scholarly journals Passive Damping of Rotationally Periodic Structures with Tuned Piezoelectric Inductive Shunt

Actuators ◽  
2018 ◽  
Vol 7 (3) ◽  
pp. 41 ◽  
Author(s):  
Bilal Mokrani ◽  
Renaud Bastaits ◽  
Iulian Romanescu ◽  
Mihaita Horodinca ◽  
Ioan Burda ◽  
...  
Keyword(s):  
Circular Plate ◽  
Periodic Structures ◽  
Mode Shapes ◽  
Passive Damping ◽  
Specific Mode ◽  
Parallel Loops ◽  
Shunt Damping ◽  
Independent Loops

This paper considers the piezoelectric resistive and inductive RL shunt damping applied to rotationally periodic structures equipped with an array of regularly spaced piezoelectric patches. A method for simplifying the hardware, by reducing the size of the inductors and eliminating the use of synthetic inductors, is described. The paper compares two different ways of using the piezoelectric array: independent loops and parallel loops. It shows that, if a specific mode with n nodal diameters is targeted, mounting 4n piezoelectric patches in two parallel loops is as efficient as mounting them in 4n independent loops, while considerably reducing the demand on the inductors, L, (by 4n2). The method takes advantage of the mode shapes of rotationally periodic structures. The proposed method is validated numerically and experimentally on a rotationally periodic circular plate (nearly axisymmetric). The proposed technique is aimed at turbomachinery applications.

scholarly journals Parallel Piezoelectric Shunt Damping of Rotationally Periodic Structures

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
Bilal Mokrani ◽  
Renaud Bastaits ◽  
Mihaita Horodinca ◽  
Iulian Romanescu ◽  
Ioanica Burda ◽  
...  
Keyword(s):  
Circular Plate ◽  
Periodic Structure ◽  
Periodic Structures ◽  
Piezoelectric Transducers ◽  
Specific Mode ◽  
Parallel Loops ◽  
Shunt Damping ◽  
Independent Loops ◽  
Piezoelectric Shunt ◽  
Rotationally Periodic Structure

This paper considers the RL shunt damping of rotationally periodic structures with an array of regularly spaced piezoelectric patches. The technique is targeted to the damping of a specific mode withnnodal diameters. For this particular case, one can take advantage of the shape of the targeted mode to organize the piezoelectric patches as a modal filter (in parallel loops) which reduces the demand on the inductors of the tuned inductive shunt. In the case of a perfectly rotationally periodic structure, it is possible to organize 4npiezoelectric transducers (PZT patches) in two parallel loops of 2npatches each. In this way, the demand on the inductors is reduced by4n2as compared to independent loops, which may allow a fully passive integration of the RL shunt in a turbomachinery application. The method is first illustrated experimentally on a circular plate; it is then applied to a prototype of an industrial bladed drum. The influence of blade mistuning is investigated.

Experimental Implementation of Negative Impedance Shunts on Periodic Structures

2009 ◽  
Author(s):  
Benjamin Beck ◽  
Kenneth A. Cunefare ◽  
Massimo Ruzzene ◽  
Manuel Collet
Keyword(s):  
Periodic Structures ◽  
Experimental Results ◽  
Periodic Array ◽  
Negative Capacitance ◽  
Experimental Implementation ◽  
Theoretical Predictions ◽  
Shunt Damping

Shunt damping of structures has been heavily researched, both passively and actively. Negative capacitance shunts actively control vibration on a structure and have been shown to obtain significant broadband suppression. The use of smaller piezoelectric patches, implemented in a periodic array, can alter the behavior of the control. Assorted shunt arrangements as well as circuit configurations will be investigated. Experimental results will be compared to theoretical predictions of shunt performance.

Geometric Mistuning Reduced-Order Model Development Utilizing Bayesian Surrogate Models for Component Mode Calculations

2019 ◽  
Vol 141 (10) ◽  
Author(s):  
Joseph A. Beck ◽  
Jeffrey M. Brown ◽  
Alex A. Kaszynski ◽  
Emily B. Carper ◽  
Daniel L. Gillaugh
Keyword(s):  
Periodic Structures ◽  
Model Development ◽  
Element Model ◽  
Forced Response ◽  
Mode Shapes ◽  
Order Model ◽  
Mode Localization ◽  
Reduced Order ◽  
Structural Periodicity ◽  
Computationally Intensive

AbstractIntegrally bladed rotors (IBRs) are meant to be rotationally periodic structures. However, unique variations in geometries and material properties from sector-to-sector, called mistuning, destroy the structural periodicity. This results in mode localization that can induce forced response levels greater than what is predicted with a tuned analysis. Furthermore, mistuning and mode localization are random processes that require stochastic treatments when analyzing the distribution of fleet responses. Generating this distribution can be computationally intensive when using the full finite element model (FEM). To overcome this expense, reduced-order models (ROMs) have been developed to accommodate fast calculations of mistuned forced response levels for a fleet of random IBRs. Usually, ROMs can be classified by two main families: frequency-based and geometry-based methods. Frequency-based ROMs assume mode shapes do not change due to mistuning. However, this assumption has been shown to cause errors that propagate to the fleet distribution. To circumvent these errors, geometry-based ROMs have been developed to provide accurate predictions. However, these methods require recalculating modal data during ROM formulations. This increases the computational expense in computing fleet distributions. A new geometry-based ROM is presented to reduce this cost. The developed ROM utilizes a Bayesian surrogate model in place of sector modal calculations required in ROM formulations. The method, surrogate modal analysis for geometry mistuning assessments (SMAGMA), will propagate uncertainties of the surrogate prediction to forced response. ROM accuracies are compared to the true forced response levels and results computed by a frequency-based ROM.

Frequency Response for MEMS Circular Plate Resonators Under Superharmonic Resonance of the Second Order

2018 ◽  
Author(s):  
Martin Botello ◽  
Julio Beatriz ◽  
Dumitru I. Caruntu
Keyword(s):  
Circular Plate ◽  
Software Package ◽  
Multiple Scales ◽  
Electrostatic Force ◽  
Micro Electro Mechanical System ◽  
Second Order ◽  
Mode Shapes ◽  
Amplitude Response ◽  
Superharmonic Resonance ◽  
Mems Resonator

A nonlinear dynamics investigation is conducted on the frequency-amplitude response of electrostatically actuated micro-electro-mechanical system (MEMS) clamped plate resonators. The Alternating Current (AC) voltage is operating in the realm of superharmonic resonance of second order. This is given by an AC frequency near one-fourth of the natural frequency of the resonator. The magnitude of the AC voltage is large enough to be considered as hard excitation. The external forces acting on the MEMS resonator are viscous air damping and electrostatic force. Two proven mathematical models are utilized to obtain a predicted frequency-amplitude response for the MEMS resonator. Method of Multiple Scales (MMS) allows the transformation of a partial differential equation of motion into zero-order and first-order problems. Hence, MMS can be directly applied to obtain the frequency-amplitude response. Reduced Order Model (ROM), based on the Galerkin procedure, uses mode shapes of vibration for undamped circular plate resonator as a basis of functions. ROM is numerically integrated using MATLAB software package to obtain time responses. Also, ROM is used to conduct a continuation and bifurcation analysis utilizing AUTO 07P software package in order to obtain the frequency-amplitude response. The time responses show the movement of the center of the MEMS circular plate as a function of time. The frequency-amplitude response allows one to observe bifurcation and pull-in instabilities within the nonlinear system over a range of frequencies. The influences of parameters (i.e. damping and voltage) are also included in this investigation.

Free Vibration Investigation of Submerged Thin Circular Plate

2020 ◽  
Vol 12 (03) ◽  
pp. 2050025
Author(s):  
Xi Yang ◽  
Adil El Baroudi ◽  
Jean Yves Le Pommellec
Keyword(s):  
Free Surface ◽  
Free Vibration ◽  
Circular Plate ◽  
Plate Theory ◽  
Fluid Pressure ◽  
Three Dimensional ◽  
Coupled System ◽  
Mode Shapes ◽  
Thin Circular Plate ◽  
Benchmark Solutions

Free vibration of coupled system including clamped-free thin circular plate with hole submerged in three-dimensional cylindrical container filled with inviscid, irrotational and compressible fluid is investigated in this work. Numerical approach based on the finite element method (FEM) is performed using the Comsol Multiphysics software, in order to analyze qualitatively the vibration characteristics of the plate. Plate modeling is based on Kirchhoff–Love plate theory. Velocity potential is deployed to describe the fluid motion since the small oscillations induced by the plate vibration is considered. Bernoulli’s equation together with potential theory is applied to get the fluid pressure on the free surface of the plate. To prove the reliability of the present numerical solution, a comparison is made with the results in the literature, which shows a very good agreement. Then, different parameters effect including fluid density, fluid height, free surface wave, hole radius and hole eccentricity on the natural frequencies of the coupled system is discussed in detail. Some three-dimensional mode shapes of the submerged plate are illustrated. Furthermore, the obtained results can serve as benchmark solutions for the vibration control, parameter identification and damage detection of plate.

Excitation of Arbitrary Displacement/Velocity Conditions in Rotationally Periodic Structures

1995 ◽  
Author(s):  
P. Schmiechen ◽  
D. J. Ewins ◽  
I. Bucher
Keyword(s):  
Natural Frequencies ◽  
Periodic Structures ◽  
Search Algorithm ◽  
Simulated Data ◽  
Travelling Wave ◽  
Modal Testing ◽  
Mode Shapes ◽  
Wave Form ◽  
Structure Interaction ◽  
Wave Patterns

Abstract For an investigation into the structural interaction between rotating and non-rotating rotationally periodic turbine components, it was required to be able to generate experimentally prescribed response conditions. In more descriptive terms, conditions were sought to excite wave-patterns such as travelling and standing waves, and to suppress certain modes. In the paper these conditions are derived from modal properties. Simulated data are presented to demonstrate some of the phenomena and to highlight the practical difficulties. For rotationally periodic structures, most natural frequencies are of multiplicity two, and are sometimes called ‘double modes’. Their associated mode shapes can rotate in the plane of symmetry. The responses due to the two modes can be combined and expressed in a wave form, which can be split into travelling and standing wave components. Theoretically, it is possible to excite a pure travelling wave in a perfectly rotationally periodic structure, but there are limits to this in practice as real structures will always exhibit some degree of imperfection. These structures are said to be mistuned, and the imperfection splits the double modes into pairs of close modes. Simulations show the predicted vibration phenomena. In particular, the case of discrete excitations relevant to modal testing is investigated. The simulations show clearly that in this case components of other modes will generally be present. In an experiment, the results for driving the excitations will not give the theoretically expected response due to non-linearities of the shaker-structure interaction. However, the effects can be reduced by employing a computerised search algorithm.

Design method of functional mode shapes using periodic structures

2017 ◽  
Vol 2017 (0) ◽  
pp. 444
Author(s):  
Sho WATANABE ◽  
Yuichi MATSUMURA ◽  
Kohei FURUYA
Keyword(s):  
Periodic Structures ◽  
Design Method ◽  
Mode Shapes ◽  
Functional Mode

Free Vibration and Tension Buckling of Circular Plates With Diametral Point Forces

1990 ◽  
Vol 57 (4) ◽  
pp. 995-999 ◽  
Author(s):  
E. F. Ayoub ◽  
A. W. Leissa
Keyword(s):  
Circular Plate ◽  
Tensile Force ◽  
Ritz Method ◽  
Compressive Force ◽  
Free Vibrations ◽  
Plane Elasticity ◽  
Mode Shapes ◽  
Simply Supported ◽  
Symmetry Classes ◽  
Tensile Forces

This paper presents the first known results for the free vibrations of a circular plate subjected to a pair of static, concentrated forces acting on the boundary at opposite ends of a diameter. The closed-form exact solution of the plane elasticity problem is used to provide the in-plane stress distribution for the vibration problem. A proper procedure using the Ritz method is developed for solving the latter problem for clamped, simply supported, or free boundary conditions. Numerical results are given for the vibration frequencies of a simply supported circular plate, which separate into four symmetry classes of mode shapes. Compressive buckling loads for each symmetry class are determined as a special case as the frequencies decrease to zero with increasing compressive force. Tracking the frequency versus loading data with increasing tensile forces shows that buckling due to tensile force can also occur, and the critical value of the force is found.

VIBRATION AND STABILITY OF A HEAVY AND HEATED VERTICAL CIRCULAR PLATE

2010 ◽  
Vol 10 (05) ◽  
pp. 1111-1121 ◽  
Author(s):  
R. MARETIC ◽  
V. GLAVARDANOV ◽  
V. MILOSEVIC-MITIC
Keyword(s):  
Circular Plate ◽  
Natural Frequencies ◽  
Mode Shapes ◽  
Plate Edge ◽  
Asymmetric Mode ◽  
Critical Weight ◽  
Transverse Vibrations ◽  
Weight Parameter ◽  
Plate Stability ◽  
Parameter Values

This paper is concerned with the vibration and stability of a standing, heavy, and circular plate when heated. This investigation also deals with the plate being exposed to inertial forces due to uniform acceleration. The plate edge is clamped. Natural frequencies of transverse vibrations depending on the plate weight and temperature were determined using the Galerkin's method. Mode shapes are given for some frequencies including the influence of weight parameter on changes in mode shapes. It is shown that frequencies split for the asymmetric mode shapes, so that there are two different frequencies in those cases. Critical weight parameter values where plate stability ceases were determined. Critical values of the weight parameter depending on Poisson's ratio are also presented herein.

scholarly journals Shape adaptation of beams (1D) and plates (2D) to maximise eigenfrequencies

2020 ◽  
Vol 12 (11) ◽  
pp. 168781402097190
Author(s):  
Simone Andresen ◽  
Laura M Lottes ◽  
Selina K Linnemann ◽  
Reinhold Kienzler
Keyword(s):  
Mode Shape ◽  
Structural Design ◽  
Mode Shapes ◽  
Simultaneous Increase ◽  
Structural Adaptation ◽  
Active Systems ◽  
Specific Mode ◽  
Additional Weight ◽  
Shape Adaptation ◽  
Structural Deformations

Finding the optimal structural design to avoid resonance has been a goal for decades. While recent applied methods often result in using additional active systems or higher mass, structural adaptation enables to shift eigenfrequencies without adding weight. The aim of this study is to investigate the influence of the structural adaptation of a beam and a plate on its eigenfrequency change, while varying the height of the structural pre-deformation according to its mode shapes. Besides the maximisation of single eigenfrequencies, also the simultaneous increase of multiple eigenfrequencies is analysed. It is possible to almost exclusively raise the frequency of the targeted [Formula: see text]-th mode shape ([Formula: see text] = 1–5) of a beam, while the increase of the [Formula: see text]-th plate mode shape frequency ([Formula: see text] = 1–4) simultaneously alters other eigenfrequencies. Both the eigenfrequencies and specific mode shape frequencies are able to be significantly increased. In conclusion, the investigated, easy applicable method allows a strong eigenfrequency raise of axially constrained 1D and 2D structures by performing only small structural deformations without adding additional weight.

Sign in / Sign up

Export Citation Format

Share Document