Out-of-plane Vibration of Arc Bar of Variable Cross-section

Abstract

The free out-of-plane vibration of an arc bar of variable cross-section is analyzed by use of the transfer matrix approach. for this purpose, the equations of out-of-plane vibration of an arc bar are written as a coupled set of first-order differential equations by using the transfer matrix of the bar. Once the matrix has been determined by the numerical integration of the equations, the natural frequencies and the mode shapes of the vibration can be calculated numerically in terms of the elements of the matrix for a given set of boundary conditions at the ends of the bar. This method is applied to bars of linearly, parabolically and exponentially varying rectangular cross-sections, and the effects of the varying cross-section and slenderness ratio are studied.