The Normal Impact of an Elastic Rod-Mass System on a Viscoelastic Half Space

1987 ◽  
Vol 54 (2) ◽  
pp. 367-372
Author(s):  
H. A. Downey ◽  
D. B. Bogy
Keyword(s):  
Integral Equation ◽  
Half Space ◽  
Elastic Rod ◽  
Lumped Mass ◽  
Normal Impact ◽  
Mass System ◽  
Viscoelastic Parameters ◽  
Large Hysteresis ◽  
Viscoelastic Effects ◽  
The Impact

The normal impact of a one-dimensional elastic rod, with a lumped mass on the trailing end, onto a viscoelastic half space is considered and the problem is solved for the time dependent interface stress and displacement. The problem is reduced to an integral equation, whose two-part kernel consists of solutions of two simpler problems. One part pertains to the half space only and the other is for the rod-mass system. The half-space portion of the kernel is obtained through a numerical inversion of the Laplace transformed solution. Given the half-space kernel contribution, which depends only on the two viscoelastic parameters and Poisson’s ratio, the integral equation is solved numerically for two families of half space materials. The viscoelastic effects on the half space are quite pronounced. Certain combinations of the parameters cause a large hysteresis in the impact, and softer half spaces require longer contact times before the rod leaves the surface.

The Normal Impact on an Elastic Half Space of an Elastic Rod-Mass System

1987 ◽  
Vol 54 (2) ◽  
pp. 359-366 ◽  
Author(s):  
H. A. Downey ◽  
D. B. Bogy
Keyword(s):  
Integral Equation ◽  
Closed Form ◽  
Half Space ◽  
Contact Stress ◽  
Elastic Half Space ◽  
Elastic Rod ◽  
Lumped Mass ◽  
Normal Impact ◽  
Mass System ◽  
The Impact

The normal impact problem of a one-dimensional elastic rod with a lumped mass on the trailing end onto an elastic half space is solved for the time-dependent interface displacement and stress. This problem is reduced to an integral equation, whose kernel is the solution of a simpler auxiliary problem, which is solved in closed form. After examining the graph of the kernel it is found that a simple linear expression adequately represents its half space contribution. This approximation allows the integral equation to be solved in closed form and provides insight into its solution. Numerical results are presented, which display the impact and rebound of the rod, and illustrate the presence of major effects from the Rayleigh wave in the half space and the reflected wave from the trailing end of the rod. Results are presented for various half-space materials, rod lengths, and masses. It is found that in the absence of the mass the maximum contact stress depends entirely on the rod material, but with the lumped mass added the contact stress can become much greater and depends on the rod, the half space, and the mass.

scholarly journals Nonlinear Dynamic Analysis of Axisymmetric Solids by the Finite Element Method

1974 ◽  
Vol 96 (2) ◽  
pp. 103-112 ◽  
Author(s):  
M. Hartzman
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Technique ◽  
Nonlinear Dynamic Analysis ◽  
Plastic Behavior ◽  
The Finite Element Method ◽  
Lumped Mass ◽  
Mass System ◽  
The Impact ◽  
Element Method

A method for calculating the dynamic response of deformable axisymmetric solids, subjected to time-dependent axisymmetric loads is described. The nonlinearities considered in this analysis include material nonlinearity (elastic-plastic behavior) and geometric nonlinearity, which includes finite deformation. The finite-element method is applied to approximate the continuum by a lumped-mass system connected by axisymmetric elements. The equations of motion are solved by applying a step-by-step numerical technique. The analysis is illustrated by application to the collapse of a built-in spherical dome with varying thickness and to the impact of a cylinder against a rigid wall. Close agreement is obtained between the results from the present technique and results obtained from the literature.

Theory for an Active Dynamic Vibration Absorber

1991 ◽  
Author(s):  
L. S. Stephens ◽  
K. E. Rouch ◽  
S. G. Tewani
Keyword(s):  
Closed Form Solution ◽  
Control Element ◽  
Vibrational Amplitude ◽  
Vibration Absorber ◽  
Vibration Absorbers ◽  
Lumped Mass ◽  
Dynamic Vibration Absorber ◽  
Mass System ◽  
Dynamic Vibration ◽  
The Impact

Abstract Research in dynamic vibration absorbers has yielded several fundamental designs. Among these are the tuned dynamic absorber, the Lanchester damper, and the impact damper. These designs utilize certain combinations of passive mechanical elements (springs and dampers) to reduce the vibrational amplitude of a system. However, with recent advances in motion sensing and actuating, the design of vibration absorbers that utilize actively actuated elements has become more attractive. This paper develops the theory for using a damped dynamic vibration absorber with an active control element to reduce the vibrational amplitude of a lumped mass system. A control law consisting of a linear combination of velocity and acceleration of the main mass is developed for the active element A closed-form solution is presented for the absorber tuning equation, and numerical methods are used to generate performance curves.

The Normal Impact of a Rod-Mass System on a Viscoelastic Layered Half Space

1988 ◽  
Vol 55 (4) ◽  
pp. 879-886
Author(s):  
H. A. Downey ◽  
D. B. Bogy
Keyword(s):  
Integral Equations ◽  
Half Space ◽  
Elastic Half Space ◽  
Substrate Material ◽  
Viscoelastic Layer ◽  
Lumped Mass ◽  
Mass System ◽  
Laplace Transform Inversion ◽  
Numerical Laplace Transform ◽  
Layered Half Space

A rod with a lumped mass attached to its trailing end travels axially with a uniform velocity and strikes an elastic half space that is covered with an adhering viscoelastic layer. The problem is reduced to integral equations for the average contact stress and the displacement of the rod tip into the contact surface. The kernels of these integral equations are composed of temporal Green’s functions for the rod and the layered half space, which represent the response of each to an impulsive uniform normal traction. The Green’s function for the rod is obtained in closed form, while that for the layered half space is obtained through a numerical Laplace transform inversion. The integral equations are solved numerically with a second-order stable scheme. Solutions are computed for a wide variety of materials and configurations, providing the stress and displacement history, as well as the stress-displacement response. The results show the effects of changes in rod material and length, lumped mass, layer material, substrate material, and viscoelastic material parameters.

The efficiency of application of virtual cross-sections method and hypotheses MELS in problems of wave signal propagation in elastic waveguides with rough surfaces

2016 ◽  
pp. 3564-3575 ◽  
Author(s):  
Ara Sergey Avetisyan
Keyword(s):  
Half Space ◽  
Cross Sections ◽  
Classical Method ◽  
Signal Propagation ◽  
Elastic Half Space ◽  
Layered Systems ◽  
Surface Layers ◽  
Inhomogeneous Surface ◽  
Wave Signal ◽  
The Impact

The efficiency of virtual cross sections method and MELS (Magneto Elastic Layered Systems) hypotheses application is shown on model problem about distribution of wave field in thin surface layers of waveguide when plane wave signal is propagating in it. The impact of surface non-smoothness on characteristics of propagation of high-frequency horizontally polarized wave signal in isotropic elastic half-space is studied. It is shown that the non-smoothness leads to strong distortion of the wave signal over the waveguide thickness and along wave signal propagation direction as well.  Numerical comparative analysis of change in amplitude and phase characteristics of obtained wave fields against roughness of weakly inhomogeneous surface of homogeneous elastic half-space surface is done by classical method and by proposed approach for different kind of non-smoothness.

Torsional Vibrations of a Boiler Feed Pump

1978 ◽  
Vol 100 (4) ◽  
pp. 637-643 ◽  
Author(s):  
A. W. Lees ◽  
K. A. Haines
Keyword(s):  
Flexural Vibration ◽  
Feed Pump ◽  
Lumped Mass ◽  
High Pressure Pump ◽  
Mass System ◽  
Order Of Magnitude ◽  
Vibration Pattern ◽  
Suitable Combination ◽  
Element Technique ◽  
Analytic Models

The paper describes an investigation into the dynamic behavior of a large steam turbine-driven boiler feed pump, following the failure of gearboxes, couplings and bearings. The line consists of a 17 MW turbine driving a four-stage high pressure pump directly and a single-stage booster pump via a 2:1 single-reduction gearbox. Flexural vibration was measured using accelerometers at the bearings and eddy current proximity transducers. The torque transmitted to the gearbox was measured using a four-arm strain gauge bridge mounted in a coupling spacer shaft, the signals being obtained via a telemetry system. The observations showed a complex vibration pattern which was compared with predictions from simple analytic models. A lumped mass system accurately predicted the order of magnitude of oscillatory torque as a function of frequency, given the inevitable errors in gear manufacture. It was shown that the choice of flexible coupling has a crucial effect on the response. The methods of calculation have been generalized to give an accurate model of a system with distributed mass. This is achieved formally using the dynamic Green’s function approach or, for detailed results by a finite-element technique. It was shown that a change of coupling alters the dynamic torque of the system. Hence the effects of a number of changes were calculated and a suitable combination of couplings and gearbox were chosen to implement the practical solution to the problem. The basis for the choice is described and the implications for more general design criteria are discussed.

Seismic response and retrofit of industrial brick masonry chimneys

1992 ◽  
Vol 19 (1) ◽  
pp. 117-128 ◽  
Author(s):  
A. Ghobarah ◽  
T. Baumber
Keyword(s):  
Seismic Response ◽  
Ground Motion ◽  
Strong Motion ◽  
Brick Masonry ◽  
Wind Loading ◽  
Earthquake Ground Motion ◽  
Lumped Mass ◽  
Mass System ◽  
Higher Modes ◽  
Recent Earthquakes

During recent earthquakes, the documented cases of collapsed unreinforced brick masonry industrial chimneys are numerous. Observed modes of structural failure are either total collapse or sometimes collapse or damage of the top third of the structure. The objective of this study is to analyze and explain the modes of observed failure of masonry chimneys during earthquake events, and to evaluate two retrofit systems for existing chimneys in areas of high seismicity. The behaviour of the masonry chimney, when subjected to earthquake ground motion, was modelled using a lumped mass system. Several actual strong motion records were used as input to the model. The shear, moment, and displacement responses to the earthquake ground motion were evaluated for various chimney configurations. It was found that the failure of the chimney at its base is the result of the fundamental mode of vibration. Failure at the top third of the structure due to the higher modes of vibration is possible when the chimney is subjected to high frequency content earthquakes. Higher modes, which are normally not of concern under wind loading, were shown to be critical in seismic design. Post-tensioning and the reinforcing steel cage were found to be effective retrofit systems. Key words: masonry, chimneys, behaviour, analysis, design, retrofit, dynamic, earthquakes, seismic response.

scholarly journals On the influence of basic thermodynamics on thermal cracking resistance of asphalt mixtures in cooling tests

2018 ◽  
Vol 3 ◽  
pp. 1-7
Author(s):  
Daniel Steiner ◽  
Bernhard Hofko
Keyword(s):  
Tensile Strength ◽  
Cooling Rate ◽  
Thermal Cracking ◽  
Radiation Condition ◽  
Asphalt Mixtures ◽  
Air Cooling ◽  
Laboratory Assessment ◽  
Cracking Resistance ◽  
Viscoelastic Parameters ◽  
The Impact

The cooling test or Thermal Stress Restrained Specimen Test (TSRST) simulates fully restrained pavements, as they occur in field for laboratory assessment of the thermal cracking resistance of asphalt mixtures. In the TSRST, cryogenic stress builds up due to cooling and prevented shrinkage until the tensile strength of the specimen is exceeded and the specimen fails by cracking. By carrying out TSRST various viscoelastic parameters, e.g. relaxation, evolution of tensile stresses, and tensile strength can be analyzed. Thus, a comprehensive view on the low temperature performance is possible. Standard TSRST is controlled by setting the cooling rate of the air within the chamber at a fixed value, e.g. -10°C/h. In thermodynamics, the actual cooling rate of objects is not only influenced by the cooling but also by external conditions like humidity, air velocity, radiation condition, etc. A current study investigates the impact of additional cooling parameters rather than just the air cooling rate. Two test machines of the same manufacturer that differ in the year of production and the setup of the climate chamber are compared. An initial wide scatter of test results from the two devices could be explained by taking thermodynamics into account and the reproducibility could be significantly enhanced.

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