The vibrational response of a fluid-loaded baffled plate near a free surface

2021 ◽  
Vol 263 (2) ◽  
pp. 4502-4510
Author(s):  
Jamie Kha
Keyword(s):  
Free Surface ◽  
Flat Plate ◽  
Acoustic Waves ◽  
Numerical Models ◽  
Equations Of Motion ◽  
Analytical Models ◽  
Fluid Loading ◽  
Infinite Domain ◽  
Vibrational Response ◽  
Admissible Functions

An analytical model to predict the vibrational response of a simply supported rectangular plate embedded in an infinite baffle with an upper free surface under heavy fluid loading and excited by a point force is presented. The equations of motion of a thin plate are solved using­­­­­­ modal decomposition technique by employing admissible functions for an in-vacuo plate and by directly solving the Helmholtz equation for acoustic waves in a fluid. The vibrational response for a flat plate in an infinite baffle and unbounded domain (semi-infinite domain) using analytical formulation available in literature is initially computed. These results are then compared against present results to observe the effect of a free surface. Predictions from analytical models are validated by comparison with results obtained by numerical models. The proposed analytical approach presents a novel formulation to describe a fluid-loaded flat plate in a waveguide and an efficient method for predicting its vibrational response.

Validation of a Belt Model for Prediction of Hub Forces from a Rolling Tire4

2009 ◽  
Vol 37 (2) ◽  
pp. 62-102 ◽  
Author(s):  
C. Lecomte ◽  
W. R. Graham ◽  
D. J. O’Boy
Keyword(s):  
Internal Pressure ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Prediction Method ◽  
Analytical Models ◽  
Beam Model ◽  
Impedance Boundary ◽  
Bending Waves ◽  
Tire Rotation ◽  
Three Dimensional Models

Abstract An integrated model is under development which will be able to predict the interior noise due to the vibrations of a rolling tire structurally transmitted to the hub of a vehicle. Here, the tire belt model used as part of this prediction method is first briefly presented and discussed, and it is then compared to other models available in the literature. This component will be linked to the tread blocks through normal and tangential forces and to the sidewalls through impedance boundary conditions. The tire belt is modeled as an orthotropic cylindrical ring of negligible thickness with rotational effects, internal pressure, and prestresses included. The associated equations of motion are derived by a variational approach and are investigated for both unforced and forced motions. The model supports extensional and bending waves, which are believed to be the important features to correctly predict the hub forces in the midfrequency (50–500 Hz) range of interest. The predicted waves and forced responses of a benchmark structure are compared to the predictions of several alternative analytical models: two three dimensional models that can support multiple isotropic layers, one of these models include curvature and the other one is flat; a one-dimensional beam model which does not consider axial variations; and several shell models. Finally, the effects of internal pressure, prestress, curvature, and tire rotation on free waves are discussed.

scholarly journals Gaining a better understanding of the extrusion process in fused filament fabrication 3D printing: a review

2021 ◽  
Author(s):  
Bahaa Shaqour ◽  
Mohammad Abuabiah ◽  
Salameh Abdel-Fattah ◽  
Adel Juaidi ◽  
Ramez Abdallah ◽  
...  
Keyword(s):  
3D Printing ◽  
Numerical Models ◽  
Extrusion Process ◽  
Analytical Models ◽  
Limiting Factor ◽  
Fused Filament Fabrication ◽  
Promising Tool ◽  
Relevant Work ◽  
3D Printing Technique ◽  
Required Quality

AbstractAdditive manufacturing is a promising tool that has proved its value in various applications. Among its technologies, the fused filament fabrication 3D printing technique stands out with its potential to serve a wide variety of applications, ranging from simple educational purposes to industrial and medical applications. However, as many materials and composites can be utilized for this technique, the processability of these materials can be a limiting factor for producing products with the required quality and properties. Over the past few years, many researchers have attempted to better understand the melt extrusion process during 3D printing. Moreover, other research groups have focused on optimizing the process by adjusting the process parameters. These attempts were conducted using different methods, including proposing analytical models, establishing numerical models, or experimental techniques. This review highlights the most relevant work from recent years on fused filament fabrication 3D printing and discusses the future perspectives of this 3D printing technology.

scholarly journals Structural and Acoustic Responses of a Submerged Stiffened Conical Shell

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Meixia Chen ◽  
Cong Zhang ◽  
Xiangfan Tao ◽  
Naiqi Deng
Keyword(s):  
Conical Shell ◽  
Element Model ◽  
Analytical Models ◽  
Superposition Method ◽  
Far Field ◽  
Fluid Loading ◽  
Low Frequencies ◽  
Structural Responses ◽  
The Individual ◽  
Field Sound

This paper studies the vibrational behavior and far-field sound radiation of a submerged stiffened conical shell at low frequencies. The solution for the dynamic response of the conical shell is presented in the form of a power series. A smeared approach is used to model the ring stiffeners. Fluid loading is taken into account by dividing the conical shell into narrow strips which are considered to be local cylindrical shells. The far-field sound pressure is solved by the Element Radiation Superposition Method. Excitations in two directions are considered to simulate the loading on the surface of the conical shell. These excitations are applied along the generator and normal to the surface of the conical shell. The contributions from the individual circumferential modes on the structural responses of the conical shell are studied. The effects of the external fluid loading and stiffeners are discussed. The results from the analytical models are validated by numerical results from a fully coupled finite element/boundary element model.

A new Reliable Numerical Algorithm Based on the First Kind of Bessel Functions to Solve Prandtl–Blasius Laminar Viscous Flow over a Semi-Infinite Flat Plate

2012 ◽  
Vol 67 (12) ◽  
pp. 665-673 ◽  
Author(s):  
Kourosh Parand ◽  
Mehran Nikarya ◽  
Jamal Amani Rad ◽  
Fatemeh Baharifard
Keyword(s):  
Viscous Flow ◽  
Flat Plate ◽  
Numerical Algorithm ◽  
Bessel Functions ◽  
Nonlinear Ordinary Differential Equation ◽  
Finite Domain ◽  
Algebraic Equations ◽  
Infinite Domain ◽  
Third Order ◽  
Domain Truncation

In this paper, a new numerical algorithm is introduced to solve the Blasius equation, which is a third-order nonlinear ordinary differential equation arising in the problem of two-dimensional steady state laminar viscous flow over a semi-infinite flat plate. The proposed approach is based on the first kind of Bessel functions collocation method. The first kind of Bessel function is an infinite series, defined on ℝ and is convergent for any x ∊ℝ. In this work, we solve the problem on semi-infinite domain without any domain truncation, variable transformation basis functions or transformation of the domain of the problem to a finite domain. This method reduces the solution of a nonlinear problem to the solution of a system of nonlinear algebraic equations. To illustrate the reliability of this method, we compare the numerical results of the present method with some well-known results in order to show the applicability and efficiency of our method.

scholarly journals Automated Insertion of Objects Into an Acoustic Robotic Gripper

Proceedings ◽  
2020 ◽  
Vol 64 (1) ◽  
pp. 40
Author(s):  
Marc Röthlisberger ◽  
Marcel Schuck ◽  
Laurenz Kulmer ◽  
Johann W. Kolar
Keyword(s):  
Acoustic Field ◽  
Acoustic Waves ◽  
Acoustic Pressure ◽  
Pressure Field ◽  
Acoustic Power ◽  
Industrial Applications ◽  
High Density ◽  
Analytical Models ◽  
Acoustic Levitation ◽  
Mechanical Contact

Acoustic levitation forces can be used to manipulate small objects and liquid without mechanical contact or contamination. To use acoustic levitation for contactless robotic grippers, automated insertion of objects into the acoustic pressure field is necessary. This work presents analytical models based on which concepts for the controlled insertion of objects are developed. Two prototypes of acoustic grippers are implemented and used to experimentally verify the lifting of objects into the acoustic field. Using standing acoustic waves and by dynamically adjusting the acoustic power, the lifting of high-density objects (>7 g/cm3) from acoustically transparent surfaces is demonstrated. Moreover, a combination of different acoustic traps is used to lift lower-density objects from acoustically reflective surfaces. The provided results open up new possibilities for the implementation of acoustic levitation in robotic grippers, which have the potential to be used in a variety of industrial applications.

Modelling of interactions between dykes, inclined sheets and faults at Santorini volcano

2021 ◽  
Author(s):  
Kyriaki Drymoni ◽  
John Browning ◽  
Agust Gudmundsson
Keyword(s):  
Tensile Strength ◽  
Fault Zone ◽  
Numerical Models ◽  
Damage Zone ◽  
Sheet Thickness ◽  
Analytical Models ◽  
Energy Conditions ◽  
Dyke Swarm ◽  
Normal Faults ◽  
Santorini Volcano

<p>Dykes and inclined sheets are known occasionally to exploit faults as parts of their paths, but the conditions that allow this to happen are still not fully understood. Here we report field observations from a well-exposed dyke swarm of the Santorini volcano, Greece, that show dykes and inclined sheets deflected into faults and the results of analytical and numerical models to explain the conditions for deflection. The deflected dykes and sheets belong to a local swarm of 91 dyke/sheet segments that was emplaced in a highly heterogeneous and anisotropic host rock and partially cut by some regional faults and a series of historic caldera collapses, the caldera walls providing, excellent exposures of the structures. The numerical models focus on a normal-fault dipping 65° with a damage zone composed of parallel layers or zones of progressively more compliant rocks with increasing distance from the fault rupture plane. We model sheet-intrusions dipping from 0˚ to 90˚ and with overpressures of alternatively 1 MPa and 5 MPa, approaching the fault. We further tested the effects of changing (1) the sheet thickness, (2) the fault-zone thickness, (3) the fault-zone dip-dimension (height), and (4) the loading by, alternatively, regional extension and compression. We find that the stiffness of the fault core, where a compliant core characterises recently active fault zones, has pronounced effects on the orientation and magnitudes of the local stresses and, thereby, on the likelihood of dyke/sheet deflection into the fault zone. Similarly, the analytical models, focusing on the fault-zone tensile strength and energy conditions for dyke/sheet deflection, indicate that dykes/sheets are most likely to be deflected into and use steeply dipping recently active (zero tensile-strength) normal faults as parts of their paths.</p>

Interaction Between the Underwater Explosion Bubble and the Structure

2008 ◽  
Author(s):  
A. M. Zhang ◽  
X. L. Yao ◽  
D. Y. Shi ◽  
J. Li
Keyword(s):  
Free Surface ◽  
Flat Plate ◽  
Dynamic Characteristics ◽  
Potential Flow ◽  
Underwater Explosion ◽  
Wall Pressure ◽  
Severe Damage ◽  
Plastic Structure ◽  
Pressure Peak ◽  
Great Damage

Based on the potential-flow assumption, BEM is applied to simulate the dynamic characteristics of underwater explosion bubble near boundaries and solve the interaction of bubble and elastic-plastic structure by coupling with FEM. A complete 3D program of underwater bubble analysis (UBA) is developed and the calculated error is within 10%. With this program, flat plate, cylinder and other simple structures are analyzed; the damages caused by retarded flow, pulsating pressure and jet and other loads on the structures are calculated, including different cases with free surface or without free surface. Results show that bubbles can cause great damage, and the specific cases can even cause greater damage. From the wall pressure and the stress curves of typical elements on the structure, it can be seen that the pressure peak occurs when the bubble collapses, which proves that the pressures caused by the bubble’s collapse and jet can result in great structure’s severe damage. It can provide reference for the research on the dynamic characteristics. The research in this paper aims to provide references for the correlated research on the dynamics of the underwater bubble.

Fourth‐order finite‐difference P-SV seismograms

Geophysics ◽  
1988 ◽  
Vol 53 (11) ◽  
pp. 1425-1436 ◽  
Author(s):  
Alan R. Levander
Keyword(s):  
Free Surface ◽  
Finite Difference ◽  
Fourth Order ◽  
Equations Of Motion ◽  
Dispersion Analysis ◽  
Numerical Dispersion ◽  
Staggered Grid ◽  
Order System ◽  
Surface Boundary ◽  
Lamb’S Problem

I describe the properties of a fourth‐order accurate space, second‐order accurate time, two‐dimensional P-SV finite‐difference scheme based on the Madariaga‐Virieux staggered‐grid formulation. The numerical scheme is developed from the first‐order system of hyperbolic elastic equations of motion and constitutive laws expressed in particle velocities and stresses. The Madariaga‐Virieux staggered‐grid scheme has the desirable quality that it can correctly model any variation in material properties, including both large and small Poisson’s ratio materials, with minimal numerical dispersion and numerical anisotropy. Dispersion analysis indicates that the shortest wavelengths in the model need to be sampled at 5 gridpoints/wavelength. The scheme can be used to accurately simulate wave propagation in mixed acoustic‐elastic media, making it ideal for modeling marine problems. Explicitly calculating both velocities and stresses makes it relatively simple to initiate a source at the free‐surface or within a layer and to satisfy free‐surface boundary conditions. Benchmark comparisons of finite‐difference and analytical solutions to Lamb’s problem are almost identical, as are comparisons of finite‐difference and reflectivity solutions for elastic‐elastic and acoustic‐elastic layered models.

scholarly journals Modelling the high temperature oxidation of titanium alloys: review of analytical models and development of a new numerical tool PyTiOx

2020 ◽  
Vol 321 ◽  
pp. 06012
Author(s):  
C. Ciszak ◽  
D. Monceau ◽  
C. Desgranges
Keyword(s):  
Numerical Models ◽  
Ecological Impact ◽  
Operating Costs ◽  
Analytical Models ◽  
Temperature Oxidation ◽  
Ti Alloys ◽  
State Diffusion ◽  
First Results ◽  
Aeronautical Industry ◽  
Numerical Tool

In order to limit the ecological impact of air traffic and its operating costs, the aeronautical industry is looking for improving engines efficiencies and substitutes to high density Ni-based superalloys. Thus, a wider use of Ti-alloys operating at higher temperatures is one of the developed solutions. Being able to predict as accurately as possible the oxidation behavior of Ti-based components at high temperatures appears therefore crucial to improve their sizing and durability. Analytical models based on the solid-state diffusion laws can be found in the litterature. They are fairly accurate in most cases, but they reveal some intrinsic limitations in specific cases such as temperature transients or thin components. Numerical models were later developed to break down these limitations. First results from a new numerical tool called “PyTiOx” (still under development are presented here. They confirm the intrinsic limitations of analytical models. In the case of thin samples, the numerical model predicts an increase of scaling kinetic when metal becomes O-saturated, whereas analytical models do not.

scholarly journals Nonlinear processes in the bunched electron beams of high-power klystrons and the limits of analytical and one-dimensional numerical models applicability for their analysis.

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
V.Y. Rodyakin ◽  
◽  
V.M. Pikunov ◽  
V.N. Aksenov ◽  
◽  
...  
Keyword(s):  
Electron Beam ◽  
High Power ◽  
Numerical Models ◽  
Nonlinear Effects ◽  
Analytical Models ◽  
Modulation Amplitude ◽  
Two Dimensional ◽  
One Dimensional ◽  
Charge Parameter ◽  
Program Data

We present the results of a comparative theoretical analysis of the electron beam bunching in a single-stage klystron amplifier using analytical models, a one-dimensional disk program, and a two-dimensional program. Data on the influence of various one-dimensional and two-dimensional nonlinear effects on the efficiency of electron beam bunching at different values of the space charge parameter and the modulation amplitude are presented. The limits of applicability of analytical and one-dimensional numerical models for electron beam bunching analysis in high-power klystron amplifiers are found.

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