scholarly journals Non-stationary diffraction problem of a plane oblique pressure wave on the shell in the form of a hyperbolic cylinder taking into account the dissipation effect

2020 ◽  
Vol 12 (S) ◽  
pp. 67-77
Author(s):  
Olga V. EGOROVA ◽  
Eduard I. STAROVOITOV
Keyword(s):  
Integral Operator ◽  
Pressure Wave ◽  
Differential Operators ◽  
Diffraction Problem ◽  
Elastic Shell ◽  
Stationary Problem ◽  
Dissipation Effect ◽  
The Difference ◽  
The Time Domain ◽  
Hyperbolic Cylinder

The plane non-stationary problem of the dynamics of a thin elastic shell in the form of a hyperbolic cylinder immersed in a liquid under the action of an oblique acoustic pressure wave is considered. To solve this problem, a system of equations is constructed in a related statement. In this case, hydroelasticity problems are reduced to equations of shell dynamics, the damping effect of the liquid (dissipation effect) is taken into account by introducing an integral operator of the convolution type in the time domain. The problem is solved approximately on the basis of the hypothesis of a thin layer taking into account the damping forces in the liquid. The integro-differential equations of shell motion are solved numerically based on the difference discretization of differential operators and the representation of the integral operator by the sum using the trapezoid rule. The kinematic and static parameters of the system are given.

scholarly journals NON-STATIONARY PROBLEM OF THE PLANE OBLIQUE PRESSURE WAVE DIFFRACTION ON THIN SHELL IN THE SHAPE OF PARABOLIC CYLINDER

2019 ◽  
Vol 16 (32) ◽  
pp. 328-337
Author(s):  
Lev N. RABINSKIY
Keyword(s):  
Wave Diffraction ◽  
Pressure Wave ◽  
Differential Operators ◽  
Convex Surface ◽  
Elastic Shell ◽  
Auxiliary Problem ◽  
Stationary Problem ◽  
Transition Function ◽  
Parabolic Cylinder ◽  
The Impact

A non-stationary plane problem of the dynamics of thin elastic shell in the form of parabolic cylinder immersed in the fluid under the impact of the plane oblique pressure wave is considered. To solve this problem, a system of equations in the related formulation is constructed. Herewith, the hydroelasticity problems are reduced to the equations of the shell dynamics, the damping effect of fluid is taken into account by introducing an integral convolution type operator in the time domain which in the first approximation allows for accounting the capillary porosity of the shell material. The operator core is a surface transition function of the auxiliary problem of the plane acoustic pressure wave diffraction on a convex surface. The problem is solved approximately based on the thin layer hypothesis. The integral and differential equations of shell motion are solved numerically based on the difference discretization of differential operators and the representation of the integral operator by sum using the trapezium rule.

scholarly journals Design of Two Novel Dual Band-Notched UWB Antennas

2012 ◽  
Vol 2012 ◽  
pp. 1-7 ◽  
Author(s):  
Bing Li ◽  
Jing-song Hong
Keyword(s):  
Time Domain ◽  
Simple Structure ◽  
The Other ◽  
Ultra Wideband ◽  
Dual Band ◽  
Uwb Antennas ◽  
Monopole Antennas ◽  
Printed Monopole ◽  
The Difference ◽  
The Time Domain

Two novel dual band-notched ultra-wideband (UWB) printed monopole antennas with simple structure and small size are presented. The size of both antennas is25×25×0.8 mm3. The bandwidth of one of the proposed antenna can be from 2.7 GHz to 36.8 GHz, except the bandwidth of 3.2–3.9 GHz for WiMAX applications and 5.14–5.94 GHz for WLAN applications. The bandwidth of the other is ranging for 2.7 to 41.1 GHz, except the bandwidth of 3.2–3.9 GHz for WiMAX applications and 4.8–5.9 GHz for WLAN applications. Bandwidths of the antennas are about 512% and 455% wider than those of conventional band-notched UWB antennas, respectively. In addition, the time-domain characteristics of the two antennas are investigated to show the difference between both antennas.

Inverse nodal problems for integro-differential operators with a constant delay

2019 ◽  
Vol 27 (4) ◽  
pp. 501-509 ◽  
Author(s):  
Murat Sat ◽  
Chung Tsun Shieh
Keyword(s):  
Integral Operator ◽  
Potential Function ◽  
Liouville Operator ◽  
Differential Operators ◽  
Constant Delay ◽  
Nodal Points ◽  
Inverse Nodal Problems ◽  
Volterra Integral Operator ◽  
Sturm Liouville

Abstract We study inverse nodal problems for Sturm–Liouville operator perturbed by a Volterra integral operator with a constant delay. We have estimated nodal points and nodal lengths for this operator. Moreover, by using these data, we have shown that the potential function of this operator can be established uniquely.

scholarly journals A Method for the Analysis of Interference from DME to ATCRBS in the Time Domain

Electronics ◽  
2019 ◽  
Vol 8 (4) ◽  
pp. 393 ◽  
Author(s):  
Guofeng Jiang ◽  
Yangyu Fan ◽  
Hongbo Yuan ◽  
Pengliang Yuan
Keyword(s):  
Time Domain ◽  
Traffic Control ◽  
Initial Time ◽  
Analysis Method ◽  
Operating Modes ◽  
The Monte Carlo Method ◽  
The Difference ◽  
The Time Domain ◽  
Overlap Method ◽  
Recurrence Frequency

Analysis of the coexistence of two or more types of equipment is increasingly important. However, at present studies on the analysis method in the time domain are scant. Therefore, the aim of this paper is to explore the characteristics of signals and relations between interfering and desired signals in the time domain. Based on the periodicity of a signal, this paper presents a Periodic Pulse Overlap Method (PPOM). Using PPOM to analyze the interference from Distance Measuring Equipment (DME) to Air Traffic Control Radar Beacon System (ATCRBS) in the time domain, we obtain almost the same result as that based on the Monte Carlo Method (MCM). Furthermore, we discover the measures to reduce or even avoid interference, such as changing the Pulse Recurrence Frequency (PRF), adjusting the difference of initial time, and switching the operating modes of the equipment.

scholarly journals Dynamics of Nonlocal Rod by Means of Fractional Laplacian

Symmetry ◽  
2020 ◽  
Vol 12 (12) ◽  
pp. 1933
Author(s):  
Vittorio Gusella ◽  
Giuseppina Autuori ◽  
Patrizia Pucci ◽  
Federico Cluni
Keyword(s):  
Fractional Laplacian ◽  
Free Vibrations ◽  
Dynamic Loads ◽  
Model Parameters ◽  
Local Response ◽  
Proposed Model ◽  
Fractional Models ◽  
Static And Dynamic Loads ◽  
The Difference ◽  
The Time Domain

The use of fractional models to analyse nonlocal behaviour of solids has acquired great importance in recent years. The aim of this paper is to propose a model that uses the fractional Laplacian in order to obtain the equation ruling the dynamics of nonlocal rods. The solution is found by means of numerical techniques with a discretisation in the space domain. At first, the proposed model is compared to a model that uses Eringen’s classical approach to derive the differential equation ruling the problem, showing how the parameters used in the proposed fractional model can be estimated. Moreover, the physical meaning of the model parameters is assessed. The model is then extended in dynamics by means of a discretisation in the time domain using Newmark’s method, and the responses to different dynamic conditions, such as an external load varying with time and free vibrations due to an initial deformation, are estimated, showing the difference of behaviour between the local response and the nonlocal response. The obtained results show that the proposed model can be used efficiently to estimate the response of the nonlocal rod both to static and dynamic loads.

scholarly journals Pressure Wave in Liquid Generated by Pneumatic Pistons and Its Interaction with a Free Surface

2017 ◽  
Vol 09 (03) ◽  
pp. 1750037 ◽  
Author(s):  
Victoria Suponitsky ◽  
David Plant ◽  
Eldad J. Avital ◽  
Ante Munjiza
Keyword(s):  
Free Surface ◽  
Pressure Wave ◽  
Equations Of State ◽  
Current System ◽  
Nonlinear Effects ◽  
Compression Process ◽  
Double Peak Structure ◽  
Peak Structure ◽  
Westervelt Equation ◽  
The Difference

Numerical analysis of a pressure wave generated in a liquid [Formula: see text] upon impact of the pneumatic pistons and its interaction with a free surface has been performed for the geometry and parameters of the plasma compression system prototype constructed by General Fusion Inc. Stress wave developing in the hammer–anvil piston assembly is first simulated using high-fidelity structural mechanics research code, then propagated through the liquid [Formula: see text] with several solvers within OpenFOAM[Formula: see text] software and also with nonlinear acoustics in-house code based on the Westervelt equation. In the current system, a pressure wave transmitted into the liquid [Formula: see text] is characterized by a complex temporal double peak structure and strong spatial amplitude variation. An imprint of discrete pulses remains detectable during the entire propagation of the combined wave. An excellent agreement between the results produced with different numerical codes is obtained. Nonlinear effects associated with equation of state are found to be significant at impact velocities of [Formula: see text], while at lower velocities of [Formula: see text] the difference between the results obtained with linear and nonlinear equations of state is negligible. Liquid–gas interface dynamics during the compression process of a spherical gas cavity is captured very well by the compressibleInterFoam within OpenFOAM.

Wet Modes of Submerged Structures—Part 2: Applications

1992 ◽  
Vol 114 (4) ◽  
pp. 440-448 ◽  
Author(s):  
R. P. Daddazio ◽  
M. M. Ettouney ◽  
N. Abboud
Keyword(s):  
Pressure Wave ◽  
Elastic Shell ◽  
Computational Procedure ◽  
Surface Velocity ◽  
Acoustic Medium ◽  
Far Field ◽  
Harmonic Response ◽  
The Individual

Using the wet mode methodology described in Part I of this paper, we examine the harmonic response of an elastic shell in an infinite acoustic medium subjected to an incident pressure wave. Both surface and far field responses are studied utilizing this computational procedure. We investigate the sensitivity of response with respect to changes in frequency of oscillation of the system and geometry of the submerged structure. In addition, we compare the wet modes of the system and in vacuo modes of the structure. The propagation of the surface velocity wet modes to the far field is illustrated. The contribution of the individual modes to the far field pressure and surface velocities as a function of frequency and location is presented.

scholarly journals Models of dielectric relaxation based on completely monotone functions

2016 ◽  
Vol 19 (5) ◽  
Author(s):  
Roberto Garrappa ◽  
Francesco Mainardi ◽  
Maione Guido
Keyword(s):  
Time Domain ◽  
Differential Operators ◽  
Dielectric Materials ◽  
Monotone Functions ◽  
Mathematical Functions ◽  
Completely Monotone Functions ◽  
Wing Model ◽  
Completely Monotone ◽  
The Time Domain

AbstractThe relaxation properties of dielectric materials are described, in the frequency domain, according to one of the several models proposed over the years: Kohlrausch-Williams-Watts, Cole-Cole, Cole-Davidson, Havriliak-Negami (with its modified version) and Excess wing model are among the most famous. Their description in the time domain involves some mathematical functions whose knowledge is of fundamental importance for a full understanding of the models. In this work, we survey the main dielectric models and we illustrate the corresponding time-domain functions. In particular, we stress the attention on the completely monotone character of the relaxation and response functions. We also provide a characterization of the models in terms of differential operators of fractional order.

Response and Stability of Linear Dynamic Systems With Many Degrees of Freedom Subjected to Nonconservative and Harmonic Forces

1975 ◽  
Vol 42 (2) ◽  
pp. 458-463 ◽  
Author(s):  
F. C. L. Fu ◽  
S. Nemat-Nasser
Keyword(s):  
Asymptotic Solution ◽  
Dynamic Systems ◽  
Autonomous System ◽  
Degrees Of Freedom ◽  
Differential Operators ◽  
Linear Dynamic Systems ◽  
Exciting Frequency ◽  
The Difference ◽  
Linear Differential ◽  
Type Oscillation

Dynamic systems whose response can be characterized by a set of linear differential equations with harmonic coefficients which are proportional to a small parameter ε, are considered. These systems are such that the corresponding autonomous sets of equations which are obtained by setting ε = 0, are defined by nonself-adjoint linear differential operators; i.e., they correspond to dynamic systems subjected to nondissipative nonconservative forces. For these systems, general asymptotic solutions are developed and their stability is examined. An interesting feature of these solutions is that, when the exciting frequency is close to, say, twice of a suitable eigenfrequency, or when it is close to the sum or the difference of two suitable frequencies of the autonomous system, then the asymptotic solution will involve negative fractional powers of ε. Hence, the nonsecular asymptotic solution, in general, may not reduce to the solution of the autonomous system as ε goes to zero. Another interesting feature of the present results is that the addition of small suitable harmonic forces does indeed stabilize an inherently unstable nondissipative nonconservative dynamical system; except when the frequency of the harmonic force resonates with one or several of the frequencies of the autonomous system in either a subharmonic or a combinational-type oscillation.

A Proposed Guideline for Applying Waterhammer Predictions Under Transient Cavitation Conditions: Part 2 — Imbalanced Forces

2018 ◽  
Author(s):  
Matthew Stewart ◽  
Trey W. Walters ◽  
Greg Wunderlich
Keyword(s):  
Stress Analysis ◽  
Pressure Wave ◽  
Transient Analysis ◽  
Liquid System ◽  
Safety Factors ◽  
Hydraulic Transient ◽  
Wave Travel ◽  
Point Forces ◽  
The Difference ◽  
Transient Forces

Waterhammer analysis (herein referred to as Hydraulic Transient Analysis or simply “HTA”) becomes more complicated when transient cavitation occurs (also known as liquid column separation). This complication is exacerbated when trying to predict imbalanced forces as this often involves comparing pressure times area (“PxA”) forces at two locations (for example at elbow pairs). Whereas the pressure at each elbow location has increased uncertainty because of transient cavitation, the difference in PxA forces at elbow pairs involves subtracting one potentially uncertain pressure from another uncertain pressure. Exacerbating this uncertainty yet further, the existence of vapor in a liquid system can dramatically affect the fluid wavespeed and, hence, the timing of the pressure wave travel between two locations such as elbow pairs; so the pressure calculated at each location would not actually occur at exactly the same time. This Part 2 discusses methods of accounting for uncertainty in HTA imbalanced force predictions due to cavitation. The criteria in this paper assume that cavitation in the HTA has been assessed and accepted per the criteria in Part 1 of this paper. A guideline is proposed for accepting and applying such results and, in particular, makes recommendations on safety factors to use in pipe stress analysis for different cases. The specific recommendations depend on numerous factors including: • Presence or absence of cavitation in hydraulically connected or isolated parts of the system • If cavitation occurs, whether the peak forces occur before or after cavitation first occurs • Size of the cavitation vapor volumes with respect to the computing volumes • Use of point forces as a conservative substitute in place of potentially less certain elbow pair forces or the manual assessment of maximum envelope values for the force. Situations are discussed where waterhammer abatement is recommended to reduce hydraulic transient forces, and for increasing confidence in HTA results in specific cases. The result is a proposed comprehensive and pragmatic guideline which practicing engineers can use to perform waterhammer analysis and apply imbalanced force predictions to pipe stress analysis.

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