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.
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References
Abali, B. E., Altenbach, H., dell’Isola, F., Eremeyev, V. A., & Ochsner, A. (Eds). (2019). New achievements in continuum mechanics and thermodynamics. In A tribute to wolfgang H. muller. Advanced structured materials (Vol. 108, 564p). Cham. Switzerland.: Springer Nature Switzerland AG. Part of Springer.
Abali, B. E., Muller, W., & dell’Isola, F. (2017). Theory and computation of higher gradient elasticity theories based on action principles. Archive of Applied Mechanics, 87(9).
Alibert, J. J., Seppecher, P., dell’Isola, F. (2003). Truss modular beams with deformation energy de-pending on higher displacement gradients. Mathematics and Mechanics of Solids, 8(1).
Andreaus, U., dell’Isola, F., & Porfiri, M. (2004). Piezoelectric passive distributed controllers for beam flexural vibrations. Journal of Vibration and Control, 10(5), 625–659.
Auffray, N., dell’Isola, F., Eremeyev, V., Madeo, A., & Rossi, G. (2013). Analytical continuum mechanics à la Hamilton-Piola: Least action principle for second gradient continua and capillary fluids. Mathematics and Mechanics of Solids.
Barchiesi, E., Spagnuolo, M., & Placidi, L. (2019). Mechanical metamaterials: A state of the art. Mathematics and Mechanics of Solids, 24(1), 212–234.
Berezhnoi, D. V., Konoplev, Yu. G., Paimushin, V. N., & Sekaeva, L. R. (2004). Investigation of the interaction between concrete collector and dry and waterlogged grounds. Trudy Vseros. nauch. konf. “Matematicheskoe modelirovanie i kraevye zadachi” [Proc. All-Russ. Sci. Conf. “Mathematical Simulation and Boundary Value Problems”]. Part 1. Mathematical Models of Mechanics, Strength and Reliability of Structures. Samara, SamGTU, pp. 37–39. (In Russian).
Del Vescovo, D., & Giorgio, I. (2014). Dynamic problems for metamaterials: review of existing models and ideas for further research. International Journal of Engineering Science, 80, 153–172.
dell’Isola, F., Andreaus, U., & Placidi, L. (2015). At the origins and in the vanguard of peridynamics, non-local and higher-gradient continuum mechanics: An underestimated and still topi-cal contribution of Gabrio Piola. Mathematics and Mechanics of Solids, 20(8).
dell’Isola, F., Della Corte, A., & Giorgio, I. (2016). Higher-gradient continua: The legacy of Piola, Mindlin, Sedov and Toupin and some future research perspectives. Mathematics and Mechanics of Solids.
dell’Isola, F., Maurini, C., & Porfiri, M. (2004). Passive damping of beam vibrations through distributed electric networks and piezoelectric transducers: prototype design and experimental validation. Smart Materials and Structures, 13(2), 299.
dell’Isola, F., Seppecher, P., & Alibert, J. J. (2019). Pantographic metamaterials: an example of math-emphatically driven design and of its technological challenges. Continuum Mechanics and Thermodynamics, 31(4), 851–884.
dell’Isola, F., Seppecher, P., & Madeo, A. (2012). How contact interactions may depend on the shape of Cauchy cuts in Nth gradient continua: approach “à la D’Alembert”. Zeitschrift für angewandte Mathematik und Physik, 63(6).
Di Cosmo, F., Laudato, M., & Spagnuolo, M. (2018). Acoustic metamaterials based on local resonances: Homogenization, optimization and applications. Chapter from a book. In: Generalized Models and Non-classical Approaches in Complex Materials. (pp. 247–274) Springer.
Gorshkov, A. G., Medvedskii, A. L., Rabinskii, L. N., & Tarlakovskii, D. V. (2004). Waves in continuum media (472p.). Moscow: FIZMATLIT (In Russian).
Ivanov, V. A., & Paimushin, V. N. (1995). Refined formulation of dynamic problems of three-layered shells with a transversally soft filler is a numerical-analytical method for solving them. Applied Mechanics and Technical Physics, 36(4), 147–151.
Ivanov, V.A., & Paimushin, V. N. (1995). Refinement of the equations of the dynamics of multilayer shells with a transversally soft filler. Izv. RAS. MTT, 3, 142–152.
Kostrov, B. V. (1964). Motion of a rigid massive wedge inserted into an elastic medium under the effect of plane wave. Prikl Mat Mekh, 28(1), 99–110. (In Russian).
Maurini, C., dell’Isola, F., & Del Vescovo, D. (2004). Comparison of piezoelectronic networks acting as distributed vibration absorbers. Mechanical Systems and Signal Processing, 18(5), 1243–1271.
Placidi, L., Barchiesi, E., Turco, E., & Rizzi, N. L. (2016). A review on 2D models for the description of pantographic fabrics. Zeitschrift für angewandte Mathematik und Physik, 67(5).
Ryl’ko, M. A. (1977). On the motion of a rigid rectangular insertion under the effect of plane wave. Mekh Tverd Tela, 1, 158–164 (In Russian).
Set of rules for the design and construction of the joint venture 23-105-2004 Evaluation of vibration in the design and construction and operation of metro facilities. Moscow: Gosstroy Russia (2014).
Sheddon, I. (1951). Fourier Transforms (p. 542). New York: McGraw Hill.
Rakhmatulin, Kh. A., & Sunchalieva, L. M. (1983). Elastic and elastoplastic properties of the ground upon dynamic loads on the foundation. Department: in VINITI, 4149–4183 (In Russian).
Umek, A. (1973). Dynamic responses of building foundations to incident elastic waves. PhD Thesis. Illinois, Ill. Inst. Technol.
Vidoli, S., & dell’Isola, F. (2001). Vibration control in plates by uniformly distributed actuators interconnected via electric networks. European Journal of Mechanics - A/Solids, 20(3), 435–456.
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The reported study was funded by Russian Foundation for Basic Research, according to the research projects Nos. 19-08-00968 A.
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Igumnov, L., Tarlakovskii, D.V., Lokteva, N.A., Phung, N.D. (2021). Interaction of Harmonic Waves of Different Types with the Three-Layer Plate Placed in the Soil. In: dell'Isola, F., Igumnov, L. (eds) Dynamics, Strength of Materials and Durability in Multiscale Mechanics. Advanced Structured Materials, vol 137. Springer, Cham. https://doi.org/10.1007/978-3-030-53755-5_8
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