Modelling the vibrations of multi-span beams and plates through adaptive global piecewise-smooth functions (A-GPSFS)

Multi-span beams and plates which are freely vibrating are analysed through suitable adaptive sets of global piecewise-smooth functions (or A-GPSFs). Such approximating functions were introduced in Messina (Int J Mech Sci 90:179-189, 2015) as an extension of an original work published in Messina (J Sound Vib 256(1):103-129, 2002), where GPSFs were in turn used in order to model physical quantities through the thickness of structural elements. Herein these functions are used on the middle plane of the structural elements to model free vibrations of thin multi-span beams and plates, thus showing the capability of the same functions to include previous classical formulations in several circumstances of engineering interest. Depending on the internal constraints in beams and plates, the A-GPSFs could require further supplementary conditions. As such functional sets are not immediately available, explicit subroutines are illustrated. The efficiency and capability of the proposed models result from the comparison between calculated eigen-parameters and those of other models presented in open literature.