A STRUCTURED APPROACH FOR SOLVING THE INVERSE EIGENVALUE PROBLEM OF A BEAM WITH A GROUNDED MASS-SPRING ATTACHEMENT

摘要

The effect of adding lumped elements to a beam on its natural frequencies and corresponding modeshapes is a problem which has been extensively studied. A good knowledge of these effects is required when considering the inverse problem of imposing the natural frequencies of a beam and subsequently determining the characteristics of the added lumped attachments such as the stiffness of a spring or the magnitude of a mass. A previous investigation focused on the effects of adding lumped masses to a Euler-Bernoulli beam on its natural frequencies and corresponding modeshapes and proposed the determinant method in order to solve the inverse problem. The inverse problem imposed up to four natural frequencies on the Euler-Bernoulli beam with either simply-supported or clamped-free boundary conditions by modifying the position and value of the masses. The current investigation widens the scope of the previous work by analyzing the effect of adding a grounded mass and spring system on the beam's natural frequencies and corresponding modeshapes. The inverse problem, using the determinant method, is then considered for this system by imposing two desired natural frequencies on the Euler-Bernoulli beam with simply-supported boundary conditions to which the grounded mass-spring system is attached at a specified location along the beam. It is then solved for the magnitude of the mass and the stiffness of the spring.