Frequency and buckling parameters of box-type structures using the Rayleigh–Ritz method and penalty parameters

The Rayleigh–Ritz method (RRM) is often used to solve eigen-problems of simple continuous systems, usually defined by a single element, but it is not easily applied to complex systems. This disadvantage is addressed in this work using the penalty function method (PFM) to define all constraints of the system and to join elements to build box-type structures. Frequency parameters of non-symmetrical structures and buckling parameters of symmetric box-type structures are presented in this work. The use of positive and negative penalty parameters added to either the elastic stiffness matrix or to the mass matrix (matrices associated with the eigenvalue) is also investigated.