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1.
曾文平 《应用数学和力学(英文版)》2000,21(9):1071-1078
IntroductionThispaperdealswiththeinitial_boundaryvalueproblemofthree_dimensionalheatconductionequationintheregionD :0≤x,y ,z≤L ,0 ≤t≤T u t= 2 u x2 2 u y2 2 u z2 ,u|x=0 =f1(y,z,t) , u|x=L =f2 (y ,z,t) ,u|y=0 =g1(z,x,t) , u|y=L =g2 (z,x,t) ,u|z=0 =h1(x ,y ,t) , u|z=L =h2 (x ,y ,t) ,u|t=0 =φ(x ,y,z) .(1 )(2 )… 相似文献
2.
Summary A probabilistic model of the geometric imperfections of a real structure is proposed, in order to provide a general theory of the stochastic response of structures in presence of small random deviations from the perfect scheme. The main statistical measures of the stochastic response are derived and an application to the study of a particular conservative elastic system is developed.
List of symbols element of the sample space of events - kn random variables modelling the structural imperfections - P(o) probability density of random variables - random imperfection of the unloaded structure - u additional displacement of the loaded structure - uo deterministic fundamental solution for the perfect structure - difference between the additional displacement of the loaded structure and the deterministic fundamental solution for the perfect structure - V1=u1 buckling mode of the perfect structure - i intrinsic coordinates of the structure - suitable measure of the magnitude of the random imperfections - scalar geometric variable representing the internal product - random imperfection divided by - single scalar variable denoting the magnitude of the prescribed loads - potential energy of the structure - potential energy of the perfect structure - difference between and - c lowest critical load - s real local maximum for the magnitude of the prescribed loads - c divided by S - E{} expected value of a random variable - 2 variance of a random variable - , random variables defined by Eq. (21) 相似文献
Sommario Si propone una teoria generale della risposta probabilistica di strutture, in presenza di piccole deviazioni aleatorie dei dati iniziali rispetto allo schema geometrico perfetto. Si deducono le principali proprietà statistiche della risposta della struttura a sollecitazioni esterne deterministiche, e si sviluppa una applicazione riguardante il comportamento aleatorio di un particolare sistema elastico conservativo.
List of symbols element of the sample space of events - kn random variables modelling the structural imperfections - P(o) probability density of random variables - random imperfection of the unloaded structure - u additional displacement of the loaded structure - uo deterministic fundamental solution for the perfect structure - difference between the additional displacement of the loaded structure and the deterministic fundamental solution for the perfect structure - V1=u1 buckling mode of the perfect structure - i intrinsic coordinates of the structure - suitable measure of the magnitude of the random imperfections - scalar geometric variable representing the internal product - random imperfection divided by - single scalar variable denoting the magnitude of the prescribed loads - potential energy of the structure - potential energy of the perfect structure - difference between and - c lowest critical load - s real local maximum for the magnitude of the prescribed loads - c divided by S - E{} expected value of a random variable - 2 variance of a random variable - , random variables defined by Eq. (21) 相似文献
3.
Summary
The present work deals with the case of a two-dimensional slider bearing with a rigid pad and an elastic bearing. Fluid viscosity is assumed to be only a pressure function. We determined the bearing deformation, the pressure distribution and the load capacity at different values of the inclination angle of the slider, with a numerical integration of the system consisting of the elasticity and Reynolds equations. The results show that, with an iso-viscous fluid, bearing elasticity causes a load capacity decrease. Instead bearing elasticity together with the variation of fluid viscosity due to pressure causes a load capacity greater than that of the iso-viscous case (=0).
Nomenclature /L - /L - x/L - x/L - - ¯C CZ/h 1 - E elasticity modulus - h film thickness - H elastic deformation of the bearing - h 1 minimum film thickness - h 2 inlet thickness - inclination of the pad - h Z/h 1 - HZ/h 1 - L pad length - viscosity - 0 viscosity with no over-pressure - p over pressure - p P ec-P rc where:ec=elastic caserc=rigid case - P h 1 2 /60VL - h 2/h 1=1+L/h 1 - FV bearing velocity - W load capacity per unit width - Wh 2 1 /60 VL 2 - Z E h 3 1 /12 0 VL 2 A first version of this paper was presented at the 7th National AIMETA congress, held at Trieste, October 2–5, 1984. This work was supported by C.N.R. 相似文献
Sommario Il presente lavoro studia il problema della coppia prismatica lubrificata con pattino rigido di allungamento infinito e cuscinetto deformabile; si suppone che la viscosità del fluido sia funzione della sola pressione. Il sistema di equazioni, costituito dall'equazione di Reynolds e dall'equazione dell'elasticità, è stato risolto numericamente, determinando la deformazione del cuscinetto, andamento della pressione e la capacità di carico per diversi valori dell'inclinazione del pattino. I risultati dimostrano che, con fluido isoviscoso, la deformabilità del cuscinetto determina una riduzione della capacità di carico. Se si considera, invece, effetto combinato dell'elasticità del cuscinetto e della variazione della viscosità del fluido, la capacità di carico risulta maggiore di quella che si ottiene con fluido isoviscoso (=0).
Nomenclature /L - /L - x/L - x/L - - ¯C CZ/h 1 - E elasticity modulus - h film thickness - H elastic deformation of the bearing - h 1 minimum film thickness - h 2 inlet thickness - inclination of the pad - h Z/h 1 - HZ/h 1 - L pad length - viscosity - 0 viscosity with no over-pressure - p over pressure - p P ec-P rc where:ec=elastic caserc=rigid case - P h 1 2 /60VL - h 2/h 1=1+L/h 1 - FV bearing velocity - W load capacity per unit width - Wh 2 1 /60 VL 2 - Z E h 3 1 /12 0 VL 2 A first version of this paper was presented at the 7th National AIMETA congress, held at Trieste, October 2–5, 1984. This work was supported by C.N.R. 相似文献
4.
Xu Lanxi 《Acta Mechanica Sinica》2000,16(2):113-120
Nonlinear stability of the motionless state of a heterogeneous fluid with constant temperature-gradient and concentration-gradient
is studied for both cases of stress-free and rigid boundary conditions. By introducing new energy functionals we have shown
that for τ=P
C
/P
T
≤1,
the motionless state is always stable and for τ≤1,
the sufficient and necessary conditions for stability coincide, whereP
C
,P
T
,C andR are the Schmidt number, Prandtl number, Rayleigh number for solute and heat respectively. Moreover, the criteria guarantees
the exponential stability.
The Project supported by SRF for ROCS, China Postdoctoral Science Foundation and the National Basic Research Project “Nonlinear
Science” 相似文献
5.
The multiaxial elongational rheometer equipped with rotary clamps is modified such that in addition to simple, equibiaxial and multiaxial elongations also tests with new modes of elongation can be performed. As an example, polyisobutylene is elongated with a ratio of the principal strain rates of
and magnitudes of the maximum strain rate
, 0.04 and 0.08 s–1. As a test result, the first elongational viscosityµ
1
(t) is obtained which follows closely the linear viscoelastic shear viscosity
. In contrast, the second elongational viscosityµ
2
(t) remains below
. By means of a further modification of the rheometer, the test modes can be varied during the deformation period. This allows one to investigate the influence of a well-defined rheological pre-history on the following rheological behaviour. As an example a variation ofm = 0.5 2 was performed. The measured normal-stress differences superpose from the single steps of deformation similar to the linear viscoelastic prediction.Dedicated to Prof. F. R. Schwarzl on the occasion of his 60th birthday 相似文献
6.
The microprocesses of deformation and fracture of Bi-segregated copper bicrystals Σ33 (
) 58.99°, Σ11 (
) 50.48° and Σ9 (
) 38.94° have been simulated by molecular dynamics in order to study the relationship between the grain boundary embrittlement
(GBE) and grain boundary (GB) structure. It is shown that GBE is related to the segregated concentration and distribution
of Bi atoms, while Bi segregation is related to the GB structure. Due to their different structures, the bicrystals Σ33, Σ11
and Σ9 show an increasing propensity for Bi segregated concentration. So under the action of external force, Σ33, Σ11 and
Σ9 show transgranular ductile, intergranular tearing and intergranular brittle fracture modes, respectively.
The subject supported by the Chinese Academy of Sciences and National Natural Science Foundation of China 相似文献
7.
Keith H. Swainger 《Meccanica》1968,3(4):283-291
Summary One-one correspondence is postulated for two coordinate continua. One continuum is regarded as the initially undeformed state of a currently deformed continuum. The two continua are orthogonal trasformations each to the other. The square root of the quadratic metric, when the appropriate self-conjugate stretch dyadic is expressed in its principal form, gives the mathematically linear form to the analysis. The self-conjugate dyadic
is expressed as
=grad grad P in terms of a scalar potential function P. The physical and mathematical continuity of the strain dyadic is ensured by curl
=0.A 4-vector analysis is evolved from a 4-vector quinternion analysis. The 4-vector analysis is of the same form as the usual 3-vector analysis that evolved from Hamilton's quaternion analysis.
A generalisation that, when particularised, applies to the finite or infinitesimal straining of elastic bodies, incremental straining of plastic or fluidic bodies in 3-dimensional continua and to the space-time continuum as a 4-dimensional continuum. 相似文献
Sommario Si postula una corrispondenza biunivoca per due continui coordinati. Un continuo viene considerato come lo stato inizialmente non deformato di un continuo attualmente deformato.I due continui sono trasformazioni ortogonali uno dell'altro. La radice quadrata della metrica quadratica, quando la relativa diade di dilatazione autoconiugata venga espressa nella sua forma principale dà la forma matematicamente lineare alla analisi.La diade coniugata viene espresse come =grad grad P in termini di una funzione potenziale scalare P. La continuità fisica e matematica della diade di deformazione è assicurata da rot =0.Una analisi tetravettoriale viene sviluppata da analisi di quinternioni tetravettoriali. L'analisi tetravettoriale è della stessa forma dell'analisi trivettoriale che viene vsiluppata dalla analisi quaternionica trivettoriale di Hamilton.
A generalisation that, when particularised, applies to the finite or infinitesimal straining of elastic bodies, incremental straining of plastic or fluidic bodies in 3-dimensional continua and to the space-time continuum as a 4-dimensional continuum. 相似文献
8.
A system is described which allows the recreation of the three-dimensional motion and deformation of a single hydrogen bubble time-line in time and space. By digitally interfacing dualview video sequences of a bubble time-line with a computer-aided display system, the Lagrangian motion of the bubble-line can be displayed in any viewing perspective desired. The u and v velocity history of the bubble-line can be rapidly established and displayed for any spanwise location on the recreated pattern. The application of the system to the study of turbulent boundary layer structure in the near-wall region is demonstrated.List of Symbols
Reynolds number based on momentum thickness u
/v
- t+
nondimensional time
-
u
shear velocity
-
u
local streamwise velocity, x-direction
-
u
+
nondimensional streamwise velocity
-
v
local normal velocity, -direction
-
x
+
nondimensional coordinate in streamwise direction
- +
nondimensional coordinate normal to wall
-
+
wire
wire nondimensional location of hydrogen bubble-wire normal to wall
-
z
+
nondimensional spanwise coordinate
-
momentum thickness
-
v
kinematic viscosity
-
W
wall shear stress 相似文献
9.
We study isolated singularities of the quasilinear equation
in an open set of
N
, where 1 < p N, p -1 q < N(p — 1)/ (N -p). We prove that, for any positive solution, if a singularity at the origin is not removable then either
or u(x)/(x) any positive constant as x 0 where is the fundamental solution of the p-harmonic equation:
. Global positive solutions are also classified. 相似文献
10.
郭艾 《应用数学和力学(英文版)》1999,20(6):683-689
1ProblemsandMainResultsInthispaper,westudythenonlinearvibrationsofinfiniterodswithviscoelasticity.Theconstitutionlawoftherods... 相似文献
11.
Let E be a Banach space. We prove the instability of the trivial solution of the differential equation
where f: [0, +∞) × E → ℝ is a continuous mapping for which
__________
Translated from Neliniini Kolyvannya, Vol. 8, No. 3, pp. 404–414, July–September, 2005. 相似文献
12.
Dr. V. Semjonow 《Rheologica Acta》1965,4(2):133-137
Zusammenfassung Es wird die Druckabhängigkeit des nicht -Newtonschen Fließverhältens von Polyolefinschmelzen (Hochdruck-, Niederdruck-,Phillips-Polyäthylen und Polypropylen) experimentell untersucht und gefunden, daß der durch Gl. [1] definierte Druckkoeffizient
mit zunehmender Deformationsgeschwindigkeit
kleiner wird und dabei die (im einzelnen in der Tabelle 1 angeführten) Werte
annimmt. Der Druckkoeffizient der Polyolefinschmelzen ist ebenso wie für vieleNewtonsche Flüssigkeiten bis 2000 kp cm–2 unabhängig vom Druck, er wird mit zunehmender Temperatur kleiner und nimmt mit zunehmender Verzweigung zu. Die Meßergebnisse werden mit Hilfe eines Aufweitungsvolumens interpretiert. Es wird gezeigt, daß eine Deutung des Fließverhaltens von Polyäthylen durch das freie Volumen allein nicht möglich ist.
Für die Diskussion und Förderung dieser Arbeit danke ich Herrn Professor Dr.K.-H. Hellwege und Herrn Dr.W. Knappe. 相似文献
Summary The influence of pressure of the non-Newtonian flow behaviour of polyolefin melts (Low- and High density Polyethylene,Phillips-Polyethylene and Polypropylene) was investigated. The results are: the coefficient of pressure as defined by eq. [1], decreases with increasing shear rate and reaches the values given in table 1 . The pressure coefficient of polyolefin melts does not depend on pressure up to 2000 kp cm–2. As observed with manyNewtonian fluids, decreases with increasing temperature and increases with the degree of branching. The experimental results are explained by means of a so called volume of expansion. It has been shown that it is impossible to explain the flow behaviour of polyethylene exclusively with the free volume.
Für die Diskussion und Förderung dieser Arbeit danke ich Herrn Professor Dr.K.-H. Hellwege und Herrn Dr.W. Knappe. 相似文献
13.
W. L. Esmeijer 《Applied Scientific Research》1949,1(1):151-168
Summary An elastically supported beam of infinite length, initially at rest, carries a variable concentrated force
at a prescribed point A. General expressions are given for the deflection and the bending moment at A (6.3 and 6.4). Three special cases are considered; the first one is defined by
=0 for
and
=K=const. for
; the second one by
=0 for 0 >
>
,
given function of
for 0
; the third one applies to problems in which, during the period of impact,
itself is an unknown. The results given here may be of use in those railway-engineering problems in which a rail can be considered as a beam of infinite length, and in which the supporting ground has the required properties. 相似文献
14.
Iterative solution of nonlinear equations with strongly accretive operators in Banach spaces 总被引:1,自引:0,他引:1
周海云 《应用数学和力学(英文版)》1999,20(3):282-289
1IntroductionandPreliminariesLetXbearealBanachspacewithnormIJ'11andadualX'.ThenormalizeddualitymappingJ:X~ZxisdefinedbyJx={x'eX*I(x,x')=11x112=11x if'},where',')denotesthegeneralizeddualitypairing.Itiswell-knownthatifX isstrictlyconvex,Jissingle-valuedandJ(tx)=tjxforallt201xeX.IfX*isuniformlyconvex,thenJisuniformlycontinuousonanyboundedsubsetSofX(of.Browde,fljandBarbuL2]).AnoperatorTwithdomainD(T)andrangeR(T)inXissaidtobeaccretiveifforeveryx,y6D(T),thereexistsajeJ(x--y)suchthat(T… 相似文献
15.
J. Meiβner 《Rheologica Acta》1971,10(2):230-242
Zusammenfassung In einem Dehnungsrheometer werden Spannungs-Dehnungs-Diagramme von Polyäthylen-Schmelzen bei 150 °C und bei konstanter Dehnungsgeschwindigkeit
gemessen (
zwischen 0,001 und 1 sec–1). Weiterhin wird der reversible (elastische) Dehnungsanteil bestimmt. Messungen mit einem Dehnungstester für Kunststoff-Schmelzen ergänzen die Ausführungen.Die Ergebnisse zeigen deutlich, daß bei Dehnung mit zunehmender Verformungsgeschwindigkeit die Dehnungsviskosität nicht abnimmt, im Gegensatz zu dem bekannten strukturviskosen Verhalten bei Scherung.Bei Dehnungen bis zu=1 kann das Verhalten unabhängig von
beschrieben werden, wenn als viskoelastische Materialfunktion die Dehnungs-Spannviskosität
betrachtet wird. In diesem Bereich von gilt dabei die BeziehungT(t)=3
s
(t) mit
s
(t) als zeitabhängige Scherviskosität im linear-viskoelastischen Bereich.Bei größeren Dehnungen und nicht zu kleinen Dehnungsgeschwindigkeiten zeigt verzweigtes Polyäthylen eine zusätzliche starke Spannungszunahme. In dem Bereich dieser zusätzlichen Verfestigung ist das Verhalten im wesentlichen eine Funktion der Dehnung und fast unabhängig von
. Die zusätzliche Verfestigung scheint eine Folge der Verzweigungsstruktur des verzweigten Polyäthylens zu sein, da bei Linear-PE ein derartiger Verlauf des Spannungs-Dehnungs-Diagramms nicht beobachtet wird.Die Betrachtung des reversiblen Dehnungsanteils
R
zeigt bei der ausführlich untersuchten Schmelze I (verzweigtes PE) drei verschiedene Bereiche: Unterhalb einer Grenzdehnungsgeschwindigkeit
ist
R
=0, unterhalb einer Versuchszeitt
** ist
R
=. Im dazwischenliegenden Bereich treten elastische und viskose Dehnungsanteile auf,=
R
+
V
, wobei für niedrige
gilt, daß
R
lg
. Die Grenze
wird der Frequenz der thermisch aktivierten Platzwechsel zugeordnet,t
** erscheint als Zeit, innerhalb der die Verhakungen wie fixierte Vernetzungen wirken.In dem Anhang wird der Einfluß der Grenzflächenspannung zwischen PE-Schmelze und Silikonöl auf die Ergebnisse der Dehnungsversuche diskutiert.
Vorgetragen auf der Deutschen Rheologen-Tagung, Berlin, 11.-13. Mai 1970.
An der Weiterentwicklung des Dehnungsrheometers, an der Durchführung und Auswertung der Messungen waren die HerrenB. Kienle, F. Landmesser, M, Reuther undF. Scherr beteiligt. Herr Dr.F.Ramsteiner und HerrH. Schroeck haben sich um die Herstellung der Stränge aus Linear-PE bemüht. Herr Dr.W. Ball besorgte die GPC-Messungen und Herr Dr.P. Simak die Ultrarot-Untersuchung. Den vorgenannten Herren sei für ihre Hilfe beim Zustandekommen dieser Arbeit gedankt. Herrn Dr.H. Baur danke ich für wertvolle Diskussionen. 相似文献
Summary Stress-strain relations for different PE melts are measured at 150 °C in an extensional rheometer under the condition of a constant extensional strain rate ( between 0,001 and 1 sec–1). Further, the recoverable (elastic) portion R of the total strain ( in Hencky's measure) is determined and additional measurements with a tensile tester for polymer melts are described.The results show clearly that in extension there is no decrease of the tensile viscosity with increasing deformation rate, in contrast to the well-known pseudoplastic behaviour in shear. Within total strains<1 the tensile behaviour can be described independently from by means of a viscoelastic material function called stressing viscosity . In this range of the relation T (t)=3 s (t) holds, where s (t) is the stressing viscosity in shear in the linear viscoelastic range. For larger tensile strains and not too small branched PB shows a remarkable increase in stress. This work-hardening behaviour is mainly a function of and almost independent from . This additional hardening seems to be due to the branches in branched PE, because linear PE does not show this effect.The discussion of the recoverable tensile strain R gives three regions of tensile rate: Below a critical there is R =0. At times shorter thant ** the equation R = is valid. Within these limits both elastic and viscous portions of the total strain= R + V exist. may correlate with the frequency of the thermally activated position changes of the molecular segments.t ** is assumed to be the time for the entanglements to act as fixed cross-links.In the appendix the influence of the interface tension between PE melt and silicone oil on the results of the tensile experiments is discussed.
Vorgetragen auf der Deutschen Rheologen-Tagung, Berlin, 11.-13. Mai 1970.
An der Weiterentwicklung des Dehnungsrheometers, an der Durchführung und Auswertung der Messungen waren die HerrenB. Kienle, F. Landmesser, M, Reuther undF. Scherr beteiligt. Herr Dr.F.Ramsteiner und HerrH. Schroeck haben sich um die Herstellung der Stränge aus Linear-PE bemüht. Herr Dr.W. Ball besorgte die GPC-Messungen und Herr Dr.P. Simak die Ultrarot-Untersuchung. Den vorgenannten Herren sei für ihre Hilfe beim Zustandekommen dieser Arbeit gedankt. Herrn Dr.H. Baur danke ich für wertvolle Diskussionen. 相似文献
16.
The characteristics of low-speed fluid streaks occurring under sheared air-water interfaces were examined by means of hydrogen
bubble visualization technique. A critical shear condition under which the streaky structure first appears was determined
to beu
τ≈0.19 cm/s. The mean spanwise streak spacing increases with distance from the water surface owing to merging and bursting
processes, and a linear relationship describing variation of non-dimensional spacing
versusy
+ was found essentially independent of shear stress on the interface. Values of
, however, are remarkably smaller than their counterparts in the near-wall region of turbulent boundary layers. Though low-speed
streaks occur randomly in time and space, the streak spacing exhibits a lognormal probability distribution behavior. A tentative
explanation concerning the formation of streaky structure is suggested, and the fact that
takes rather smaller values than that in wall turbulence is briefly discussed.
The project supported by the National Natural Science Foundation of China (19672070) 相似文献
17.
Aldo Belleni Morante 《Meccanica》1973,8(1):11-15
Summary We prove existence and uniqueness of the solution of a linearized version of the kinetic equation of vehicular traffic on a highway by using the theory of semigroups of linear bounded operators.We assume that a perturbation is introduced at the entrance of the highway, i. e., at x=0 and that it continues for a given time interval [0,
].We then study the behaviour of such a perturvation at values of x close to zero by using perturbation theory for linear operators.Finally, we prove that the perturbation attenuates and approaches zero as x+, i. e. at a large distance from the entrance of the highway.
Work performed under the auspices of the National Research Council (C.N.R., Gruppo Nazionale per la Fisica Matematica). 相似文献
Sommario Si prova l'esistenza e l'unicità della soluzione dell'equazione linearizzata del traffico automobilistico su un'autostrada con un'entrata in corrispondenza di x=0.Si studia poi il comportamento di una perturbazione, dovuta per esempio all'uscita da una partita di calcio, e si mostra come tale perturbazione si attenui al crescere della distanza dall'ingresso dell'autostrada.
Work performed under the auspices of the National Research Council (C.N.R., Gruppo Nazionale per la Fisica Matematica). 相似文献
18.
The transient response of a central crack in an orthotropic strip under the in-plane shear impact loading is studied by using
the dual integral equation method proposed by Copson and Sih. The general formula for the shear stress intensity factor
near the crack tip is derived. Numerical results of
with
in various cases are obtained by solving the second kind Fredholm integral equation and by performing the inverse Laplace
transform. 相似文献
19.
Kōhei Uchiyama 《Archive for Rational Mechanics and Analysis》1985,90(4):291-311
The paper concerns the asymptotic behavior as
of solutions u(t, x) of the Cauchy problem for the inhomogeneous equation
, x>0, with a mass-preserving boundary condition at x=0. It is assumed that F C
1[0, 1] F(0)=F(1)=0, and that one of the following conditions holds: (i) F has just one zero in (0, 1) and the derivative F is negative at 0 and 1, (ii) F is zero in (0, ) and positive in (, 1) with 0<<1, (iii) F is positive in (0, 1) and c
0
2
>2F(0) (the pushed case). Here c
0 is the minimum of possible speeds of travelling waves for the equation with k(x) replaced by zero. Under a natural restriction imposed on k(x) we prove, for a wide class of initial functions, that u(t, x) approaches w(x + m(t)) as
uniformly in x>0, where w is a travelling wave with the speed c
0 and m is a solution of dm/dt = c
0-k(m). The result has immediate applications to the multidimensional non-linear diffusion equations arising in population genetics, combustion theory, etc. 相似文献
20.
L. Debnath 《Applied Scientific Research》1969,21(1):24-36
A linearized theory is developed for the derivation of an asymptotic solution of the initial value problem of axisymmetric surface waves in an infinitely deep fluid produced by an arbitrary oscillating pressure distribution. An asymptotic treatment of the problem is presented in detail to obtain the solution for the surface elevation for sufficiently large time. Finally, the main prediction of this analysis for some particular pressure distributions of physical interest is exhibited.Nomenclature
R, , Y
cylindrical polar coordinates
-
frequency
-
g
acceleration due to gravity
-
density of fluid
-
T
time
-
(R, Y; T)
velocity potential
-
E(R, T)
vertical surface elevation
-
P(R, T)
applied surface pressure
-
r, y
nondimensional cylindrical polar coordinates,
-
p(r, t)
nondimensional surface pressure
-
t
nondimensional time, T
-
(r, y; t)
nondimensional velocity potential,
-
(r, t)
nondimensional vertical surface elevation,
-
(k)
Hankel transform of a function p(r) with respect to r
-
I
1
transient wave integral
-
I
2
steady state wave integral 相似文献