Random Response of Multi-Segment Beam May Exceed Response of Homogeneous Counterparts by Order of Magnitude

This paper investigates the dynamic properties of an inhomogeneous, Bernoulli–Euler multi-segment beam composed of different materials. To the best of knowledge of the authors, the problem of random vibrations of beams composing of different chunks of the beams, namely, strong and weak parts, has not been studied in the literature. In this paper, exact solution of the natural frequencies and associated mode shapes of the multi-segment Bernoulli–Euler beam are obtained using Krylov–Duncan functions, followed by free, forced, and random vibration analyses using the normal mode method. Special emphasis is placed on two special configurations of multi-segment beam, namely, the ‘rigid-soft-rigid beam’ (RSR beam) and ‘soft-rigid-soft beam’ (SRS beam) as simplest manifestations of the multi-chunked structures. Some remarkable properties exhibited by the dynamic response of multi-segment beam are demonstrated through this work, which may be of considerable engineering significance, and could not have been anticipated in advance, especially quantitatively.

ANALYTICAL TIME DOMAIN NORMAL MODE SOLUTION OF AN ACOUSTIC WAVEGUIDE WITH PERFECTLY REFLECTING WALLS

Solution of wide-band underwater acoustic problems with the classical Normal Mode method in the frequency domain needs to solve the problem repeating for every frequency component of the wide-band source signal. In this paper, a direct and causal analytical Time Domain Normal Mode Method is presented for arbitrary time-dependent acoustic sources for a single layered isovelocity waveguide. An incomplete separation of variables technique is used to solve the inhomogeneous wave equation, directly in the time domain. Therefore, it becomes possible to calculate the time domain acoustic pressure in a single run.