Moving Load on a Fluid-Solid Interface: Supersonic Regime

1973 ◽  
Vol 40 (1) ◽  
pp. 137-142 ◽  
Author(s):  
T. C. Kennedy ◽  
G. Herrmann
Keyword(s):  
Steady State ◽  
Closed Form ◽  
Moving Load ◽  
Closed Form Solution ◽  
Point Load ◽  
Form Solution ◽  
Steady State Response ◽  
Entire Space ◽  
State Response ◽  
Supersonic Regime

The steady-state response of a semi-infinite solid with an overlying semi-infinite fluid subjected at the plane interface to a moving point load is determined for supersonic load velocities. The exact, closed-form solution valid for the entire space is presented. Some numerical results for the displacements at the interface are calculated and compared to the results obtained when no fluid is present.

Closed-Form Steady-State Response Solution of the Twin Rotor Damper and Experimental Validation

2017 ◽  
Vol 139 (2) ◽  
Author(s):  
Richard Bäumer ◽  
Uwe Starossek
Keyword(s):  
Steady State ◽  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
Design Parameters ◽  
Control Force ◽  
Steady State Response ◽  
Active Mass ◽  
State Response ◽  
Twin Rotor

In previous research, the twin rotor damper (TRD), an active mass damper, was presented including control algorithms for monofrequent vibrations. In a preferred mode of operation, the continuous rotation mode, two eccentric masses rotate in opposite directions about two parallel axes with a mostly constant angular velocity. The resulting control force is harmonic. Within this paper, the steady-state response of a single-degree-of-freedom (SDOF) oscillator subjected to a harmonic excitation force with and without the TRD is studied. A closed-form solution is presented and validated experimentally. It is shown that the TRD provides damping to the SDOF oscillator until a certain frequency ratio is reached. The provided damping is not only dependent on the design parameters of the TRD but also depends on the steady-state vibration amplitude. The solution serves as a powerful design tool for dimensioning the TRD. The analytical closed-form solution is applicable for other active mass dampers.

Closed-Form Representation of Beam Response to Moving Line Loads

2000 ◽  
Vol 68 (2) ◽  
pp. 348-350 ◽  
Author(s):  
Lu Sun
Keyword(s):  
Closed Form ◽  
Moving Load ◽  
Closed Form Solution ◽  
Form Solution ◽  
Winkler Foundation ◽  
Line Load ◽  
State Response ◽  
Form Representation ◽  
Mach Numbers ◽  
Moving Line

Fourier transform is used to solve the problem of steady-state response of a beam on an elastic Winkler foundation subject to a moving constant line load. Theorem of residue is employed to evaluate the convolution in terms of Green’s function. A closed-form solution is presented with respect to distinct Mach numbers. It is found that the response of the beam goes to unbounded as the load travels with the critical velocity. The maximal displacement response appears exactly under the moving load and travels at the same speed with the moving load in the case of Mach numbers being less than unity.

Moving Load on a Fluid-Solid Interface: Subsonic and Intersonic Regimes

1973 ◽  
Vol 40 (4) ◽  
pp. 885-890 ◽  
Author(s):  
T. C. Kennedy ◽  
G. Herrmann
Keyword(s):  
Steady State ◽  
Moving Load ◽  
Point Load ◽  
Numerical Results ◽  
Plane Interface ◽  
Steady State Response ◽  
State Response ◽  
Solid Interface

The steady-state response of a semi-infinite solid, with an overlying semi-infinite fluid, subjected at the plane interface to a moving point load is determined for subsonic and intersonic load velocities. Some numerical results for the displacements at the interface are presented and compared to the results obtained in the absence of the fluid.

Closed-Form, Steady-State Solution for the Unbalance Response of a Rigid Rotor in Squeeze Film Damper

1983 ◽  
Vol 105 (3) ◽  
pp. 551-556 ◽  
Author(s):  
D. L. Taylor ◽  
B. R. K. Kumar
Keyword(s):  
Steady State ◽  
Closed Form ◽  
Closed Form Solution ◽  
Steady State Solution ◽  
State Solution ◽  
Squeeze Film ◽  
Steady State Response ◽  
Rigid Rotor ◽  
Squeeze Film Damper ◽  
State Response

This paper considers the steady-state response due to unbalance of a planar rigid rotor carried in a short squeeze film damper with linear centering spring. The damper fluid forces are determined from the short bearing, cavitated (π film) solution of Reynold’s equation. Assuming a circular centered orbit, a change of coordinates yields equations whose steady-state response are constant eccentricity and phase angle. Focusing on this steady-state solution results in reducing the problem to solutions of two simultaneous algebraic equations. A method for finding the closed-form solution is presented. The system is nondimensionalized, yielding response in terms of an unbalance parameter, a damper parameter, and a speed parameter. Several families of eccentricity-speed curves are presented. Additionally, transmissibility and power consumption solutions are present.

Exact closed-form solutions for Lamb’s problem—II: a moving point load

2020 ◽  
Vol 223 (2) ◽  
pp. 1446-1459
Author(s):  
Xi Feng ◽  
Haiming Zhang
Keyword(s):  
Point Source ◽  
Closed Form ◽  
High Speed ◽  
Moving Load ◽  
Closed Form Solution ◽  
Point Load ◽  
Form Solution ◽  
High Speed Rail ◽  
Lamb’S Problem ◽  
Homogeneous Half Space

SUMMARY In this paper, we report on an exact closed-form solution for the displacement in an elastic homogeneous half-space elicited by a downward vertical point source moving with constant velocity over the surface of the medium. The problem considered here is an extension to Lamb’s problem. Starting with the integral solutions of Bakker et al., we followed the method developed by Feng and Zhang, which focuses on the displacement triggered by a fixed point source observed on the free surface, to obtain the final solution in terms of elementary algebraic functions as well as elliptic integrals of the first, second and third kind. Our closed-form results agree perfectly with the numerical results of Bakker et al., which confirms the correctness of our formulae. The solution obtained in this paper may lay a solid foundation for further consideration of the response of an actual physical moving load, such as a high-speed rail train.

Steady State Response of a Piezoelectric Power Harvesting System

Aerospace ◽  
2006 ◽  
Author(s):  
Y. C. Shu ◽  
I. C. Lien
Keyword(s):  
Steady State ◽  
Electromechanical Coupling ◽  
Damping Ratio ◽  
Closed Form Solution ◽  
Form Solution ◽  
Electromechanical Coupling Coefficient ◽  
Steady State Response ◽  
Power Normalization ◽  
Power Harvesting ◽  
State Response

We study the steady state response of a piezoelectric generator connected to an AC-DC bridge rectifying circuit plus a resistor as the basis for design analysis. In contrast with estimates obtained by various degrees of approximations in recent literature, a closed form solution is derived under the steady-state operation. We show that the average harvested power density depends on the input vibration characteristics (frequency and acceleration), the electric load, the natural frequency, the density, the mechanical damping ratio, and the overall electromechanical coupling coefficient of the system. With it an effective power normalization scheme is provided in order to compare power harvesting devices of different sizes and with different vibration inputs to estimate efficiencies. The theoretical predictions are validated and found in good agreement with our recent experiment.

Analytical evaluation of track response in the vertical direction due to a moving load

2016 ◽  
Vol 23 (18) ◽  
pp. 2989-3006 ◽  
Author(s):  
Wlodzimierz Czyczula ◽  
Piotr Koziol ◽  
Dariusz Kudla ◽  
Sergiusz Lisowski
Keyword(s):  
Steady State ◽  
Moving Load ◽  
Vertical Direction ◽  
Vertical Displacement ◽  
Steady State Response ◽  
Concentrated Force ◽  
State Response ◽  
Weakly Coupled ◽  
Wide Range ◽  
Rail Deflection

In the literature, typical analytical track response models are composed of beams (which represent the rail) on viscoelastic or elastic foundations. The load is usually considered as a single concentrated force (constant or varying in time) moving with constant speed. Concentrated or distributed loads or multilayer track models have rarely been considered. One can find some interesting results concerning analysis of distributed loads and multilayer track structures that include both analytical and numerical approaches. However, there is a noticeable lack of sufficient comparison between track responses under concentrated or distributed load and between one and multilayer track models. One of the unique features of the present paper is a comparison of data obtained for a series of concentrated and distributed loads, which takes into account a wide range of track parameters and train speeds. One of the fundamental questions associated with the multilayer track model is the level of coupling between the rail and the vibrations of the sleepers. In this paper, it is proved that sleepers are weakly coupled with the rail if the track is without significant imperfections, and the steady-state response is analyzed for this case. In other words, sleeper vibrations do not influence the rail vibrations significantly. Therefore the track is analyzed by means of a two-stage model. The first step of this model determines rail vibration under a moving load, and then the sleeper vibration is calculated from previously obtained kinematic excitation. The model is verified by comparison of the obtained results with experimental data. Techniques based on Fourier series are applied to the solution of the steady-state track response. Another important problem associated with track response under moving loads arises from the analysis of the effect of longitudinal forces in rails on vertical displacement. It is shown that, in the case of the steady-state response, longitudinal forces do not influence rail displacements significantly and this observation remains correct for a wide range of track parameters and train speeds. The paper also analyzes the legitimacy of the statement that additional rail deflection between sleepers, compared to the continuous rail support, can be considered as a track imperfection.

DLSFEM–PML formulation for the steady-state response of a taut string on visco-elastic support under moving load

Meccanica ◽  
2019 ◽  
Vol 55 (4) ◽  
pp. 765-790 ◽  
Author(s):  
Diego Froio ◽  
Egidio Rizzi ◽  
Fernando M. F. Simões ◽  
António Pinto da Costa
Keyword(s):  
Steady State ◽  
Moving Load ◽  
Elastic Support ◽  
Steady State Response ◽  
State Response ◽  
Taut String

Design and Analysis of Automotive Serpentine Belt Drive Systems for Steady State Performance

1997 ◽  
Vol 119 (2) ◽  
pp. 162-168 ◽  
Author(s):  
R. S. Beikmann ◽  
N. C. Perkins ◽  
A. G. Ulsoy
Keyword(s):  
Steady State ◽  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
Design Parameters ◽  
Belt Drive ◽  
Automotive Engine ◽  
Theoretical Predictions ◽  
Serpentine Belt ◽  
Drive Systems

Serpentine belt drive systems with spring-loaded tensioners are now widely used in automotive engine accessory drive design. The steady state tension in each belt span is a major factor affecting belt slip and vibration. These tensions are determined by the accessory loads, the accessory drive geometry, and the tensioner properties. This paper focuses on the design parameters that determine how effectively the tensioner maintains a constant tractive belt tension, despite belt stretch due to accessory loads and belt speed. A nonlinear model predicting the operating state of the belt/tensioner system is derived, and solved using (1) numerical, and (2) approximate, closed-form methods. Inspection of the closed-form solution reveals a single design parameter, referred to as the “tensioner constant,” that measures the effectiveness of the tensioner. Tension measurements on an experimental drive system confirm the theoretical predictions.

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