Resonance Frequency Detuning in Regions of High Modal Density

2017 ◽  
Author(s):  
Garrett K. Lopp ◽  
Jeffrey L. Kauffman
Keyword(s):  
Resonance Frequency ◽  
Frequency Detuning ◽  
Modal Density ◽  
High Modal Density

Power Flow and Energy Sharing between an Oscillator and a Continuous Receiver Structure

2011 ◽  
Vol 189-193 ◽  
pp. 1914-1917
Author(s):  
Lin Ji
Keyword(s):  
High Frequency ◽  
Power Flow ◽  
Energy Analysis ◽  
Statistical Energy Analysis ◽  
Coupled Subsystems ◽  
Modal Density ◽  
Vibration Problems ◽  
Energy Sharing ◽  
High Modal Density ◽  
Vibration Modeling

A key assumption of conventional Statistical Energy Analysis (SEA) theory is that, for two coupled subsystems, the transmitted power from one to another is proportional to the energy differences between the mode pairs of the two subsystems. Previous research has shown that such an assumption remains valid if each individual subsystem is of high modal density. This thus limits the successful applications of SEA theory mostly to the regime of high frequency vibration modeling. This paper argues that, under certain coupling conditions, conventional SEA can be extended to solve the mid-frequency vibration problems where systems may consist of both mode-dense and mode-spare subsystems, e.g. ribbed-plates.

Influence of Internal Structures of High Modal Density on Shell’s Radiation

1997 ◽  
Author(s):  
Lionel Oddo ◽  
Bernard Laulagnet ◽  
Jean-louis Guyader
Keyword(s):  
Cylindrical Shell ◽  
Sound Radiation ◽  
Numerical Results ◽  
Structural Damping ◽  
Radiation Spectra ◽  
Modal Density ◽  
Internal Structures ◽  
High Modal Density

Abstract The aim of this paper is to study the sound radiation by a cylindrical shell internally coupled with mechanical structures of high modal density. The model is based on a mobility technique. The numerical results show a smoothing of the cylinder’s velocity and radiation spectra associated with an increase of the apparent damping. The use of the S.E.A. method allows us to calculate an additional structural damping of the shell, equivalent to the effect of the internal structures.

Switch Triggers for Optimal Vibration Reduction via Resonance Frequency Detuning

2014 ◽  
Author(s):  
Garrett K. Lopp ◽  
Jeffrey L. Kauffman
Keyword(s):  
Resonance Frequency ◽  
Coupling Coefficient ◽  
Electromechanical Coupling ◽  
Damping Ratio ◽  
Vibration Reduction ◽  
Electromechanical Coupling Coefficient ◽  
Peak Strain ◽  
Frequency Detuning ◽  
Optimal Frequency ◽  
Response Dynamics

For systems subjected to linear frequency sweep excitation, piezoelectric-based resonance frequency detuning provides vibration reduction by altering the stiffness state of the material as it passes through resonance. This vibration reduction technique applies to turbomachinery experiencing changes in rotation speed, for example on spool-up and spool-down. The peak response dynamics are determined by the system’s sweep rate, modal damping ratio, electromechanical coupling coefficient, and, most importantly, the frequency at which the stiffness state is altered. An analytical approach is employed to solve the nondimensional single degree of freedom equation of motion and is scaled to incorporate the altered system frequency following the stiffness state switch. This paper provides an extensive study over a range of sweep rates, damping ratios, and electromechanical coupling coefficients to determine the optimal frequency switch trigger that minimizes the response envelope. This switch trigger is primarily a function of the electromechanical coupling coefficient and the phase of vibration at which the switch occurs. As the coupling coefficient increases, the switch trigger decreases and is approximately linear with the square of this coupling coefficient. Furthermore, as with other state-switching techniques, the optimal frequency switch occurs when the phase of vibration is at the point of maximum displacement, or peak strain energy.

Nonlinear Parametric Reduced-Order Model for the Structural Dynamics of Hybrid Electric Vehicle Batteries

2017 ◽  
Vol 140 (2) ◽  
Author(s):  
Jauching Lu ◽  
Kiran D'Souza ◽  
Matthew P. Castanier ◽  
Bogdan I. Epureanu
Keyword(s):  
Hybrid Electric Vehicle ◽  
Vibration Response ◽  
Point Of View ◽  
Reduced Order Models ◽  
Structural Variations ◽  
Order Model ◽  
Reduced Order ◽  
Modal Density ◽  
Battery Packs ◽  
High Modal Density

Battery packs used in electrified vehicles exhibit high modal density due to their repeated cell substructures. If the excitation contains frequencies in the region of high modal density, small commonly occurring structural variations can lead to drastic changes in the vibration response. The battery pack fatigue life depends strongly on their vibration response; thus, a statistical analysis of the vibration response with structural variations is important from a design point of view. In this work, parametric reduced-order models (PROMs) are created to efficiently and accurately predict the vibration response in Monte Carlo calculations, which account for stochastic structural variations. Additionally, an efficient iterative approach to handle material nonlinearities used in battery packs is proposed to augment the PROMs. The nonlinear structural behavior is explored, and numerical results are provided to validate the proposed models against full-order finite element approaches.

scholarly journals Development of a hybrid SmEdA/SEA model for predicting the power exchanged between low and high modal density subsystems

2021 ◽  
Vol 263 (3) ◽  
pp. 3824-3832
Author(s):  
Guang Zhu ◽  
Laurent Maxit ◽  
Nicolas Totaro ◽  
Alain Le Bot
Keyword(s):  
Power Flow ◽  
The Other ◽  
Mode Shapes ◽  
Distribution Analysis ◽  
Coupled Subsystems ◽  
Modal Density ◽  
Spectrum Density ◽  
Energy Equipartition ◽  
Cavity System ◽  
High Modal Density

Statistical modal Energy distribution Analysis (SmEdA) was developed from classical Statistical Energy Analysis (SEA). It allows computing power flow between coupled subsystems from the deterministic modes of uncoupled subsystems without assuming the SEA modal energy equipartition. SmEdA is well adapted in mid-frequency when the subsystems have not a very high modal density. However, for some systems e.g. the plate-cavity system, one subsystem can exhibit a low modal density while the other one a high one. The goal of the paper is then to propose an extension of SmEdA formulation that allows describing one subsystem by its deterministic modes, and the other one as a diffuse field statistically supposing modal energy equipartition. The uncertain subsystem is then characterized by sets of natural frequencies and mode shapes constructed based on Gaussian Orthogonal Ensemble matrix and the cross-spectrum density of a diffuse field, respectively. This formulation permits not only the computation of mean noise response but also the variance generated by the uncertainties and furthermore without bringing in much computation. It is demonstrated that the obtained analytical results from the proposed hybrid SmEdA/SEA are consistent with numerical results computed by FEM with an appropriate degree of uncertainty.

Friction Damping of Hollow Airfoils: Part II—Experimental Verification

1998 ◽  
Vol 120 (1) ◽  
pp. 126-130 ◽  
Author(s):  
Y. M. EL-Aini ◽  
B. K. Benedict ◽  
W.-T. Wu
Keyword(s):  
Essential Element ◽  
Forced Response ◽  
Friction Damping ◽  
Modal Density ◽  
Speed Range ◽  
Manufacturing Tolerances ◽  
Hollow Cavity ◽  
Microslip Friction ◽  
High Modal Density ◽  
Damping Model

The use of hollow airfoils in turbomachinery applications, in particular fans and turbines, is an essential element in reducing the overall engine weight. However, state-of-the-art airfoil geometries are of low aspect ratio and exhibit unique characteristics associated with plate like modes. These modes are characterized by a chordwise form of bending and high modal density within the engine operating speed range. These features combined with the mistuning effects resulting from manufacturing tolerances make accurate frequency and forced response predictions difficult and increase the potential for High Cycle Fatigue (HCF) durability problems. The present paper summarizes the results of an experimental test program on internal damping of hollow bladelike specimens. Friction damping is provided via sheet metal devices configured to fit within a hollow cavity with various levels of preload. The results of the investigation indicate that such devices can provide significant levels of damping, provided the damper location and preload is optimized for the modes of concern. The transition of this concept to actual engine hardware would require further optimization with regard to wear effects and loss of preload particularly in applications where the preload is independent of rotational speed. Excellent agreement was achieved between the experimental results and the analytical predictions using a microslip friction damping model.

scholarly journals Modal Tests and Analysis of a Radial Impeller at Rest: Influence of Surrounding Air on Damping

2012 ◽  
Author(s):  
C. Gibert ◽  
L. Blanc ◽  
P. Almeida ◽  
X. Leblanc ◽  
J.-P. Ousty ◽  
...  
Keyword(s):  
Ambient Pressure ◽  
Damping Ratio ◽  
Flexural Mode ◽  
Aerodynamic Damping ◽  
Basic Fluid ◽  
Modal Density ◽  
Single Piece ◽  
Direct Interpretation ◽  
Turbomachinery Blades ◽  
High Modal Density

HCF risk assessment for turbomachinery blades requires the prediction of vibratory levels, which in turn requires fine damping quantification. This issue is especially sensitive for structures with low structural damping such as monobloc centrifugal compressor disks (blisks). The material composing blisks and aero-dynamic flow both contribute to damping phenomena. A strategy for non-aerodynamic damping characterization is to perform experiments in vacuum. This paper focuses on the use of modal tests in vacuum to estimate material damping under non-rotating conditions. Experiments are performed on an isolated impeller manufactured from a single piece in a vacuum chamber at different air pressure levels ranging from 10 mbar to 1 bar. Strong dependency of damping ratios on pressure can be found on the first flexural mode, leading to two types of application. Firstly, measurements enable assessing the validity of extrapolations of non-aerodynamic damping from measurements sometimes performed under less thorough vacuum conditions. Basic fluid-structure interaction models are used to interpret and quantify the evolution of modal quantities when air is progressively removed. Secondly, vacuum measurements can give frequency response functions (FRFs) with much greater separation between resonance peaks. In this study, the damping ratio found in vacuum condition are 3% of these at ambient pressure corresponding to a magnitude 30dB higher at resonance peaks. This contrasts with in-air measurements on cyclic symmetry structures, like blisks, with high modal density that make the direct interpretation of FRFs and their modal analysis more difficult.

Inter-Modal Couplings between Two Sea Subsystems with an Arbitrary Interface

2011 ◽  
Vol 130-134 ◽  
pp. 824-828
Author(s):  
Lin Ji ◽  
Zhen Yu Huang
Keyword(s):  
Energy Analysis ◽  
Simple Technique ◽  
Dynamic Stiffness ◽  
Statistical Energy Analysis ◽  
Coupling Loss ◽  
Simple Manner ◽  
Modal Density ◽  
Modal Coupling ◽  
Coupling Stiffness ◽  
High Modal Density

A simple technique is introduced to estimate the inter-modal coupling relations of two Statistical Energy Analysis (SEA) subsystems connected via an arbitrary interface. Based on a subsystem modal approach, the dynamic stiffness matrix of a generic built-up system is derived analytically. The coupling stiffness terms between any pair of subsystem modes can then be determined in explicit expressions. Under the proper SEA conditions, e.g. each subsystem has a high modal density and the couplings between SEA subsystems are sufficiently weak, these inter-modal coupling stiffness expressions can be greatly simplified. The results can then be easily accommodated within the standard SEA modeling procedure to predict the SEA response of generic built-up systems in a simple manner. Theoretical applications are made to estimate the SEA coupling loss factors between two subsystems connected by two rigid points.

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