Oscillations of Viscoelastic Mechanical Systems with Finite Freedom
DOI:
https://doi.org/10.22105/kmisj.v2i3.100Keywords:
Mechanical systems, Non-stationary oscillations, Movements, Decrement of damping, Finite number of degrees of freedomAbstract
The study investigates the natural and externally excited oscillations of viscoelastic mechanical systems possessing a finite number of degrees of freedom. Based on Lagrange’s second-order equations, the dynamical model of systems with dissipation was derived. Particular attention is paid to periodic as well as transient forced vibrations in multi-degree-of-freedom structures.The system of equations of motion is written in matrix form relative to the matrix - column The characteristic parameters were found, where and are real numbers called damping coefficients. The attenuation decrement ratio was also determined. Non-stationary oscillations of mechanical systems are solved by the Fourier transform method.
References
Kalnins, A. (1961). On vibrations of shallow spherical shells. The journal of the acoustical society of America, 33(8), 1102–1107. https://doi.org/10.1121/1.1908908
Kalnins, A., & Naghdi, P. M. (1960). Axisymmetric vibrations of shallow elastic spherical shells. The journal of the acoustical society of America, 32(3), 342–347. https://doi.org/10.1121/1.1908055
Safarov, I. I., Teshayev, M. H., Juraev, S. I., & Khomidov, F. F. (2024). Vibrations of viscoelastic plates with attached concentrated masses. Lobachevskii journal of mathematics, 45(4), 1729–1737. https://doi.org/10.1134/S1995080224601474
Teshaev, M. K., Safarov, I. I., & Mirsaidov, M. (2019). Oscillations of multilayer viscoelastic composite toroidal pipes. Journal of the serbian society for computational mechanics, 13(2). 10.24874/jsscm.2019.13.02.08%0A
Safarov, I. I., Teshaev, M. K., & Boltaev, Z. I. (2017). Distribution natural waves on the viscoelastic cylindrical body in plane strain state. Case studies journal, 6(1). https://ssrn.com/abstract=3418206
Safarov, I. I., Boltaev, Z. I., & Axmedov, M. (2017). Sh. Rajabov O. Numerical solution of the problem on the impact plane non-stationary elastic waves by a cylindrical body. Discover, 53(256), 255-265. https://www.discoveryjournals.org/discovery/current_issue/v53/n256/A4.pdf?
Safarov, I. I., Kh, T. M., & Sh, A. M. (2016). Vibrations dissipative plate mechanical systems with point. The international ouarterlu journal/science & technology, 2(8), 437–450.
Safarov, I. I., Teshaev, M. K., & Boltaev, Z. I., Sharipovich, A. M. (2017). About distribution of own waves in the dissipative layered cylindrical bodies interacting with Wednesday. Discovery, 53(253), 16–28. https://www.discoveryjournals.org/discovery/current_issue/v53/n253/A2.pdf?
Trotsenko, Y. V. (2006). Frequencies and modes of vibration of a cylindrical shell with attached rigid body. Journal of sound and vibration, 292(3), 535–551. https://doi.org/10.1016/j.jsv.2005.08.015
Issue 1