STABILITY OF A THREE-LAYER ORTHOTROPIC PLATE IN A SUPERSONIC GAS FLOW,
FOREIGN TECHNOLOGY DIV WRIGHT-PATTERSON AFB OHIO
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The report attempts to solve the problem of non-linear flutter of three-layer rectangular plates, streamlined by a supersonic gas stream with a zero angle of attack. The layers are symmetrical w.r. to the neutral plane and the materials obey a generalized Hooks law. Normal displacements were assumed to be comparable with the thickness of the plate. A system non-linear differential equations was given together with the expression for a transverse load, and boundary conditions. An approximate solution was assumed to be trigonometric and, on substitution, the original equations were shown to reduce to a non-linear system of two equations in dimensionless variables, for the case of one-sided streamlining with different stream velocities. The periodic solution near the critical value was sought by the method of successive approximations and the amplitude and frequency of established flutter vibrations were found by the Bubnov-Galerkin method. The amplitude of second approximation was also obtained. Two possible cases were discussed and a numerical example was given. The conclusions reached were that critical flutter velocity found by the above method is significantly smaller than that found from the classical theory, and that the difference between two values increases with the value of h1a, where h1 is thickness of the plate and a is length of the plate.
- Fluid Mechanics