MODELING AND ANALYSIS OF MEMBRANE VIBRATIONS SUBJECTED TO EXTERNAL FORCES
DOI:
https://doi.org/10.30890/2567-5273.2025-40-01-048Keywords:
Membrane oscillation model, wave equation, two-point in time problem, differential-symbol method, wave process, mathematical modelling.Abstract
Vibrational processes in thin-walled structural components play a crucial role in modern mechanical engineering and machine science. Membrane- and plate-like elements are widely used in engineering applications such as acoustic diaphragms, thin mechanicalReferences
Folland, G. (1995). Introduction to Partial Differential Equations, Princeton University Press, Princeton.
Wazwaz, A.-M. (2009). Partial Differential Equations and Solitary Waves Theory. Springer.
Li, B. (2008). Wave Equations for Regular and Irregular Water Wave Propagation. Journal of Waterway, Port, Coastal, and Ocean Engineering, vol. 134, issue 2, pp.121–142.
DOI: http://dx.doi.org/10.1061/(ASCE)0733-950X(2008)134:2(121)
Friedman, A. (1961). The wave equation for differential forms. Pacific Journal of Mathematics, vol.11, issue 4, pp.1267–1279.
DOI: 10.2140/pjm.1961.11.1267
Alkhadhr S., Almekkawy M. (2023). Wave Equation Modeling via Physics Informed Neural Networks: Models of Soft and Hard Constraints for Initial and Boundary Conditions. Sensors, vol. 23, issue 5, pp. 2792.
DOI: 10.3390/s23052792
He X., Wang Q., Zhou Y., Huang J., Huang X. (2024). An Effective Discontinuous Galerkin Method for Solving Acoustic Wave Equations in Heterogeneous Media. Journal of Geophysics and Engineering, issue 1, pp. 105–118.
DOI: 10.1093/jge/gxae119
Chorfi S.E., El Guermai G., Maniar L., Zouhair W. (2024). Lipschitz stability for an inverse source problem of the wave equation with kinetic boundary conditions. arXiv:2402.12902.
https://arxiv.org/abs/2402.12902v1
Hoonhout, D. & Urzúa Torres, C. (2025). Towards Stable Second Kind Boundary Integral Equations for Transient Wave Problems.
DOI:10.48550/arXiv.2502.01374
Malanchuk, O., Nytrebych, Z., (2017). Homogeneous two-point problem for PDE of the second order in time variable and infinite order in spatial variables. Open Mathematics, vol.15, issue 1, pp.101–110.
DOI: 10.1515/math-2017-0009
Nytrebych, Z. M., Malanchuk, O. M. (2017). The differential-symbol method of solving the problem two-point in time for a nonhomogeneous partial differential equation. Journal of Mathematical Sciences, vol. 227, issue 1, pp. 68–80.
DOI: 10.1007/s10958-017-3574-2
Nytrebych, Z. M., Malanchuk, O. M. (2017). The differential-symbol method of solving the two-point problem with respect to time for a partial differential equation. Journal of Mathematical Sciences, vol. 224, issue 4, pp. 541–554.
DOI: 10.1007/s10958-017-3434-0
Nitrebich, Z.M. (1996). An operator method of solving the Cauchy problem for a homogeneous system of partial differential equations. Journal of Mathematical Sciences, vol. 81, issue 6, pp. 3034–3038.
DOI: 10.1007/bf02362589
Kalenyuk, P.I., Kohut, I.V., Nytrebych, Z.M. (2012). Problem with integral condition for a partial differential equation of the first order with respect to time. Journal of Mathematical Sciences. vol.181, issue 3, pp. 293–304.
DOI: 10.1007/s10958-012-1081-z
Nytrebych, Z.M., Malanchuk, O.M., Il'kiv, V.S., Pukach, P.Ya. (2017). Homogeneous problem with two-point conditions in time for some equations of mathematical physics. Azerb. Journal of Mathematics, vol.7, issue 2, pp. 180–196.
Nytrebych, Z., Malanchuk, O., Il'kiv, V., Pukach, P. (2017). On the solvability of two-point in time problem for PDE. Italian Journal of Pure and Applied Mathematics, vol.38, pp.715–726.
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