A Technique for the Systematic Choice of Admissible Functions in the Rayleigh–ritz Method

The use of negative penalty functions in solving partial differential equations

“…If this is proved to be true in general, this would solve a long standing problem of selecting appropriate penalty parameters [4,5] and would give conÿdence in the asymptotic modelling that is being used widely since 1943 [6][7][8][9][10].…”

Vibration Analysis for Monitoring of Ancient Tie-Rods

“…Amabili et al [1][2][3][4][5][6] developed a two-step method consisting of in situ measurements of tie-rods' natural frequencies and further elaboration of the data via an optimization algorithm based on the Rayleigh-Ritz method [7]. Varying certain parameters, the main of which was the sought axial load, this algorithm matched estimated sets of frequencies with those determined from experiments.…”

“…This approach combines in situ dynamic tests and computations that make use of a beam model with complex boundary conditions. The method was tested and improved throughout some years since it was applied for multiple case studies of monitoring such famous Italian historic buildings as Duomo di Parma (Cathedral of Parma), Basilica della Madonna dell'Umiltà in Pistoia (Church of Our Lady of Humility), Rocca Sanvitale di Fontanellato (Sanvitale Fortress of Fontanellato), and Casa Romei (Romeì House) in Ferrara, as reported by the authors Collini et al in [1][2][3][4][5][6][7].…”

Seismic response of the outer shell of a liquefied natural gas storage tank using a semi-analytical dynamic substructuring technique

“…The linear dynamic response of the complete system is derived in the frequency domain using a semi-analytical approach which is based on the dynamic substructuring technique. The dynamic substructuring technique, together with the Rayleigh-Ritz method, has been previously introduced by Amabili (1997), Amabili et al (1998) and Amabili and Garziera (1999) for the solution of similar problems. In contrast to other methods, the concept of frequency-and wavenumber-dependent dynamic spring stiffness is introduced here for the exact satisfaction of the displacement continuity and the force equilibrium at the interfaces between the different subsystems.…”