Chapter 8
Interaction of Harmonic Waves
of Different Types with the Three-Layer
Plate Placed in the Soil
Leonid Igumnov, Dmitrii V. Tarlakovskii, Natalia A. Lokteva,
and Nguyen Duong Phung
Abstract The solution of two-dimensional task about interaction of harmonic wave
with plate with finite length is placed in the soil. Plate’s mechanical behavior is
described by Pimushin V.N. equations system, and soil mechanical behavior is
described by linear propulsion theory equation. Research of vibration-absorbing
properties of the plate dependent on frequency and form of harmonic wave acting
on the plate was conducted. From practical point of view, this task is connected with
protection of underground buildings from vibration impact, formed by moving trains
of underground in different distances from object being protected.
Keywords Soil · Plate · Paimushin V.N. Model · Harmonic wave · Oscillation
frequency · Vibration absorption · Vibrational acceleration
8.1 Introduction
Due to implementation of new infrastructure in existing city environment, there is
more often required to protect already existing buildings and constructions from negative technogenic influence. For residential buildings and public buildings, vibration is
the most dangerous event. In buildings engineering equipment, industrial plants and
transport (small-scale underground, heavy trucks, cars, trains) are vibrations sources,
which are emitting high dynamic loads, which cause spreading vibration in soil and
buildings. These vibrations are often are often causing noises inside buildings.
L. Igumnov · D. V. Tarlakovskii
Research Institute for Mechanics, National Research Lobachevsky State University of Nizhny
Novgorod, Gagarin ave., 23, 603950 Nizhny Novgorod, Russia
D. V. Tarlakovskii · N. A. Lokteva (B)
Institute of Mechanics, Lomonosov Moscow State University, Moscow, Russia
e-mail: nlok@rambler.ru
N. A. Lokteva · N. D. Phung
Moscow Aviation Institute (National Research University), Moscow, Russia
© Springer Nature Switzerland AG 2021
F. dell’Isola and L. Igumnov (eds.), Dynamics, Strength of Materials and Durability
in Multiscale Mechanics, Advanced Structured Materials 137,
https://doi.org/10.1007/978-3-030-53755-5_8
111
Interaction of Harmonic Waves
of Different Types with the Three-Layer
Plate Placed in the Soil
Leonid Igumnov, Dmitrii V. Tarlakovskii, Natalia A. Lokteva,
and Nguyen Duong Phung
Abstract The solution of two-dimensional task about interaction of harmonic wave
with plate with finite length is placed in the soil. Plate’s mechanical behavior is
described by Pimushin V.N. equations system, and soil mechanical behavior is
described by linear propulsion theory equation. Research of vibration-absorbing
properties of the plate dependent on frequency and form of harmonic wave acting
on the plate was conducted. From practical point of view, this task is connected with
protection of underground buildings from vibration impact, formed by moving trains
of underground in different distances from object being protected.
Keywords Soil · Plate · Paimushin V.N. Model · Harmonic wave · Oscillation
frequency · Vibration absorption · Vibrational acceleration
8.1 Introduction
Due to implementation of new infrastructure in existing city environment, there is
more often required to protect already existing buildings and constructions from negative technogenic influence. For residential buildings and public buildings, vibration is
the most dangerous event. In buildings engineering equipment, industrial plants and
transport (small-scale underground, heavy trucks, cars, trains) are vibrations sources,
which are emitting high dynamic loads, which cause spreading vibration in soil and
buildings. These vibrations are often are often causing noises inside buildings.
L. Igumnov · D. V. Tarlakovskii
Research Institute for Mechanics, National Research Lobachevsky State University of Nizhny
Novgorod, Gagarin ave., 23, 603950 Nizhny Novgorod, Russia
D. V. Tarlakovskii · N. A. Lokteva (B)
Institute of Mechanics, Lomonosov Moscow State University, Moscow, Russia
e-mail: nlok@rambler.ru
N. A. Lokteva · N. D. Phung
Moscow Aviation Institute (National Research University), Moscow, Russia
© Springer Nature Switzerland AG 2021
F. dell’Isola and L. Igumnov (eds.), Dynamics, Strength of Materials and Durability
in Multiscale Mechanics, Advanced Structured Materials 137,
https://doi.org/10.1007/978-3-030-53755-5_8
111