Asymptotic Approaches in Nonlinear Dynamics: New Trends and by Jan Awrejcewicz, Igor V. Andrianov, Leonid I. Manevitch

By Jan Awrejcewicz, Igor V. Andrianov, Leonid I. Manevitch

This booklet covers advancements within the box of the idea of oscillations from the various viewpoints, reflecting the field's multidisciplinary nature. Addressing researchers in mechanics, physics, utilized arithmetic, and engineering, in addition to scholars, the ebook provides an creation to the state-of-the-art during this quarter and to numerous purposes. For the 1st time a therapy of the asymptotic and homogenization tools within the conception of oscillations together with Padé approximations is gifted. due to its wealth of attention-grabbing examples this publication will turn out necessary as an creation to the sphere for beginners and a reference for experts.

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Additional info for Asymptotic Approaches in Nonlinear Dynamics: New Trends and Applications (Springer Series in Synergetics)

Example text

A small portion of this infinite matrix of image rooms in twodimensional space is shown in Fig. 9. Assuming that the point source generates an impulse at t = 0, each image source must also generate an identical impulse at t = 0. This ensures that all propagation paths have the correct time lag/gain relative to each other. e. propagation paths with reflections) with propagation times less than t. 8 Source and image source. 9 Source ( ) and image sources ( ) for a box-shaped room (dark solid lines) and some of its image rooms (dotted lines).

11). The term ‘local mode’ is used because the modes are ‘local’ to a space that is defined by its boundaries; in a similar way we will define local modes of vibration for structure-borne sound on plates and beams in Chapter 2. For rooms this definition assumes that there is no interaction between the sound waves in the room and the structure-borne sound waves on the walls and floors that face into that room. The walls and floors are only considered as boundaries that determine the fraction of wave energy that is reflected and the phase change that occurs upon reflection.

13) describes propagation in a single direction; hence each mode is comprised of more than one plane wave. For each mode we can define equivalent angles, θx , θy , and θz ; these angles are defined from lines that are normal to the x, y, and z-axis respectively. They are defined in k-space for any eigenvalue in the lattice (see Fig. 15). For each mode, one plane wave points in the direction of this vector in k-space. The direction of the other plane waves can be found by reflecting the vector into the other octants of k-space.

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