Longitudinal vibration of functionally graded tapered microbars embedded in an elastic medium basedon SGT

In this article, longitudinal free vibration analysis ofaxially functionally graded tapered microbars embeddedin a Pasternak modulus on the basis of strain gradientelasticity theory is investigated. In this research, thematerial property of microbars smoothly varied along theaxial direction. Rayleigh–Ritz technique is considered asan approximate solution for free longitudinal vibrationproblem of strain gradient microbars. Also, the effects offoundation constant coefficients, material length scaleparameters on the free longitudinal vibration areillustrated. The results show that at the specified value ofslenderness ratio, the dimensionless natural frequency forstrain gradient theory (SGT) is more than for classicaltheory (CT). Also it is concluded that the differencebetween natural frequencies obtained by CT and SGTbecomes more significant for higher modes.

کلیدواژه ها:

Longitudinal vibration ، functionally gradedtapered microbars ، Elastic foundation ، Rayleigh–Ritzmethod ، SGT.