamics) should be supplemented with all the forces that are participating in the formation of the bending moment of the considered mode. This yields the difference in the structure of Euler–Bernoulli equations for each mode. The stiffness matrix is a full matrix. Mathematical model of the actuators also comprises coupling between elasticity forces. Particular integral of Daniel Bernoulli should be supplemented with the stationary character of elastic deformation of any point of the considered mode, caused by the present forces. General form of the elastic line is a direct outcome of the system motion dynamics, and can not be described by one scalar equation but by three equations for position and three equations for orientation of every point on that elastic line. Simulation results are shown for a selected robotic example involving the simultaneous presence of elasticity of the joint and of the link (two modes), as well the environment force dynamics.

scholarly journals Investigation of Liquid Crystal Ripple Using Ericksen-Leslie Theory for Displays Subject to Tactile Force

2013 ◽  
Vol 2013 ◽  
pp. 1-11
Author(s):  
Y. J. Lee ◽  
T. S. Liu ◽  
Mao-Hsing Lin ◽  
Kun-Feng Huang
Keyword(s):  
Liquid Crystal ◽  
Liquid Crystals ◽  
Tilt Angle ◽  
Optical Transmission ◽  
Liquid Crystal Display ◽  
Viscosity Coefficient ◽  
Equation Of Motion ◽  
Angle Variation ◽  
Analytical Derivation ◽  
Molecule Equation

Liquid crystal display panels subjected to tactile force will show ripple propagation on screens. Tactile forces change tilt angles of liquid crystal molecules and alter optical transmission so as to generate ripple on screens. Based on the Ericksen-Leslie theory, this study investigates ripple propagation by dealing with tilt angles of liquid crystal molecules. Tactile force effects are taken into account to derive the molecule equation of motion for liquid crystals. Analytical results show that viscosity, tactile force, the thickness of cell gap, and Leslie viscosity coefficient lead to tilt angle variation. Tilt angle variations of PAA liquid crystal molecules are sensitive to tactile force magnitudes, while those of 5CB and MBBA with larger viscosity are not. Analytical derivation is validated by numerical results.

Vibration Analysis of Axially Compressed Nanobeams and its Critical Pressure Using a New Nonlocal Stress Theory

2011 ◽  
Vol 105-107 ◽  
pp. 1788-1792 ◽  
Author(s):  
Cheng Li ◽  
C.W. Lim ◽  
Zhong Kui Zhu
Keyword(s):  
Differential Equation ◽  
Numerical Solutions ◽  
Multiple Scales ◽  
Separation Of Variables ◽  
Classical Mechanics ◽  
Bending Moment ◽  
Nonlocal Elasticity Theory ◽  
Equation Of Motion ◽  
Basic Element ◽  
Mode Shapes

The transverse vibration of a nanobeam subject to initial axial compressive forces based on nonlocal elasticity theory is investigated. The effects of a small nanoscale parameter at molecular level unavailable in classical mechanics theory are presented and analyzed. Explicit solutions for natural frequency, vibration mode shapes are derived through two different methods: separation of variables and multiple scales. The respective numerical solutions are in close agreement. Validity of the models and approaches presented in the work are verified. Unlike the previous studies for a nonlocal nanostructure, this paper adopts the effective nonlocal bending moment instead of the pure traditional nonlocal bending moment. The analysis yields an infinite-order differential equation of motion which governs the vibrational behaviors. For practical analysis and as examples, an eight-order governing differential equation of motion is solved and the results are discussed. The paper presents a complete nonlocal nanobeam model and the results may be helpful for the application and design of various nano-electro-mechanical devices, e.g. nano-drivers, nano-oscillators, nano-sensors, etc., where a nanobeam acts as a basic element.

scholarly journals Model Calculations of Plastic Deformation of Two-Phase Materials With Fibre Structure

1993 ◽  
Vol 22 (1) ◽  
pp. 29-42 ◽  
Author(s):  
H. J. Bunge ◽  
W. Böcker
Keyword(s):  
Plastic Deformation ◽  
Fibre Structure ◽  
Two Phase ◽  
Model Calculations ◽  
Fibre Composites ◽  
Deformation Work ◽  
Minimum Deformation ◽  
Inhomogeneous Flow ◽  
Deformation Ratio ◽  
Distribution Of Flow

Plastic flow in two-phase fibre composites during axially symetric deformation is modelled assuming homogeneous deformation of the fibres of the harder phase and inhomogeneous flow in the softer matrix. The distribution of flow between fibres and matrix is described by the deformation ratio α which follows from the assumption of minimum deformation work. The main features of the model agree quite well with experimental results obtained in several powder metallurgically prepared two-phase composites.

Comparison of Recovery and Recrystallization in Stainless Steel Following Plane-Wave Shock Loading and Explosive Forming

1970 ◽  
Vol 28 ◽  
pp. 428-429 ◽  
Author(s):  
J. A. Korbonski ◽  
L. E. Murr
Keyword(s):  
Stainless Steel ◽  
Shock Loading ◽  
Pressure Pulse ◽  
Shock Pressure ◽  
304 Stainless Steel ◽  
Strain Rates ◽  
Two Dimensional ◽  
Aisi 304 Stainless Steel ◽  
Aisi 304 ◽  
Explosive Forming

Comparison of recovery rates in materials deformed by a unidimensional and two dimensional strains at strain rates in excess of 104 sec.−1 was performed on AISI 304 Stainless Steel. A number of unidirectionally strained foil samples were deformed by shock waves at graduated pressure levels as described by Murr and Grace. The two dimensionally strained foil samples were obtained from radially expanded cylinders by a constant shock pressure pulse and graduated strain as described by Foitz, et al.

Solid Solution Effects and Deformation Micros trueture of Shock-Loaded Iron Manganese Alloys

1970 ◽  
Vol 28 ◽  
pp. 420-421
Author(s):  
A. Christou ◽  
J. V. Foltz ◽  
N. Brown
Keyword(s):  
Solid Solution ◽  
Shock Loading ◽  
High Strain ◽  
Local Stress ◽  
Strain Rates ◽  
Local Stress Concentration ◽  
Bcc Metals ◽  
Manganese Alloys ◽  
Iron Manganese ◽  
Transmission Microscope

In general, all BCC transition metals have been observed to twin under appropriate conditions. At the present time various experimental reports of solid solution effects on BCC metals have been made. Indications are that solid solution effects are important in the formation of twins. The formation of twins in metals and alloys may be explained in terms of dislocation mechanisms. It has been suggested that twins are nucleated by the achievement of local stress-concentration of the order of 15 to 45 times the applied stress. Prietner and Leslie have found that twins in BCC metals are nucleated at intersections of (110) and (112) or (112) and (112) type of planes.In this paper, observations are reported of a transmission microscope study of the iron manganese series under conditions in which twins both were and were not formed. High strain rates produced by shock loading provided the appropriate deformation conditions. The workhardening mechanisms of one alloy (Fe - 7.37 wt% Mn) were studied in detail.

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