Effect of decoupled fluid loading on nonlinear vibration of a flat plate

Numerical simulations of nonlinear responses of a flat plate subject to decoupled fluid loading are carried out. Under clamped boundary conditions and subject to forced vibration at its natural frequency corresponding to the (5,1) mode, the various response modes of the plate are determined. It is found that increasing the excitation amplitude, the response changed from periodic to chaotic. In addition, the fluid-wall shear stresses are found to change the response from linear to nonlinear and vice versa depending on their magnitudes. When a static pressure load is combined with fluid-wall shear stresses and low excitation amplitude, the resulting response was chaotic.     

On the orthogonality of natural modes of vibration

The natural modes of a discrete linear system are orthogonal with respect to the mass and stiffness matrices in a generalized sense. However, these modes are usually not orthogonal to each other in the ordinary sense. The purpose of this paper is to document a number of conditions under which the modes are also orthogonal in an ordinary fashion.     

Experimental flow study over a blunt-nosed axisymmetric body at incidence

The flowfield over a blunt-nosed cylinder was examined experimentally at a low subsonic speed for Re=1.88×10⁵ and angles of attack up to 40°. Velocity measurements were carried out (employing a seven-hole Pitot tube) as well as wall static pressure and wall shear-stress measurements. Surface flow visualization was applied using liquid crystals and a mixture of oil–TiO₂. For all the examined cases no flow asymmetries were found. For high angles of attack (20° and above) a separation “bubble” appears at the leeside of the nose area (streamwise flow separation). The basic feature of the circumferential pressure distribution at the after body area for these angles of attack is a plateau close to the suction peak and a fast recovery next to it. One streamwise vortex on each side of the symmetry plane is formed as well as a separation bubble about 90° far from this plane, where the cross-flow primary separation line is located. Each cross-flow primary separation line starts at the leeside nose area and moves towards the windward side along the cylindrical after body. The space between the two primary separation lines close to the wall is characterized by high flow fluctuations on the leeside, compared to the low fluctuations of the windward side.     

Forces along Equidistant Particle Paths

Two particles on the sphere leave the equator moving due south and travel at a constant and equal speed along a geodesic colliding at the south pole. An observer who is unaware of the curvature of the space will conclude that there is an attractive force acting between the particles. On the other hand, if particles travel at the same speed (initially parallel) along geodesics in the hyperbolic plane, then the particle paths diverge. Imagine two particles in the hyperbolic plane that are bound together at a constant distance with their center of mass traveling along a geodesic path at a constant velocity, then the force due to the curvature of the space acts to break the bond and increases as a quadratic function of the velocity. We consider this problem for the sphere and the hyperbolic plane and we give the exact formula for the apparent force between the particles. This revised version was published online in July 2006 with corrections to the Cover Date.