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

چکیده مقاله

In this article, longitudinal free vibration analysis of axially functionally graded tapered microbars embedded in a Pasternak modulus on the basis of strain gradient elasticity theory is investigated. In this research, the material property of microbars smoothly varied along the axial direction. Rayleigh–Ritz technique is considered as an approximate solution for free longitudinal vibration problem of strain gradient microbars. Also, the effects of foundation constant coefficients, material length scale parameters on the free longitudinal vibration are illustrated. The results show that at the specified value of slenderness ratio, the dimensionless natural frequency for strain gradient theory (SGT) is more than for classical theory (CT). Also it is concluded that the difference between natural frequencies obtained by CT and SGT becomes more significant for higher modes