Nonlinear wave generation on a fluid in a moving parabolic tank

Abstract

The cooperative motion of a fluid and a parabolic tank is modeled. Use is made of a discrete model based on the Hamilton-Ostrogradsky principle for an arbitrary body of revolution and a non-Cartesian parametrization of the domain occupied by the fluid. A set of coordinate functions satisfying kinematic boundary conditions and solvability conditions is set up. The discrete model is used to study the transients in the system. It is shown that the model adequately describes the nonlinear dynamic properties of the system Introduction. Dynamic problems for fluids with free surface in moving tanks are of considerable theoretical and practical interest. This kind of structures requires high-accuracy modeling in connection with the development and sophistication of new space-, air-, and sea-craft. The chief results on dynamic modeling of such systems were obtained in [3, 5-10, etc.]. Despite the long path of development of theoretical methods for solving such problems, the overwhelming majority of publications deal with the dynamics of fluids in cylindrical tanks moving in a prescribed manner. Though problems for noncylindrical structures and cooperative motion of bodies and fluids were formulated long ago [6,7], relevant quantitative results are yet to be obtained. It is interesting that the available approaches to studying the dynamics of noncylindrical bodies based on point discretization of the domain occupied by the fluid, as well as analytic methods encounter difficulties of meeting the requirement of conservation of volume and energy in the system [5]. Actually, such a state of the art in the dynamics of fluid with free surface in noncylindrical tanks suggests that the problem formulation for the motion of noncylindrical tanks with fluid is incomplete and incorrect and should be modified.1. Problem Formulation. We will now address the nonlinear vibrations of fluid with free surface in a moving parabolic tank. Assume that the fluid is perfect, homogeneous, incompressible and its motion is irrotational. Then it is possible to use a velocity potential j to describe the motion of the fluid [5][6][7][8].Let us formulate a dynamic problem for a fluid with free surface:

Features of a generalized parametric resonance for a hyperboloidal reservoir

“…Поведінку системи розглянуто для частот параметричного резонансу, визначених як на основі класичного параметричного резонансу Фарадея, так і на основі узагальненої задачі про параметричний резонанс. Для вивчення задачі побудована математична модель механічної системи «резервуар -рідина із вільною поверхнею» [2,7], яка була протестована на прикладі перехідних процесів для задач динаміки І н ф о р м а ц і й н і с и с т е м и , м е х а н і к а т а к е р у в а н н…”

Dynamical behavior of liquid in reservoir of revolution under harmonic force disturbance in the below resonant frequency range

“…Known publication [1][2][3][4][5][6][7][8] considered nonlinear problems of oscillations of liquid in reservoirs of cylindrical and conic shapes. We investigate problems of waves generation for other shapes of the reservoirs in combined mode of motion.…”

Influence of Spring Attachment on the Dynamics of a Fluid-Filled Cylindrical Tank on a Moving Platform

“…The technological advancement motivates solving the dynamic problem for structures partially filled with a fluid and subjected to different boundary conditions. Fluid-filled tanks on a moving platform are used as components of engineering structures in mechanical engineering, rocket technology, aircraft construction, fluid carriers and storages [1,13,14]. Various aspects of the behavior of such systems without elastic elements were addressed in [3-9, 13, 14, 16-20].…”