Effect of longitudinal compression on transient vibrations of an elastic plate floating on the surface of a liquid

2009

J Appl Mech Tech Phy

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Equations for three nonlinear approximations of a wave perturbation in a homogeneous ideal incompressible fluid covered by a thin elastic plate are obtained using the method of multiple scales and taking into account that the acceleration of vertical flexural displacements of the plate is nonlinear. Based on the obtained equations, asymptotic expansions up third-order terms are constructed for the fluid velocity potential and the perturbations of the plate-fluid interface (plate bending) caused by a traveling periodic wave of finite amplitude. The wave characteristics are analyzed as functions of the elastic modulus and thickness of the plate and the length and tilt of the initial fundamental harmonic wave.Introduction. Wave perturbations in a fluid with a floating elastic plate in a linear formulation were studied in [1][2][3][4][5][6][7]. Finite-amplitude waves in a homogeneous fluid with an elastic ice plate neglecting the nonlinearity of vertical displacements of the plate were investigated in [8,9]. In [10], the characteristics of progressive surface finite-amplitude waves were analyzed as functions of the thickness and nonlinearity of vertical vibrations of an absolutely flexible plate (broken ice). In the present work, the effect of a floating elastic plate on the propagation of periodic finite-amplitude waves is studied using the method of multiscale asymptotic expansion and taking into account that the acceleration of vertical flexural displacements of the plate is nonlinear.Formulation of the Problem. Let a thin elastic plate float on the surface of a homogeneous ideal incompressible fluid filling an unbounded pool of constant depth H. Assuming that the fluid motion is potential and the plate performs vibrations without separation, we examine the effect of the elasticity and thickness of the plate on the propagation of finite-amplitude flexural-gravity waves. In the dimensionless variables x = kx 1 , z = kz 1 , and t = √ kg t 1 (k is the wavenumber), the problem reduces to solving the Laplace equation

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confidence: 99%

Finite-amplitude waves in a homogeneous fluid with a floating elastic plate

2009

J Appl Mech Tech Phy

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“…The chosen limiting value of Q~= 1.4v~ x does not exceed the value of Q0 in the neighborhood of which the wave perturbation structure changes and, under certain conditions, fracture of the ice is possible [14,15]. In order to estimate quantitatively the effect of ice compression on the wave perturbations induced by the impingement of a progressive wave on the edge of the ice, we made numerical calculations for the following values: h=l m, p=1025 kg'm 3, p1=870 kgan 3, and v=0.33.…”

Section: G__ Ir'i T= Ts~a(~'~ Ir'lmentioning

confidence: 99%

Impingement of surface waves on the edge of compressed ice

Zav’yalov

1995

Fluid Dyn

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“…The oscillations of a floating elastic plate were studied in a linear formulation in [2,7,8,11,14] disregarding the compressive force and in [1,6,10,[12][13][14] taking the compressive force into account. The nonlinear oscillations of a floating absolutely flexible plate were studied in [9].…”

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confidence: 99%

Nonlinear oscillations of a floating elastic plate

2011

Int Appl Mech

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The multi-scales method is used to derive third-order equations of gravitational bending oscillations of a thin elastic plate floating on the surface of a homogeneous perfect incompressible fluid of finite depth. The equations incorporate the compressive force and nonlinear acceleration of vertical displacements of the plate. Based on these equations, the deflection of the plate and the velocity potential of the fluid induced by a traveling periodic wave of finite amplitude are expanded into asymptotic series to terms of the third order of smallness. The dependence of the oscillation characteristics on the elastic modulus and thickness of the plate, compressive force, the initial length and steepness of the wave is analyzed Keywords: thin elastic plate, fluid of finite depth, gravitational bending oscillations, initial wave length, wave steepnessIntroduction. The oscillations of a floating elastic plate were studied in a linear formulation in [2,7,8,11,14] disregarding the compressive force and in [1,6,10,[12][13][14] taking the compressive force into account. The nonlinear oscillations of a floating absolutely flexible plate were studied in [9]. The finite-amplitude bending oscillations of a floating elastic plate were analyzed in [3,4] disregarding the fact that the acceleration of vertical displacement is nonlinear.We will study the oscillations of a longitudinally compressed elastic plate floating on the surface of a homogeneous perfect incompressible fluid of constant depth in which a periodic wave of finite amplitude propagates. We will use the method of multiple-scale asymptotic expansions [5] and take into account the fact that the acceleration of the vertical displacements of the plate is nonlinear.1. Problem Formulation. Governing Equations. Consider a thin elastic plate floating on the surface of a homogeneous perfect incompressible fluid of constant depth. The plate and fluid are unbounded in the horizontal directions. Let the oscillations of the plate be nonlinear and the motion of the fluid be potential. With dimensionless variables x kx = 1 , z kz = 1 ,