Steady-State Response and Stability of Rotating Composite Blades With Frictional Damping

1998 ◽  
Vol 120 (1) ◽  
pp. 131-139 ◽  
Author(s):  
T. N. Shiau ◽  
J. S. Rao ◽  
Y. D. Yu ◽  
S. T. Choi
Keyword(s):  
Steady State ◽  
Stability Analysis ◽  
Excitation Frequency ◽  
Harmonic Balance Method ◽  
Composite Plates ◽  
Steady State Response ◽  
Friction Damping ◽  
State Response ◽  
Direct Integration Method ◽  
Composite Blades

Friction dampers are widely used to improve the performance of rotating blades. This paper is concerned with the steady state response and stability analysis of rotating composite plates in the presence of non linear friction damping. Direct Integration Method (DIM) and Harmonic Balance Method (HBM) are used to determine the steady state response due to periodic lateral external forces. In addition, an alternate procedure, Hybrid Method (HM) is proposed for this analysis to substantiate the results from DIM and HBM. The analysis shows that the steady state response is a function of friction damping magnitude as well as its location besides the excitation frequency and the rotational speed. A stability analysis of the composite blades is also made by including periodic in-plane excitation using Floquet-Liapunov theory.

Steady State Response and Stability of Rotating Composite Blades With Frictional Damping

1996 ◽  
Author(s):  
T. N. Shiau ◽  
J. S. Rao ◽  
Y. D. Yu ◽  
S. T. Choi
Keyword(s):  
Steady State ◽  
Stability Analysis ◽  
Excitation Frequency ◽  
Harmonic Balance Method ◽  
Composite Plates ◽  
Steady State Response ◽  
Friction Damping ◽  
State Response ◽  
Direct Integration Method ◽  
Composite Blades

Friction dampers are widely used to improve the performance of rotating blades. This paper is concerned with the steady stale response and stability analysis of ratating composite plates in the presence of non linear friction damping. Direct Integration Method (DIM) and Harmonic Balance Method (HBM) are used to determine the steady state response due to periodic lateral external forces. In addition, an alternate procedure, Hybrid Method (HM) is proposed for this analysis to substantiate the results from DIM and HBM. The analysis shows that the steady state response is a function of friction damping magnitude as well as its location besides the excitation frequency and the rotational speed. A stability analysis of the composite blades is also made by including periodic in-plane excitation using Floquet-Liapunov theory.

New Insight Into Energy Harvesting via Axially-Loaded Beams

2009 ◽  
Author(s):  
Mohammed F. Daqaq
Keyword(s):  
Steady State ◽  
Energy Harvesting ◽  
Axial Load ◽  
Excitation Frequency ◽  
Axial Loading ◽  
Response Amplitude ◽  
Resistive Load ◽  
Steady State Response ◽  
State Response ◽  
Axially Loaded

Driven by the study of Leland and Wright [1], this manuscript delves into the qualitative understanding of energy harvesting using axially-loaded beams. Using a simple nonlinear electromechanical model and the method of multiple scales, we study the general nonlinear physics of energy harvesting from a piezoelectric beam subjected to static axial loading and traversal dynamic excitation. We obtain analytical expressions for the steady-state response amplitude, the voltage drop across a resistive load, and the output power. We utilize these expression to study the effect of the axial loading on the overall nonlinear behavior of the harvester. It is demonstrated that, in addition to the ability of tuning the harvester to the excitation frequency via axial load variations, the axial load aids in i) increasing the electric damping in the system thereby enhancing the energy transfer from the beam to the electric load, ii) amplifying the effect of the external excitation on the structure, and hence, increases the steady-state response amplitude and output voltage, and iii) increasing the bandwidth of the harvester by enhancing the effective nonlinearity of the system.

scholarly journals Experiment and Theory on the Nonlinear Vibration of a Shallow Arch Under Harmonic Excitation at the End

2005 ◽  
Vol 74 (6) ◽  
pp. 1061-1070 ◽  
Author(s):  
Jen-San Chen ◽  
Cheng-Han Yang
Keyword(s):  
Steady State ◽  
Excitation Frequency ◽  
Multiple Scale ◽  
Steady State Response ◽  
Scale Analysis ◽  
Jump Phenomenon ◽  
Shallow Arch ◽  
State Response ◽  
Geometrical Imperfection ◽  
Multiple Scale Analysis

In this paper we study, both theoretically and experimentally, the nonlinear vibration of a shallow arch with one end attached to an electro-mechanical shaker. In the experiment we generate harmonic magnetic force on the central core of the shaker by controlling the electric current flowing into the shaker. The end motion of the arch is in general not harmonic, especially when the amplitude of lateral vibration is large. In the case when the excitation frequency is close to the nth natural frequency of the arch, we found that geometrical imperfection is the key for the nth mode to be excited. Analytical formula relating the amplitude of the steady state response and the geometrical imperfection can be derived via a multiple scale analysis. In the case when the excitation frequency is close to two times of the nth natural frequency two stable steady state responses can exist simultaneously. As a consequence jump phenomenon is observed when the excitation frequency sweeps upward. The effect of geometrical imperfection on the steady state response is minimal in this case. The multiple scale analysis not only predicts the amplitudes and phases of both the stable and unstable solutions, but also predicts analytically the frequency at which jump phenomenon occurs.

Electromechanical Modeling and Nonlinear Analysis of Axially Loaded Energy Harvesters

2010 ◽  
Vol 133 (1) ◽  
Author(s):  
Ravindra Masana ◽  
Mohammed F. Daqaq
Keyword(s):  
Steady State ◽  
Output Power ◽  
Axial Load ◽  
Excitation Frequency ◽  
Response Amplitude ◽  
Steady State Response ◽  
Smart Mater ◽  
Energy Harvesters ◽  
State Response ◽  
Piezoelectric Vibration

To maximize the electromechanical transduction of vibratory energy harvesters, the resonance frequency of the harvesting device is usually tuned to the excitation frequency. To achieve this goal, some concepts call for utilizing an axial static preload to soften or stiffen the structure (Leland and Wright, 2006, “Resonance Tuning of Piezoelectric Vibration Energy Scavenging Generators Using Compressive Axial Preload,” Smart Mater. Struct., 15, pp. 1413–1420; Morris et al., 2008, “A Resonant Frequency Tunable, Extensional Mode Piezoelectric Vibration Harvesting Mechanism,” Smart Mater. Struct., 17, p. 065021). For the most part, however, models used to describe the effect of the axial preload on the harvester’s response are linear lumped-parameter models that can hide some of the essential features of the dynamics and, sometimes, oppose the experimental trends. To resolve this issue, this study aims to develop a comprehensive understanding of energy harvesting using axially loaded beams. Specifically, using nonlinear Euler–Bernoulli beam theory, an electromechanical model of a clamped-clamped energy harvester subjected to transversal excitations and static axial loading is developed and discretized using a Galerkin expansion. Using the method of multiple scales, the general nonlinear physics of the system is investigated by obtaining analytical expressions for the steady-state response amplitude, the voltage drop across a resistive load, and the output power. These theoretical expressions are then validated against experimental data. It is demonstrated that in addition to the ability of tuning the harvester to the excitation frequency via axial load variations, the axial load aids in (i) increasing the electric damping in the system, thereby enhancing the energy transfer from the beam to the electric load, (ii) amplifying the effect of the external excitation on the structure, and (iii) enhancing the effective nonlinearity of the device. These factors combined can increase the steady-state response amplitude, output power, and bandwidth of the harvester.

Steady-State Response of Continuous Nonlinear Rotor-Bearing Systems Using Analytical Approach

1998 ◽  
Vol 120 (4) ◽  
pp. 751-758 ◽  
Author(s):  
J. W. Zu ◽  
Z. Y. Ji
Keyword(s):  
Steady State ◽  
Harmonic Balance Method ◽  
Beam Theory ◽  
Distributed Parameter ◽  
Steady State Response ◽  
State Response ◽  
Rotor Bearing ◽  
Continuous Modeling ◽  
Close Form ◽  
First Time

A continuous modeling of nonlinear rotor-bearing systems is presented in this paper. The shaft is treated as a distributed parameter system using Timoshenko beam theory. A close form, steady-state response of the system is solved analytically for the first time. For cubic nonlinear bearings, the response is composed of three components, synchronous vibration, subsynchronous, and supersynchronous vibration. The harmonic balance method is used to calculate the nonlinear bearing forces. Two examples of nonlinear rotor-bearing systems are shown to illustrate the analysis procedure and the nonlinear characteristics of the system. Solutions from simplified systems are also derived for comparison.

scholarly journals Local Sensitivity Analysis of Steady-State Response of Rotors with Rub-Impact to Parameters of Rubbing Interfaces

2021 ◽  
Vol 11 (3) ◽  
pp. 1307
Author(s):  
Minghong Jiang ◽  
Zhaoli Zheng ◽  
Yonghui Xie ◽  
Di Zhang
Keyword(s):  
Sensitivity Analysis ◽  
Steady State ◽  
Duffing Oscillator ◽  
Harmonic Balance Method ◽  
Friction Model ◽  
Design Parameters ◽  
Steady State Response ◽  
Local Sensitivity ◽  
Local Sensitivity Analysis ◽  
State Response

Local sensitivity analysis, which describes the relative importance of specific design parameters to the response of systems, is crucial for investigating dominant factors in optimal design. In this paper, local sensitivity analysis of the response of rotors with rub-impact to parameters of rubbing interfaces is carried out. The steady-state motion of the rotor is evaluated by a harmonic balance method and the sensitivity coefficients for every rotation speed over the speed range are derived analytically. Two classical models, including the Duffing oscillator and the gap model, are utilized to validate the accuracy and capability of the adopted methods and high accuracy is shown. Numerical investigations of sensitivities of steady-state response of rotors to parameters of rubbing interfaces are then carried out, based on a lumped Jeffcott rotor and a finite element model respectively. Conclusions are drawn that the response of rotors subjected to rubbing problems is more sensitive to initial clearance than other parameters of the applied friction model. With increase of initial gap, the response of rotors becomes more sensitive and the range of region subjected to rub-impact forces shrinks until the separation of rotor and stator.

Modeling and Analysis of Friction Rim Dampers for Blisks

2005 ◽  
Author(s):  
Denis Laxalde ◽  
Jean-Jacques Sinou ◽  
Fabrice Thouverez ◽  
Jean-Pierre Lombard
Keyword(s):  
Steady State ◽  
Harmonic Balance ◽  
Harmonic Balance Method ◽  
Design Guidelines ◽  
Lumped Parameter Model ◽  
Dynamical Analysis ◽  
Steady State Response ◽  
Modeling And Analysis ◽  
State Response ◽  
Lumped Parameter

A damping strategy for blisks of turbomachinery involving a friction rim is investigated. These rims, located in grooves underside the wheel of the blisks, are held in by centrifugal loads and the energy is dissipated when relative motions between the rim and the disk occur. A method of dynamical analysis of a cyclic blisk nonlinearly coupled with a split rim is presented: the steady-state response being calculated using an multi-harmonic balance method. Numerical simulations on a lumped-parameter model are presented for several damper characteristics and several excitation configurations. From these results, the performance of this damping strategy is discussed and some design guidelines are given. Finally the influence of mistuning on the damping performances is analysed.

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