A assume that your question is in connection with sound waves. It looks as if you would like to (1) assign a soft-boundary reflection conditions to a flat wall, while at the same time (2) assigning a prescribed vibration (acceleration) to the plane wall. I believe that this is not OK. The two conditions that you have here are generally inconsistent and over-determined.
Presumably the soft wall is undergoing two different kinds of forcing, namely, (1) due to impinging sound waves, and (2) due to some form of applied mechanical force. If so, then I think that you must work in terms of forces rather than acceleration. That is to say, the wall experiences forces due to incident acoustic waves and forces due to some kind of mechanical drive, with the vibration of the wall being the result of the net forcing, with a normal acceleration and displacement to be determined as the result of that net forcing.
On the principle of independence of the boundary conditions of structure direction of turbulence
Lu Panming
Abstract
This is an introduction to the turbulence modeling theory of the present author, which can take the boundary conditions of turbulence structure into consideration ( the main contents have either not been published in normal journals or only published in chinese papers). It is included that: (I)。Difficulty Problems Encountered in “Second-Moment-Closure” turbulence modelling ,i.e. “Gao-Ge Anomaly” ; (II)。The improvement to the ”Second-Moment-Closure” turbulence modelling in order to allows the boundary conditions of turbulence structure direction could be prescribed; (III)。An explanation to the principle of independence of the boundary conditions of
turbulence structure direction ; (IV)。Six suggestions to the possible future work directions; (V)。 An explanation to the ”Gao-Ge Anomaly”.
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dear professors:
4. The principle of the independence of the boundary conditions is not only to the turbulence modelling, but also suitable to the other subject, because it is frequently meet the equations are not easy to solve, so there is often a need of modelling or predigestion. For example, both the D‘Alembert anomaly (~1752) and the Stokes anomaly (~1856), are due to breach the principle of independence of the boundary conditions, according to today`s point of view .This is because, first, by using the inviscid potential flow`s dynamic equations it is not possible to affiliate the slip-less condition of the real fluid at the wall, and second, using the Stokes equation it is not possible to affiliate the boundary conditions both at the wall of cylinder and at the infinite to the cylinder. The first anomaly lead to the discovery of the Prandlt`s boundary layer theory(1904), and the second anomaly was solved by Oseen(1910)with introducing a modification. All these reflect the scientific worthiness and broad latency of the present principle of the independence of the boundary conditions.
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