An analytical model is developed for the flexural wave propagation of a continuous Timoshenko beam resting on elastic and metamaterial foundations. The metamaterial foundation consists of positive and negative springs with a damper. This added negative stiffness component is constructed in such a way to provide the same static stiffness and the same damping component with the equivalent reference beam on elastic foundation. Numerical examples are used to investigate the effect of the shear on wavenumber and damping for beam with elastic and metamaterial foundations. The effects of engineering safety, damping coefficient and resonating mass on the dissipative property of the beam is investigated analytically. The simulation results provide indication of an enhanced damping characteristics for the damping ratio of the flexural waves propagating within the beam.
Abohadima S, Taha M, Abdeen MAM. General analysis of Timoshenko beams on elastic foundation. In: *Mathematical Problems in Engineering*. 2015. p. 1–11.
2.
Antoniadis I, Chronopoulos D, Spitas V, Koulocheris D. Hyper-damping properties of a stiff and stable linear oscillator with a negative stiffness element. *Journal of Sound and Vibration*. 2015;346:37–52.
3.
Abbas BAH, Thomas J. Dynamic stability of Timoshenko beams on an elastic foundation. *Journal of Sound and Vibration*. 1978;60(1):33–4.
4.
Capsoni A, Capsoni A, Maria G, Bani-hani K. On damping effects in Timoshenko beams. *International Journal of Mechanical Sciences*. 2013;73:27–39.
5.
Chronopoulos D, Antoniadis I, Collet M, Ichchou M. Enhancement of wave damping within metamaterials having embedded negative stiffness inclusions. *Wave Motion*. 2015;58:165–79.
6.
Haldar S, Basu D. Response of Euler-Bernoulli beam on spatially random elastic soil. *Computers and Geotechnics*. 2013;30:110–28.
7.
Kahrobaiyan MH, Asghari M, Ahmadian MT. A Timoshenko beam element based on the modified couple stress theory. *International Journal of Mechanical Sciences*. 2014;79:75–83.
8.
Lee SY, Kuo YH, Lin FY. Stability of a Timoshenko beam resting on a Winkler elastic foundation. *Journal of Sound and Vibration*. 1992;153(2):193–202.
9.
Liu X, Shi Z, Mo YL. Effect of initial stress on periodic Timoshenko beams resting on an elastic foundation. *Journal of Vibration and Control*. 2016;1–14.
Wang XQ, So RMC. Timoshenko beam theory: A perspective based on the wave-mechanics approach. *Wave Motion*. 2015;57:64–87.
12.
Yu D, Liu Y, Wang G, Zhao H, Qiu J. Flexural vibration band gaps in Timoshenko beams with locally resonant structures. *Journal of Applied Physics*. 2006;100(12).
13.
Zhang H. Free vibration of Timoshenko beams on elastic foundation with horizontal frictions. *Journal of Vibration Engineering & Technologies*. 2019;2(3):305–14.
14.
Zhou J, Wang K, Xu D, Ouyang H. Multi-low-frequency flexural wave attenuation in Euler–Bernoulli beams using local resonators containing negative-stiffness mechanisms. 2017.
15.
Zhu R, Liu XN, Hu GK, Sun CT, Huang GL. A chiral elastic metamaterial beam for broadband vibration suppression. *Journal of Sound and Vibration*. 2014;333(10):2759–73.
16.
Zuo SL, Li FM, Zhang C. Numerical and experimental investigations on the vibration band-gap properties of periodic rigid frame structures. *Acta Mechanica*. 2016;227(6):1653–69.
The statements, opinions and data contained in the journal are solely those of the individual authors and contributors and not of the publisher and the editor(s). We stay neutral with regard to jurisdictional claims in published maps and institutional affiliations.
