Loss factors and resonant frequencies of encastré damped sandwich beams

The differential equation for the damped normal modes of a three-layer encastré sandwich beam is used, in conjunction with appropriate boundary conditions, to determine the characteristic equation for the resonant frequency, loss factor and modal roots. An iterative method of solving this equation is presented, and computed values for a wide range of parameter values are shown. The six modal roots are critically examined, and it is observed that all of them have both real and imaginary parts. The implication of this is that beams with different boundary conditions have different loss-factor/resonant frequency relationships. The loss factors of the encastré beams vary with the shear parameter, geometric parameter and core loss factor in a manner similar to those of simply-supported beams, but reach their maxima at values of the shear parameter which are greater than the simply-supported values. An approximate method of determining the resonant frequency and loss factor is presented.