In this paper, we consider the problem of the free longitudinal vibrations of a beam made of a bimodular material, i.e. an elastic material whose in-tension Young's modulus is a fraction of that under compression. After recalling the exact solutions for an infinite beam and for a beam with fixed ends calculated via the characteristics method, we apply high-resolution methods based on the finite-element approach to solve the nonlinear equation of the motion. In particular, we compare the exact solutions with the numerical solutions calculated using the collocation and least-squares method developed in the present study, the space-time element method, as well as total variation diminishing (TVD) and Newmark methods.
Free longitudinal vibrations of bimodular beams: a comparative study
Cristina Padovani;Andrea Pagni;Giuseppe Pasquinelli;
2011
Abstract
In this paper, we consider the problem of the free longitudinal vibrations of a beam made of a bimodular material, i.e. an elastic material whose in-tension Young's modulus is a fraction of that under compression. After recalling the exact solutions for an infinite beam and for a beam with fixed ends calculated via the characteristics method, we apply high-resolution methods based on the finite-element approach to solve the nonlinear equation of the motion. In particular, we compare the exact solutions with the numerical solutions calculated using the collocation and least-squares method developed in the present study, the space-time element method, as well as total variation diminishing (TVD) and Newmark methods.File | Dimensione | Formato | |
---|---|---|---|
prod_199538-doc_43736.pdf
solo utenti autorizzati
Descrizione: Paper
Tipologia:
Versione Editoriale (PDF)
Dimensione
1.25 MB
Formato
Adobe PDF
|
1.25 MB | Adobe PDF | Visualizza/Apri Richiedi una copia |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.