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.

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.

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.

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.

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.

scholarly journals Nodal Control in a Vibrating Beam

2002 ◽  
Author(s):  
Akshay N. Singh ◽  
Yitshak M. Ram ◽  
Su-Seng Pang
Keyword(s):  
Steady State ◽  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
Control Force ◽  
Euler Beam ◽  
Steady State Motion ◽  
Control Gain ◽  
Displacement Information ◽  
Nodal Control

A method to achieve nodal control at the point of excitation in a Bernoulli-Euler beam is developed. It is shown that, for a uniform Bernoulli-Euler beam, the steady state motion at the point of excitation can be absorbed by means of a control force determined from displacement information at the point of application. A closed form solution for the control gain is presented.

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.

A New Accurate Closed-Form Analytical Solution for Junction Temperature of High-Powered Devices

2014 ◽  
Vol 136 (1) ◽  
Author(s):  
J. H. L. Ling ◽  
A. A. O. Tay
Keyword(s):  
Analytical Solution ◽  
Closed Form ◽  
Material Properties ◽  
Heat Dissipation ◽  
Field Effect Transistors ◽  
Closed Form Solution ◽  
Form Solution ◽  
Junction Temperature ◽  
Design Parameters ◽  
Closed Form Analytical Solution

The peak junction temperature has a profound effect on the operational lifetime and performance of high powered microwave devices. Although numerical analysis can help to estimate the peak junction temperature, it can be computationally expensive and time consuming when investigating the effect of the device geometry and material properties on the performance of the device. On the other hand, a closed-form analytical method will allow similar studies to be done easily and quickly. Although some previous analytical solutions have been proposed, the solutions either require over-long computational times or are not so accurate. In this paper, an accurate closed-form analytical solution for the junction temperature of power amplifier field effect transistors (FETs) or monolithic microwave integrated circuits (MMICs) is presented. Its derivation is based on the Green's function integral method on a point heat source developed through the method of images. Unlike most previous works, the location of the heat dissipation region is assumed to be embedded under the gate. Since it is a closed-form solution, the junction temperature as well as the temperature distribution around the gate can be easily calculated. Consequently, the effect of various design parameters and material properties affecting the junction temperature of the device can be easily investigated. This work is also applicable to multifinger devices by employing superposition techniques and has been shown to agree well with both numerical and experimental results.

A Dishing Model for Chemical Mechanical Polishing of Plug Structures

2010 ◽  
Vol 126-128 ◽  
pp. 276-281
Author(s):  
Shih Hsiang Chang
Keyword(s):  
Steady State ◽  
Closed Form ◽  
Chemical Mechanical Polishing ◽  
Closed Form Solution ◽  
Form Solution ◽  
Mechanical Polishing ◽  
Quantitative Prediction ◽  
Wafer Surface ◽  
Maximum Value ◽  
Pattern Density

It is well known that dishing occurring in chemical mechanical polishing of plug structures leads to considerable wafer surface non-planarity and reduces the current/charge conduction. Thus, a closed-form solution for quantitative prediction of dishing is needed. A contact-mechanics-based approach to describe the steady-state dishing occurring in chemical mechanical polishing of plug structures is presented. The model is then applied to investigate the effect of pattern geometry on dishing in details. It was shown that plug dishing strongly depends on plug size, but minimally on pattern density. In addition, the maximum value of dishing occurs at a critical pattern density for fixed pitch.

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