The Solution of Boundary Value Problems for the Natural Frequencies of Laminated, Elastic, Visco-elastic Beams Having Unsymetrical Mountings

摘要

An analytical study was performed to deter-mine methods of solution for boundary value problems dealing with the natural frequencies and the system loss factor of composite beams having different types of attachment at each end. The composite beam is a laminate composed of a thin layer of a visco-elastic material which is sandwiched between two layers of an elastic material. Damping is provided by the visco-elastic shearing. The material shear modulus is assumed to be a complex number.nThe results of this study is a method for determining the matrix polynomials which provide multi-valued solutions. In addition a Fortran program was developed in order to determine the natural frequencies and system loss factors for cases where the beam is mounted with a fixed simple support or with a cantilever support. The program was not successful in handling the damped cases and only partially successful for the undamped cases.