Elasto-Dynamic Behavior of a Two-Dimensional Square Lattice With Entrained Fluid II: Microstructural and Homogenized Models

2014 ◽  
Vol 136 (3) ◽  
Author(s):  
Vladimir Dorodnitsyn ◽  
Alessandro Spadoni
Keyword(s):  
Relative Density ◽  
Coupled System ◽  
Element Model ◽  
Square Lattice ◽  
Porous Solids ◽  
Cellular Solid ◽  
Resonance Frequencies ◽  
Shear Modes ◽  
Structural Deformations ◽  
Analysis Of Dispersion

This paper presents a detailed study of the pressure waves and effective mechanical properties of a closed-cell cellular solid with entrained fluid. Plane-harmonic-waves are analyzed in a periodic square with a finite-element model of a representative-volume element, which explicitly considers fluid-structure interactions, structural deformations, and the fluid dynamics of entrained fluid. The wall, cavity, and coupled-system resonance frequencies are identified as key parameters that describe the propagation characteristics. A tube-piston model based on computed microstructural deformations allows us to determine the effective stiffness tensor of an equivalent continuum at the macroscale. The analysis of dispersion surfaces indicates a single isotropic pressure mode for frequencies below resonance of the lattice walls, unlike Biot's theory which predicts two pressure modes. Shear modes are instead strongly anisotropic for all values of relative density ρ* describing both cellular ρ*<0.3 and porous solids ρ*≥0.3. The dependence of the pressure wave phase velocity on the relative density is analyzed for varying properties of the entrained fluid. Depending on the relative density and mass coupling of the solid and fluid phases, the microstructural deformations can be of three types: bending, through-the-thickness, and the combination of the two. For heavy and stiff entrained fluid, the bending regime is confined to extremely small values of relative density, whereas for light fluid such as a gas, deformations are of the bending-type for ρ*<0.1. Through-the-thickness deformations appear only for the heavy entrained fluid for large values of ρ*.

Elastodynamics of a Two-Dimensional Square Lattice With Entrained Fluid—Part I: Comparison With Biot's Theory

2014 ◽  
Vol 136 (2) ◽  
Author(s):  
Vladimir Dorodnitsyn ◽  
Alessandro Spadoni
Keyword(s):  
Wave Propagation ◽  
Shear Waves ◽  
Wave Spectrum ◽  
Fluid Pressure ◽  
Element Model ◽  
Square Lattice ◽  
Porous Solids ◽  
Cellular Solids ◽  
Biot’S Theory ◽  
Biot's Theory

In the present paper, the performance of Biot's theory is investigated for wave propagation in cellular and porous solids with entrained fluid for configurations with well-known drained (no fluid) mechanical properties. Cellular solids differ from porous solids based on their relative density ρ*<0.3. The distinction is phenomenological and is based on the applicability of beam (or plate) theories to describe microstructural deformations. The wave propagation in a periodic square lattice is analyzed with a finite-element model, which explicitly considers fluid-structure interactions, structural deformations, and fluid-pressure variations. Bloch theorem is employed to enforce symmetry conditions of a representative volume element and obtain a relation between frequency and wavevector. It is found that the entrained fluid does not affect shear waves, beyond added-mass effects, so long as the wave spectrum is below the pores' natural frequency. One finds strong dispersion in cellular solids as a result of resonant scattering, in contrast to Bragg scattering dominant in porous media. Configurations with 0.0001≤ρ*≤1 are investigated. One finds that Biot's theory, derived from averaged microstructural quantities, well estimates the phase velocity of pressure and shear waves for cellular porous solids, except for the limit ρ*→1. For frequencies below the first resonance of the lattice walls, only the fast-pressure mode of the two modes predicted by Biot's theory is found. It is also shown that homogenized models for shear waves based on microstructural deformations for drained conditions agree with Biot's theory.

Quantify Resonance Inspection With Finite-Element-Based Modal Analyses

2010 ◽  
Author(s):  
K. Lai ◽  
X. Sun ◽  
C. Dasch
Keyword(s):  
Finite Element ◽  
High Stress ◽  
Mesh Size ◽  
Element Model ◽  
Sensitivity Study ◽  
Production Level ◽  
Mode Shapes ◽  
Resonance Spectroscopy ◽  
Frequency Spectra ◽  
Resonance Frequencies

Resonance inspection uses the natural acoustic resonances of a part to identify anomalous parts. Modern instrumentation can measure the many resonant frequencies rapidly and accurately. Sophisticated sorting algorithms trained on sets of good and anomalous parts can rapidly and reliably inspect and sort parts. This paper aims at using finite-element-based modal analysis to put resonance inspection on a more quantitative basis. A production-level automotive steering knuckle is used as the example part for our study. First, the resonance frequency spectra for the knuckle are measured with two different experimental techniques. Next, scanning laser vibrometry is used to determine the mode shape corresponding to each resonance. The material properties including anisotropy are next measured to high accuracy using resonance spectroscopy on cuboids cut from the part. Then, finite element model (FEM) of the knuckle is generated by meshing the actual part geometry obtained with computed tomography (CT). The resonance frequencies and mode shapes are next predicted with a natural frequency extraction analysis after extensive mesh size sensitivity study. The good comparison between the predicted and the experimentally measured resonance spectra indicate that finite-element-based modal analyses have the potential to be a powerful tool in shortening the training process and improving the accuracy of the resonance inspection process for a complex, production level part. The finite element based analysis can also provide a means to computationally test the sensitivity of the frequencies to various possible defects such as porosity or oxide inclusions especially in the high stress regions that the part will experience in service.

scholarly journals System-Level Model and Simulation of a Frequency-Tunable Vibration Energy Harvester

Micromachines ◽  
2020 ◽  
Vol 11 (1) ◽  
pp. 91 ◽  
Author(s):  
Sofiane Bouhedma ◽  
Yongchen Rao ◽  
Arwed Schütz ◽  
Chengdong Yuan ◽  
Siyang Hu ◽  
...  
Keyword(s):  
Energy Harvester ◽  
Element Model ◽  
Industrial Applications ◽  
System Level ◽  
Dual Frequency ◽  
Frequency Range ◽  
Vibration Energy Harvester ◽  
Resonance Frequencies ◽  
Level Model ◽  
System Level Model

In this paper, we present a macroscale multiresonant vibration-based energy harvester. The device features frequency tunability through magnetostatic actuation on the resonator. The magnetic tuning scheme uses external magnets on linear stages. The system-level model demonstrates autonomous adaptation of resonance frequency to the dominant ambient frequencies. The harvester is designed such that its two fundamental modes appear in the range of (50,100) Hz which is a typical frequency range for vibrations found in industrial applications. The dual-frequency characteristics of the proposed design together with the frequency agility result in an increased operative harvesting frequency range. In order to allow a time-efficient simulation of the model, a reduced order model has been derived from a finite element model. A tuning control algorithm based on maximum-voltage tracking has been implemented in the model. The device was characterized experimentally to deliver a power output of 500 µW at an excitation level of 0.5 g at the respected frequencies of 63.3 and 76.4 Hz. In a design optimization effort, an improved geometry has been derived. It yields more close resonance frequencies and optimized performance.

Vibration Control With Magnetically Mounted Piezoelectric Actuators

2008 ◽  
Author(s):  
J. C. Collinger ◽  
W. C. Messner ◽  
J. A. Wickert
Keyword(s):  
Vibration Control ◽  
Permanent Magnets ◽  
Control Method ◽  
Contact Stiffness ◽  
Unit Length ◽  
Piezoelectric Actuators ◽  
Coupled System ◽  
Element Model ◽  
Magnetic Attraction ◽  
Piezoelectric Control

A novel vibration control method utilizing magnetically mounted piezoelectric actuators is described. Piezoelectric actuators are bonded to permanent magnets, which are attached to the surface of a steel cantilever beam through their magnetic attraction. The magnetic-piezoelectric control mounts are an alternative to traditional epoxy attachment methods for piezoelectrics which allows easy in-the-field reconfiguration. In model and laboratory measurements, the beam is driven through base excitation and the resonant shunt and synchronized switching techniques are applied to two magnetic-piezoelectric control mounts to attenuate vibration. The coupled system is discretized using a Galerkin finite element model that incorporates relative axial motion between the beam and the mounts, which is governed by the sticking contact stiffness per unit length of the beam-magnet interface. The control mounts are designed using a magnetic array configuration which increases the attraction force for a given magnet thickness. Results show that the magnetic-piezoelectric control mounts provide attenuation, while also providing the flexibility to easily adjust the actuators along the length of the beam.

Effects of tip relief on vibration responses of a geared rotor system

2013 ◽  
Vol 228 (7) ◽  
pp. 1132-1154 ◽  
Author(s):  
Hui Ma ◽  
Jian Yang ◽  
Rongze Song ◽  
Suyan Zhang ◽  
Bangchun Wen
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Element Model ◽  
Spur Gear ◽  
Rotor System ◽  
Time Varying ◽  
Frequency Range ◽  
Mesh Stiffness ◽  
Resonance Frequencies ◽  
Vibration Responses

Considering tip relief, a finite element model of a spur gear pair in mesh is established by ANSYS software. Time-varying mesh stiffness under different amounts of tip relief is calculated based on the finite element model. Then, a finite element model of a geared rotor system is developed by MATLAB software considering the effects of time-varying mesh stiffness and constant load torque. Emphasis is given to the effects of tip relief on the lateral–torsional coupling vibration responses of the system. The results show that as the amount of tip relief increases, the saltation of time-varying mesh stiffness reduces at the position of approach action and transition mesh region from the single tooth to double tooth. A number of primary resonances and some super-harmonic of gears 1 and 2 are excited by time-varying mesh stiffness in amplitude frequency responses. As the amount of tip relief increases, some super-harmonic responses change due to the variation in the higher frequency components of time-varying mesh stiffness. After tip relief, the vibration and meshing force decrease obviously at lower mesh frequency range except at some resonance frequencies; however, tip relief is not effective in reducing the vibration at higher mesh frequency range. The amplitude fluctuation of the vibration acceleration reduces evidently after considering tip relief, which is not remarkable with the increase of meshing frequency.

SPECTRAL PROPERTIES OF AN ELASTIC ROD-SPRING COUPLED SYSTEM IMMERSED IN A FLUID

1992 ◽  
Vol 02 (04) ◽  
pp. 441-460 ◽  
Author(s):  
J. SANCHEZ-HUBERT ◽  
S. BÉRÉTÉ ◽  
J. PLANCHARD
Keyword(s):  
Heat Exchangers ◽  
Spectral Properties ◽  
Nuclear Reactor ◽  
Dynamical Behavior ◽  
Coupled System ◽  
Elastic Tube ◽  
Elastic Rod ◽  
Resonance Frequencies ◽  
Continuous Material ◽  
Very High

The study of vibrations of elastic tube bundles immersed in a fluid is very important in Engineering, for example concerning the dynamical behavior of heat exchangers, nuclear reactor cores, etc. This paper is concerned with the investigation of the resonance frequencies when the number of rods is very high. That requires us to use the homogenization technique for modelling this coupled system by an equivalent continuous material. We then show that this equivalent system may have an essential spectrum.

scholarly journals Vibro-acoustic analysis of a trapezoidal cavity with a clamped flexible wall

2018 ◽  
Vol 37 (4) ◽  
pp. 801-815 ◽  
Author(s):  
Yuan Wang ◽  
Jianrun Zhang ◽  
Xinzhou Zhang ◽  
Bo Wu
Keyword(s):  
Acoustic Analysis ◽  
Coupled Model ◽  
Coupled System ◽  
Coupling Theory ◽  
Incident Plane ◽  
Resonance Frequencies ◽  
Modal Coupling ◽  
Cavity Coupling ◽  
Flexible Wall ◽  
Matching Degree

The coupled model between trapezoidal cavity and its clamped flexible wall is developed using classical modal coupling theory. Based on the coupled model, the resonance frequencies of coupled system are obtained and compared with the corresponding uncoupled one. Meanwhile, the reason for the variation of resonance frequencies of coupled system modes is analyzed in detail. Then, the response of coupled system is investigated using the acoustic potential energy in the cavity and panel vibration kinetic energy when it is excited by an incident plane wave outside of the cavity. Coupling coefficient between trapezoidal cavity and its clamped flexible wall is proposed to assess the modal matching degree between them. It is shown that the coupling selection is not satisfied except in the axis direction which is parallel to the inclined wall. In addition, a rectangular cavity with a clamped flexible wall is also considered and compared with that of the trapezoidal one.

Dynamic Analysis of Flexible Structures Using Component Mode Synthesis

1989 ◽  
Vol 56 (4) ◽  
pp. 874-880 ◽  
Author(s):  
M. De Smet ◽  
C. Liefooghe ◽  
P. Sas ◽  
R. Snoeys
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Degrees Of Freedom ◽  
Flexible Structures ◽  
Element Model ◽  
Component Mode Synthesis ◽  
Mode Shapes ◽  
Flexible Robot ◽  
Preliminary Calculation ◽  
Resonance Frequencies

In this paper a dynamic model of a flexible robot is built out of a finite element model of each of its links. The number of degrees-of-freedom of these models is strongly reduced by applying the Component Mode Synthesis technique which involves the preliminary calculation of a limited number of mode shapes of the separate links. As can be seen from examples, the type of boundary conditions thereby imposed in the nodes in which one link is connected to the others, strongly determines the accuracy of the calculated resonance frequencies of the robot. The method is applied to an industrial manipulator. The reduced finite element model of the robot is changed in order to match the numerically and experimentally (modal analysis) determined resonance data. Further, the influence of the position of the robot on its resonance frequencies is studied using the optimized numerical model.

Highly Tunable Electrothermally Actuated Arch Resonator

2016 ◽  
Author(s):  
Amal Z. Hajjaj ◽  
Abdallah Ramini ◽  
Nouha Alcheikh ◽  
Mohammad I. Younis
Keyword(s):  
Resonance Frequency ◽  
Axial Stress ◽  
Beam Theory ◽  
Element Model ◽  
Shallow Arches ◽  
Tunable Resonators ◽  
Resonance Frequencies ◽  
Wide Range ◽  
Euler Bernoulli Beam ◽  
Thermal Voltage

This paper demonstrates experimentally, theoretically, and numerically a wide-range tunability of electrothermally actuated MEMS arch beams. The beams are made of silicon and are intentionally fabricated with some curvature as in-plane shallow arches. Analytical results based on the Galerkin discretization of the Euler Bernoulli beam theory are generated and compared to the experimental data and results of a multi-physics finite-element model. A good agreement is found among all the results. The electrothermal voltage is applied between the anchors of the clamped-clamped MEMS arch beam, generating a current that passes through the MEMS arch beam and controls its axial stress caused by thermal expansion. When the electrothermal voltage increases, the compressive stress increases inside the arch beam. This leads to increase in its curvature, thereby increases the resonance frequencies of the structure. We show here that the first resonance frequency can increase up to twice its initial value. We show also that after some electro-thermal voltage load, the third resonance frequency starts to become more sensitive to the axial thermal stress, while the first resonance frequency becomes less sensitive. These results can be used as guidelines to utilize arches as wide-range tunable resonators.

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