Random vibration of uniform beams with varying boundary conditions by the dynamic-edge-effect method Original Research Article

In this paper, Bolotinʹs dynamic-edge-effect method is applied to determine both the normal modes of free undamped vibration, the cross-spectral densities of generalized random forces and random response of uniform beams with arbitrary boundary conditions. In particular, a uniform beam restrained at each end by a rotational and a translational spring is considered. Arbitrary boundary conditions can be simulated by varying each of the spring constants from zero to infinity. Cross spectral densities of generalized forces are then calculated for a random pressure field which is probabilistically weakly-stationary in time and weakly-homogeneous in space with respect to a special convecting frame of reference. Such a pressure field is believed to be a good model for jet or rocket noise in the near field. It is demonstrated that for a specific set of rotational spring constants the mean-square response attains the minimum.