Free vibration analysis of a multiple straight-line structure regarded as a distributed mass system by the transfer influence coefficient method

This paper describes the general formulation for the in-plane flexural free vibration analysis of a multiple-layered straight-line structure by the transfer influence coefficient method. The structure is modeled as a distributed mass system with lumped masses and lumped inertia moments, and massless linear and rotational springs. The results of the simple numerical computational examples demonstrate the validity of the present method giving the numerical high accuracy and the numerical high speed, compared with the transfer matrix method on a personal computer. The main features of this method are the unification of the frequency equation for all boundary conditions, and the elimination method of the false roots when the bisection method is used for solving the frequency equation. The cancelling attributable to the adding and subtracting of hyperbolic and trigonometric functions is overcome by partitioning the uniformly distributed beams.