Computational routine for obtaining the Rayleigh quotient for a truss system using its self-weight and corresponding static deformation

Abstract

When subjected to dynamic loads, structural systems can lose stability or undergo material failure. Furthermore, if the frequency of the loads in the system approaches one of its natural vibration frequencies, resonance can occur, which can potentially increase the failure. In general, the first natural frequency of the structure is the most important for excitation loads with low frequencies. Therefore, a simplified analysis to obtain this frequency and vibration mode can be highly useful. This study aims to assess the application of the deformation of a spatial truss under static loading (self-weight) as an approximation of its first vibration mode. In this way, the Rayleigh Quotient is determined, and consequently, an approximation of the fundamental natural frequency of the system is obtained. A computational routine implemented in FORTRAN© was used for calculating this Quotient, and the routine's validation was performed by comparing its result with that obtained in the SAP2000© program. A good agreement between the results was observed, thus validating the mentioned routine.