scholarly journals Resonant Steady-State Sloshing in Upright Tanks: Effect of Three-Dimensional Excitations and Viscosity

2018 ◽  
Author(s):  
Alexander N. Timokha ◽  
Ihor A. Raynovskyy
Keyword(s):  
Steady State ◽  
Order Approximation ◽  
Three Dimensional ◽  
Primary Resonance ◽  
Resonance Phenomenon ◽  
Phase Lag ◽  
Response Curves ◽  
Sloshing Frequency ◽  
Theoretical Results ◽  
Good Agreement

Bearing in mind recent experimental and theoretical results showing that viscous damping can qualitatively affect resonant sloshing in clean tanks, the Narimanov-Moiseev multimodal sloshing theory for an upright circular container is revised to analytically analyze steady-state surface waves when the container performs a small-amplitude sway/roll/pitch/surge prescribed periodic motion with the forcing frequency close to the lowest natural sloshing frequency. The revised theory is applicable for the radius-scaled mean liquid depths h > 1 providing the secondary resonance phenomenon does not occur at the primary resonance zone. A focus is on how the damping influences the phase lag as well as on the amplitude response curves versus the forcing type, which can in the lowest-order approximation be treated as if the container translatory moves along an elliptic orbit in the horizontal plane. The analytical results are compared with existing experiments for longitudinal and circular orbital tank excitations. Whereas a good agreement is found for longitudinal excitations, a discrepancy is detected for the circular orbital forcing. The discrepancy may, most probably, be explained by the wave breaking and mean angular mass-transport (Ludwig Prandtl, 1949) phenomena. Occurrence of the Prandtl phenomenon makes inapplicable the existing analytical inviscid sloshing theories, even if they are modified to account for damping.

scholarly journals Transient and Steady-State Responses of an Asymmetric Nonlinear Oscillator

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Alex Elías-Zúñiga ◽  
Oscar Martínez-Romero
Keyword(s):  
Approximate Solution ◽  
Steady State ◽  
Duffing Oscillator ◽  
Primary Resonance ◽  
Elliptic Functions ◽  
Dynamical Response ◽  
Response Curves ◽  
Resonance Response ◽  
Steady State Responses ◽  
Transient And Steady State

We study the dynamical response of an asymmetric forced, damped Helmholtz-Duffing oscillator by using Jacobi elliptic functions, the method of elliptic balance, and Fourier series. By assuming that the modulus of the elliptic functions is slowly varying as a function of time and by considering the primary resonance response of the Helmholtz-Duffing oscillator, we derived an approximate solution that provides the time-dependent amplitude-frequency response curves. The accuracy of the derived approximate solution is evaluated by studying the evolution of the response curves of an asymmetric Duffing oscillator that describes the motion of a damped, forced system supported symmetrically by simple shear springs on a smooth inclined bearing surface. We also use the percentage overshoot value to study the influence of damping and nonlinearity on the transient and steady-state oscillatory amplitudes.

scholarly journals Resonant three-dimensional nonlinear sloshing in a square-base basin. Part 4. Oblique forcing and linear viscous damping

2017 ◽  
Vol 822 ◽  
pp. 139-169 ◽  
Author(s):  
Odd M. Faltinsen ◽  
Alexander N. Timokha
Keyword(s):  
Steady State ◽  
Three Dimensional ◽  
Finite Depth ◽  
Width Ratio ◽  
Viscous Damping ◽  
Response Curves ◽  
Viscous Boundary Layer ◽  
Wave Regime ◽  
Modal Theory ◽  
Nonlinear Sloshing

Faltinsen et al. (J. Fluid Mech., vol. 487, 2003, pp. 1–42) (henceforth, Part 1) examined an undamped nonlinear resonant steady-state sloshing in a square-base tank by developing an approximate (asymptotic) Narimanov–Moiseev-type multimodal theory. The focus was on longitudinal and diagonal harmonic tank excitations. Neglecting the linear viscous boundary-layer damping was justified for model tanks with breadths of the order of metres. However, nonlinear sloshing in clean tanks of smaller size (count in centimetres) may be affected by damping in finite depth conditions. Qualitative and quantitative properties of the damped resonant steady-state sloshing in a square-base tank are now studied by using the modal theory from Part 1 equipped with the linear damping terms. The tank harmonically oscillates along an arbitrary horizontal (oblique) direction. An analytical asymptotic steady-state undamped solution is derived and the corresponding response curves are analysed versus the forcing direction. When the tank width $=$ breadth $=$ $L\sim 10$  cm, the surface tension effect on the free-surface dynamics can be neglected but the linear viscous damping should be included into the Narimanov–Moiseev nonlinear asymptotic modal theory. We analytically show that the steady-state damped sloshing possesses a series of distinguishing features so that, e.g. the square-like standing wave regime fully disappears and becomes replaced by swirling. Typical response curves of the damped steady-state resonant sloshing are studied for the liquid depth-to-width ratio exceeding 0.5. The computational results of the steady-state resonant response amplitudes are in a satisfactory agreement with observations and measurements by Ikeda et al. (J. Fluid Mech., vol. 700, 2012, pp. 304–328), which were conducted with a relatively small laboratory container.

A New Method to “Lock-in” Elastic Effects for Experimental Stress Analysis

1958 ◽  
Vol 25 (2) ◽  
pp. 189-195
Author(s):  
J. W. Dally ◽  
A. J. Durelli ◽  
W. F. Riley
Keyword(s):  
Three Dimensional ◽  
New Method ◽  
Experimental Stress Analysis ◽  
Gravitational Loading ◽  
Distorted Grid ◽  
Gravitational Stress ◽  
Lock In ◽  
Modified Epoxy ◽  
Theoretical Results ◽  
Good Agreement

Abstract A new method is described for “locking-in” an optical interference pattern and a mechanical distortion. The transparent model is cast from a modified epoxy resin with an embedded rubber-thread grid. The model is permitted partially to cure before it is loaded, then held under load while the plastic continues to cure. Upon removal of the load an isochromatic fringe pattern remains which is proportional to the elastic distribution of the maximum shearing stress. In addition, the permanently distorted grid has deformations which are proportional to the elastic distribution of strains. The method is applied to a disk under diametrical compression and a disk under gravitational loading. A comparison of experimental and theoretical results for these two cases shows, in general, good agreement. Most of the discrepancies between experimental and theoretical results are due to the large deformations in the neighborhood of the points of load application. An application of the method to the solution of a three-dimensional problem, namely, the gravitational stress distribution in a buttress-type dam, is discussed briefly.

On the response of a poro-elastic bed to water waves

1978 ◽  
Vol 87 (1) ◽  
pp. 193-206 ◽  
Author(s):  
Tokuo Yamamoto ◽  
H. L. Koning ◽  
Hans Sellmeijer ◽  
Ep Van Hijum
Keyword(s):  
Porous Medium ◽  
Pore Water ◽  
Water Waves ◽  
Pore Water Pressure ◽  
Water Pressure ◽  
Three Dimensional ◽  
Fine Sand ◽  
Present Solution ◽  
Theoretical Results ◽  
Good Agreement

The problem of the response of a porous elastic bed to water waves is treated analytically on the basis of the three-dimensional consolidation theory of Biot (1941). Exact solutions for the pore-water pressure and the displacements of the porous medium are obtained in closed form for the case of waves propagating over the poro-elastic bed. The theoretical results indicate that the bed response to waves is strongly dependent on the permeabilitykand the stiffness ratioG/K’, whereGis the shear modulus of the porous medium andK’is the apparent bulk modulus of elasticity of the pore fluid. The earlier solutions for pore-water pressure by various authors are given as the limiting cases of the present solution. For the limitsG/K′→ 0 ork→ ∞, the present solution for pressure approaches the solution of the Laplace equation by Putnam (1949). For the limitG/K′→ ∞, the present solution approaches the solution of the heat conduction equation by Nakamuraet al.(1973) and Moshagen & Tørum (1975).The theoretical results are compared with wave tank experimental data on pore-water pressure in coarse and fine sand beds which contain small amounts of air. Good agreement between theory and experiment is obtained.

Torque and Cavitation Characteristics of Butterfly Valves

1961 ◽  
Vol 28 (4) ◽  
pp. 511-518 ◽  
Author(s):  
Turgut Sarpkaya
Keyword(s):  
Approximate Solution ◽  
Three Dimensional ◽  
Relaxation Technique ◽  
Dimensional Case ◽  
Practical Case ◽  
Two Dimensional ◽  
Actual Flow ◽  
Theoretical Results ◽  
Good Agreement

The present study deals with torque and cavitation characteristics of idealized two-dimensional and axially symmetrical butterfly valves. Theoretical results obtained for the two-dimensional case are compared with the ones obtained experimentally and by a relaxation technique. Based on the results of the two-dimensional case, an approximate solution is presented for the more general and practical case of three-dimensional butterfly valves. The results are in good agreement with the actual flow tests.

Dynamic Characteristics of Hydrostatic Thrust Air Bearing With Actively Controlled Restrictor

1988 ◽  
Vol 110 (1) ◽  
pp. 156-161 ◽  
Author(s):  
Yuichi Sato ◽  
K. Maruta ◽  
M. Harada
Keyword(s):  
Dynamic Characteristics ◽  
Dynamic Stiffness ◽  
Phase Lag ◽  
Air Bearing ◽  
Plate Vibrations ◽  
Damping Coefficients ◽  
Stiffness And Damping ◽  
Air Film ◽  
Theoretical Results ◽  
Good Agreement

The dynamic characteristics of a hydrostatic thrust air bearing with an actively controlled orifice restrictor are investigated theoretically and experimentally. Theoretical results show that the dynamic stiffness and damping coefficients can be increased simultaneously when the restrictor area is controlled with appropriate phase-lag to the change of air film thickness, that is, plate vibrations. Consequently stability of the bearing can be improved. Experimental results show fairly good agreement with theoretical ones.

APPLICATION OF ELASTIC MATERIALS IN PROTECTION FROM STRONG IMPACTS

2004 ◽  
Vol 18 (14) ◽  
pp. 1977-1990
Author(s):  
MASKOVIC D. LJILJANA ◽  
MOHORA EMILIJAN ◽  
TOSIC S. BRATISLAV ◽  
VUJOVIC R. RATKO
Keyword(s):  
Elastic Material ◽  
Short Pulse ◽  
Three Dimensional ◽  
Polymer Materials ◽  
Elastic Materials ◽  
One Dimensional ◽  
Spherical Surfaces ◽  
The Impact ◽  
Theoretical Results ◽  
Good Agreement

The analysis of the behavior of elastic material subject to strong short pulse impact has shown that only one-dimensional structures support the impact without destruction. Compact two- and three-dimensional structures are destroyed during the impact along circular lines and spherical surfaces. For that reason, web-like shields are proposed for the protection of man and equipment. Polymer materials are most suitable for the production of web-like shields since they are made of fibers and highly stress resistant. Theoretical results are experimentally tested and the good agreement with theory was found.

Resonant sloshing in an upright annular tank

2016 ◽  
Vol 804 ◽  
pp. 608-645 ◽  
Author(s):  
Odd M. Faltinsen ◽  
Ivan A. Lukovsky ◽  
Alexander N. Timokha
Keyword(s):  
Steady State ◽  
Harmonic Excitation ◽  
Irregular Waves ◽  
Elliptic Type ◽  
Response Curves ◽  
Modal Theory ◽  
Resonant Forcing ◽  
Sloshing Frequency ◽  
Amplitude Component ◽  
Liquid Depth

Resonant sloshing in an upright annular tank is studied by using a new nonlinear modal theory, which is complete within the framework of the Narimanov–Moiseev asymptotics. The applicability is justified for a fairly deep liquid (the liquid-depth-to-outer-tank-radius ratio $1.5\lesssim h=\bar{h}/\bar{r}_{2}$) and away from the non-dimensional inner radii $r_{1}=\bar{r}_{1}/\bar{r}_{2}=0.08546$, 0.17618, 0.27826, 0.31323, 0.31855, 0.43444, 0.46015, 0.48434, 0.68655, 0.70118. The theory is used to describe steady-state (stable and unstable) resonant waves due to a harmonic excitation with the forcing frequency close to the lowest natural sloshing frequency. We show that the surge-sway-pitch-roll excitation is always of either longitudinal or elliptic type. Existing experimental results on the horizontally excited steady-state wave regimes in an upright circular tank ($r_{1}=0$) are utilised for validation. Inserting an inner pole with the radii $r_{1}\approx 0.25$ and 0.35 ($1.5\lesssim h$) causes that no stable swirling and/or irregular waves exist. The response curves for an elliptic-type excitation are examined versus the minor-axis forcing-amplitude component. Stable swirling is then expected being co- and counter-directed to the angular forcing direction. Passage to the rotary (circular) excitation keeps the co-directed swirling stable for all resonant forcing frequencies but the stable counter-directed swirling disappears.

scholarly journals The Experimental Registration of the Evanescent Acoustic Wave in YX LiNbO3 Plate

Sensors ◽  
2021 ◽  
Vol 21 (6) ◽  
pp. 2238
Author(s):  
Andrey Smirnov ◽  
Boris Zaitsev ◽  
Andrey Teplykh ◽  
Ilya Nedospasov ◽  
Egor Golovanov ◽  
...  
Keyword(s):  
Acoustic Wave ◽  
Acoustic Waves ◽  
Three Dimensional ◽  
Evanescent Waves ◽  
Electrical Boundary Conditions ◽  
3D Finite Element Method ◽  
First Time ◽  
Theoretical Results ◽  
Good Agreement ◽  
Piezoelectric Plates

Evanescent acoustic waves are characterized by purely imaginary or complex wavenumbers. Earlier, in 2019 by using a three dimensional (3D) finite element method (FEM) the possibility of the excitation and registration of such waves in the piezoelectric plates was theoretically shown. In this paper the set of the acoustically isolated interdigital transducers (IDTs) with the different spatial periods for excitation and registration of the evanescent acoustic wave in Y-cut X-propagation direction of lithium niobate (LiNbO3) plate was specifically calculated and produced. As a result, the possibility to excite and register the evanescent acoustic wave in the piezoelectric plates was experimentally proved for the first time. The evanescent nature of the registered wave has been established. The theoretical results turned out to be in a good agreement with the experimental ones. The influence of an infinitely thin layer with arbitrary conductivity placed on a plate surface was also investigated. It has been shown that the frequency region of an evanescent acoustic wave existence is very sensitive to the changes of the electrical boundary conditions. The results obtained may be used for the development of the method of the analysis of thin films electric properties based on the study of evanescent waves.

scholarly journals On the Nonlinear Dynamics of a Doubly Clamped Microbeam Near Primary Resonance

2017 ◽  
Vol 139 (4) ◽  
Author(s):  
Nizar R. Jaber ◽  
Karim M. Masri ◽  
Mohammad I. Younis
Keyword(s):  
Frequency Response ◽  
Primary Resonance ◽  
Single Frequency ◽  
Response Curves ◽  
Shooting Technique ◽  
Softening Behavior ◽  
Dc Bias ◽  
The Stability ◽  
Good Agreement ◽  
Structural Layer

This work aims to investigate theoretically and experimentally various nonlinear dynamic behaviors of a doubly clamped microbeam near its primary resonance. Mainly, we investigate the transition behavior from hardening, mixed, and then softening behavior. We show in a single frequency–response curve, under a constant voltage load, the transition from hardening to softening behavior demonstrating the dominance of the quadratic electrostatic nonlinearity over the cubic geometric nonlinearity of the beam as the motion amplitudes becomes large, which may lead eventually to dynamic pull-in. The microbeam is fabricated using polyimide as a structural layer coated with nickel from top and chromium and gold layers from the bottom. Frequency sweep tests are conducted for different values of direct current (DC) bias revealing hardening, mixed, and softening behavior of the microbeam. A multimode Galerkin model combined with a shooting technique are implemented to generate the frequency–response curves and to analyze the stability of the periodic motions using the Floquet theory. The simulated curves show a good agreement with the experimental data.

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