On propagation of elastic waves in an embedded sigmoid functionally graded curved beam

This investigation studies the characteristics of wave dispersion in sigmoid functionally graded (SFG) curved beams lying on an elastic substrate for the first time. Homogenization process was performed with the help of sigmoid function and two power laws. Moreover, various materials such as Zirconia, Alumina, Monel and Nickel steel were explored as curved beams materials. In addition, curved beams were rested on an elastic substrate which was modelled based on Winkler-Pasternak foundation. The SFG curved beams' governing equations were derived according to Euler-Bernoulli curved beam theory which is known as classic beam theory and Hamilton's principle. The resulted governing equations were solved via an analytical method. In order to validate the utilized method, the obtained outcomes were compared with other researches. Finally, the influences of various parameters, including wave number, opening angle, gradient index, Winkler coefficient and Pasternak coefficient were evaluated and indicated in the form of diagrams.

Automated summary

This study investigates the dispersion characteristics of wave in sigmoid functionally graded curved beams on an elastic substrate for the first time. The homogenization process is performed using sigmoid function and two power laws. The study explores different materials as curved beam materials and models the elastic substrate based on Winkler-Pasternak foundation. The governing equations of the sigmoid functionally graded curved beams are derived and solved analytically. The obtained results are validated by comparing with other studies, and the influences of various parameters are shown in diagrams.