Non-reciprocal wave propagation in periodically structured Timoshenko beams
Апстракт
In this paper we will investigate non-reciprocal wave propagation in Timoshenko beams,
due to space and time modulation of its elastic properties. To that end, an analytical approach
is used: the Bloch theorem is applied when choosing the solution form for displacement
components and the angle of rotation, which figure in the equations of motion along with the
elastic properties. Also, the Fourier expansion is used to express the periodic nature of the
modulation. By solving the eigenvalue problem for different modulation parameters, we obtain
the band diagrams which can be used to analyze the directionality of wave propagation. These
diagrams clearly represent the breakage of symmetry as a consequence of modulation. Thus, a
modulated beam behaves as a kind of metamaterial, in which one-way propagation of elastic
waves is possible. When shear and rotational effects are neglected, these results converge to
the results for the Euler-Bernoulli beam, which are already present in ...scientific literature.
Кључне речи:
Metamaterials / Phononic bandgap / Non-reciprocal wave propagation / Elastic wave / Timoshenko beam theoryИзвор:
Book of abstracts : 1st International Conference on Mathematical Modelling in Mechanics and Engineering Mathematical Institute SANU, 08-10. September, 2022., 2022, 125-125Издавач:
- Univerzitet u Beogradu, Mašinski fakultet
Финансирање / пројекти:
- Министарство науке, технолошког развоја и иновација Републике Србије, институционално финансирање - 200105 (Универзитет у Београду, Машински факултет) (RS-MESTD-inst-2020-200105)
Колекције
Институција/група
Mašinski fakultetTY - CONF AU - Rosić, Nevena AU - Karličić, Danilo AU - Cajić, Milan AU - Lazarević, Mihailo PY - 2022 UR - https://machinery.mas.bg.ac.rs/handle/123456789/4078 AB - In this paper we will investigate non-reciprocal wave propagation in Timoshenko beams, due to space and time modulation of its elastic properties. To that end, an analytical approach is used: the Bloch theorem is applied when choosing the solution form for displacement components and the angle of rotation, which figure in the equations of motion along with the elastic properties. Also, the Fourier expansion is used to express the periodic nature of the modulation. By solving the eigenvalue problem for different modulation parameters, we obtain the band diagrams which can be used to analyze the directionality of wave propagation. These diagrams clearly represent the breakage of symmetry as a consequence of modulation. Thus, a modulated beam behaves as a kind of metamaterial, in which one-way propagation of elastic waves is possible. When shear and rotational effects are neglected, these results converge to the results for the Euler-Bernoulli beam, which are already present in scientific literature. PB - Univerzitet u Beogradu, Mašinski fakultet C3 - Book of abstracts : 1st International Conference on Mathematical Modelling in Mechanics and Engineering Mathematical Institute SANU, 08-10. September, 2022. T1 - Non-reciprocal wave propagation in periodically structured Timoshenko beams EP - 125 SP - 125 UR - https://hdl.handle.net/21.15107/rcub_machinery_4078 ER -
@conference{ author = "Rosić, Nevena and Karličić, Danilo and Cajić, Milan and Lazarević, Mihailo", year = "2022", abstract = "In this paper we will investigate non-reciprocal wave propagation in Timoshenko beams, due to space and time modulation of its elastic properties. To that end, an analytical approach is used: the Bloch theorem is applied when choosing the solution form for displacement components and the angle of rotation, which figure in the equations of motion along with the elastic properties. Also, the Fourier expansion is used to express the periodic nature of the modulation. By solving the eigenvalue problem for different modulation parameters, we obtain the band diagrams which can be used to analyze the directionality of wave propagation. These diagrams clearly represent the breakage of symmetry as a consequence of modulation. Thus, a modulated beam behaves as a kind of metamaterial, in which one-way propagation of elastic waves is possible. When shear and rotational effects are neglected, these results converge to the results for the Euler-Bernoulli beam, which are already present in scientific literature.", publisher = "Univerzitet u Beogradu, Mašinski fakultet", journal = "Book of abstracts : 1st International Conference on Mathematical Modelling in Mechanics and Engineering Mathematical Institute SANU, 08-10. September, 2022.", title = "Non-reciprocal wave propagation in periodically structured Timoshenko beams", pages = "125-125", url = "https://hdl.handle.net/21.15107/rcub_machinery_4078" }
Rosić, N., Karličić, D., Cajić, M.,& Lazarević, M.. (2022). Non-reciprocal wave propagation in periodically structured Timoshenko beams. in Book of abstracts : 1st International Conference on Mathematical Modelling in Mechanics and Engineering Mathematical Institute SANU, 08-10. September, 2022. Univerzitet u Beogradu, Mašinski fakultet., 125-125. https://hdl.handle.net/21.15107/rcub_machinery_4078
Rosić N, Karličić D, Cajić M, Lazarević M. Non-reciprocal wave propagation in periodically structured Timoshenko beams. in Book of abstracts : 1st International Conference on Mathematical Modelling in Mechanics and Engineering Mathematical Institute SANU, 08-10. September, 2022.. 2022;:125-125. https://hdl.handle.net/21.15107/rcub_machinery_4078 .
Rosić, Nevena, Karličić, Danilo, Cajić, Milan, Lazarević, Mihailo, "Non-reciprocal wave propagation in periodically structured Timoshenko beams" in Book of abstracts : 1st International Conference on Mathematical Modelling in Mechanics and Engineering Mathematical Institute SANU, 08-10. September, 2022. (2022):125-125, https://hdl.handle.net/21.15107/rcub_machinery_4078 .