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The first development was to extend the wave equation to other kinds of vibrations for example, the vibrations of drums.
As a numerical example the vibrations of the system consisting of two identical membranes subjected to harmonic uniform distributed load are treated in detail.
As an example the vibrations of rotating cylindrical shells have been calculated by the finite element method and the results are compared with the analytical solutions for cylindrical shells with special boundary conditions.
For example, the vibrations of a guy wire of uniform cross-section composed of N parts of different densities can be set up as a multi-point boundary value problem.
For example, the vibrations of a guy wire of a uniform cross section and composed of N parts of different densities can be set up as a multi-point boundary value problem [3].
For example, the vibrations of a guy wire of uniform cross section and composed of N parts of different densities, and some problems in the theory of elastic stability, can be modeled by multi-point boundary value problems (see [26, 27]).
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As an example, the vibration problem of a layered cantilever beam with base excitation is considered.
Taking a typical short cable as an example, the vibration reduction ability with optimally controlled MR dampers is verified numerically by comparison with the viscous damper tuned to a single mode response.
For example, the vibration of a guy wire composed of parts with a uniform cross-section and different densities in different parts can be modeled as a Multipoint boundary value problem [1].
For examples, the vibrations of a guy wire of a uniform cross-section, composed of m sections of different densities can be molded as a multipoint boundary value problem.
However, the frequency of the broad band centered at 1,645 cm−1 is higher than those reported by Vinkler et al. [35] also in the case of covalent humates with Fe and Al (1,625 cm−1) and should be overlapped by other absorptions, for example, the OH vibration of water molecules bonded to silica gel which occurs at 1,630 cm−1[33].
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