8 Interaction of Harmonic Waves of Different Types …
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8.9 Example
As an example, we considered a plate with the following dimensions, and here,
the plates’ parameters are L = 5 m, h = 0.015 m, t = 0.004 m. The bearing
layers are made of DIN17100-type steel with density of ρ 0 = 7859 kg/m
3 , Young’s
modulus E 0 = 2 × 10
5 MPa , and Poisson’s ratio of ν 0 = 0.28. Filler material is
aluminum of Al–Mn type with density of ρ 0 = 2730 kg/m
3 , Young’s modulus of
E 0 = 0.71 × 10
−5 MPa, and Poisson’s ratio of ν 0 = 0.3. The materials of the media
“1” and “2” are assumed to be fill-up ground compacted under the humidity degree
of 0.5, Young’s modulus of E = 10
8 MPa, and density of ρ = 1600 kg/m
3 .
The results of calculations of the module of the acceleration field at various points
in the medium are presented on Fig. 8.2. The figure shows that a significant decrease
in the vibration acceleration module occurs with distance from the plate boundary.
Similarly, a cylindrical wave overcomes an obstacle better than a plane wave.
As you know, the greatest danger to the foundations of buildings and structures represent low frequencies. In accordance with (set of rules for the design and
construction of the joint venture 23-105-2004), the vibration assessment is carried
out in octave bands with geometric mean frequencies of 16, 31.5, and 63 Hz. By
changing the plate geometrically, it is possible to avoid coincidence of the resonance
with these frequencies
8.10 Notes and Comments
In this article, solution method of couple problem of relation between plane harmonic
wave and the simply supported plate is presented. The results depend on the plate‘s
materials and its geometrics. In this way, it becomes possible to choose optimal
parameters of the material, the plate is made from, and its geometrics, which is of
practical interest.
121
8.9 Example
As an example, we considered a plate with the following dimensions, and here,
the plates’ parameters are L = 5 m, h = 0.015 m, t = 0.004 m. The bearing
layers are made of DIN17100-type steel with density of ρ 0 = 7859 kg/m
3 , Young’s
modulus E 0 = 2 × 10
5 MPa , and Poisson’s ratio of ν 0 = 0.28. Filler material is
aluminum of Al–Mn type with density of ρ 0 = 2730 kg/m
3 , Young’s modulus of
E 0 = 0.71 × 10
−5 MPa, and Poisson’s ratio of ν 0 = 0.3. The materials of the media
“1” and “2” are assumed to be fill-up ground compacted under the humidity degree
of 0.5, Young’s modulus of E = 10
8 MPa, and density of ρ = 1600 kg/m
3 .
The results of calculations of the module of the acceleration field at various points
in the medium are presented on Fig. 8.2. The figure shows that a significant decrease
in the vibration acceleration module occurs with distance from the plate boundary.
Similarly, a cylindrical wave overcomes an obstacle better than a plane wave.
As you know, the greatest danger to the foundations of buildings and structures represent low frequencies. In accordance with (set of rules for the design and
construction of the joint venture 23-105-2004), the vibration assessment is carried
out in octave bands with geometric mean frequencies of 16, 31.5, and 63 Hz. By
changing the plate geometrically, it is possible to avoid coincidence of the resonance
with these frequencies
8.10 Notes and Comments
In this article, solution method of couple problem of relation between plane harmonic
wave and the simply supported plate is presented. The results depend on the plate‘s
materials and its geometrics. In this way, it becomes possible to choose optimal
parameters of the material, the plate is made from, and its geometrics, which is of
practical interest.