1. MMC
  2. All Volumes and Issues
  3. Volume 5, Number 2, 2018
  4. Vibration of orthotropic doubly curved panel with a set of inclusions of arbitrary configuration with different types of connections with the panel

Vibration of orthotropic doubly curved panel with a set of inclusions of arbitrary configuration with different types of connections with the panel

MMC.
2018;
Volume 5, Number 2
: 221-234
https://doi.org/10.23939/mmc2018.02.221
Received: September 07, 2018

Math. Model. Comput. Vol. 5, No. 2, pp. 221-234 (2018)

Authors:
  1. T. Shopa
1
Pidstryhach Institute for Applied Problems of Mechanics and Mathematics of the National Academy of Sciences of Ukraine

In the framework of the refined theory of shells, which takes into account transverse shear deformation and all inertial components, the solution of the problem on  the steady-state vibration of the orthotropic doubly curved panel with the arbitrary number of absolutely rigid inclusions  of the arbitrary geometrical form and location is constructed. The inclusions have different types of connections with the panel and perform the translational motion in the normal direction to the middle surface of the panel. The external boundary of the panel is of the arbitrary geometrical configuration. The arbitrary mixed, harmonic in time, boundary conditions are considered on the external boundary of the panel. The solution is built on the basis of the indirect boundary elements method. The sequential approach to the representation of the Green's functions is used. The integral equations are solved by the collocation method.

orthotropic doubly curved panel
inclusions
vibration
indirect boundary elements method
  1. Mykhas’kiv V., Kunets Ya., Matus V., Khay O. Elastic wave dispersion and attenuation caused by multiple types of disc-shaped inclusions. International Journal of Structural Integrity. 9 (2), 219–232 (2018).
  2. Kit H. S., Mykhas’skiv V. V., Khaj O. M. Analysis of the steady oscillations of a plane absolutely rigid inclusion in a three-dimensional elastic body by the boundary element method. Journal of applied mathematics and mechanics. 66 (5), 817–824 (2002).
  3. Mykhas’kiv V. V., Khay O. M., Zhang C., Boström A. Effective dynamic properties of 3D composite materials containing rigid penny-shaped inclusions. Waves in Random and Complex Media. 20 (3), 491–510 (2010).
  4. Mykhas’kiv V. Transient response of a plane rigid inclusion to an incident wave in an elastic solid. Wave motion. 41 (2), 133–144 (2005).
  5. Kit G. S., Kunets Ya. I., Mykhas’kiv V. V. Interaction of a stationary wave with a thin low stiffness penny-shaped inclusion in an elastic body. Mechanics of solids. 39 (5), 64–70 (2004).
  6. Burak Ja. J., Rudavsky Ju. K., Sukhorolsky M. A. Analitychna mechanika lokalno navantazhenyh obolonok. Lviv, Intelekt-Zakhid (2007), (in Ukrainian).
  7. Shopa T. Do pobudovy rozvazku zadachi pro kolyvanna ortotropnoi nepolohoji zylindrychnoi paneli z vkluchennam dovilnoi konfigurazii. Mashynoznavstvo. 7, 38–42 (2010), (in Ukrainian).
  8. Shopa T. Kolyvanna ortotropnoi paneli podvijnoi kryvyny z mnozhynoju vkluchen dovilnoi konfihurazii. Suchasni problemy mechaniky ta matematyky. 2, 187–188 (2013), (in Ukrainian).
  9. Shopa T. Kolyvanna ortotropnoi paneli podvijnoi kryvyny z mnozhynoju vkluchen dovilnoi konfihurazii z pruzhnymy prosharkamy. Visnyk Ternopilskoho nazionalnonho tekhnichnoho universytety. 1, 71–84 (2013), (in Ukrainian).
  10. Shopa T. Kolyvanna ortotropnoi paneli podvijnoi kryvyny z mnozhynoju sharnirno opertyh vkluchen dovilnoi konfihurazii. Prykarpatskij visnyk naukovoho tovarystva Shevchenka. 2, 114–121 (2017), (in Ukrainian).
  11. Shopa T. Kolyvanna ortotropnoi paneli podvijnoi kryvyny z mnozhynoju otvoriv dovilnoji konfihurazii. Visnyk Ternopilskoho nazionalnonho tekhnichnoho universytety. 3, 63–74 (2012), (in Ukrainian).
  12. Lighthill J. Introduction to Fourier Analysis and Generalised Functions. Cambridge University Press (1958).
  13. Sukhorolsky M. A. Funkzionalni poslidovnosti i rady. Lviv, Rastr-7 (2010), (in Ukrainian).