Novel local/nonlocal formulation of the stress-driven model through closed form solution for higher vibrations modes. (15th November 2020)

• Record Type: Journal Article
• Authors: Apuzzo, Andrea; Bartolomeo, Chiara; Luciano, Raimondo; Scorza, Daniela
• Is Part Of: Composite structures. Volume 252(2020)
• Publication Date: 2020-11-15
• Subjects: Closed form solution -- High frequency -- Local/nonlocal model -- Mixture parameter -- Vibration mode; Composite construction -- Periodicals; Composites -- Périodiques; 624.18
• DOI: 10.1016/j.compstruct.2020.112688
• Languages: English
• ISSNs: 0263-8223

Abstract

Highlights: New two-phases stress-based closed form solution for free vibrations is proposed. Local/nonlocal model is defined by a convex combination through mixture parameter. Normalised natural frequencies for four study cases are determined. Effectiveness is discussed through a comparison with literature results. Normalised frequency for higher vibrations modes is computed for each study case. Abstract: In the present work, an innovative two-phases local/nonlocal constitutive mixture model based on the stress-driven model for free vibrations problems is presented. The above two-phases model has been formulated by defining a convex combination of local/nonlocal phases through a mixture parameter and the closed form solution for free vibrations problems is given. The proposed local/nonlocal model has been applied to compute the natural frequencies of four nanobeams study cases. The results are presented in terms of normalised natural frequency as function of both nonlocal and mixture parameters. First, the influence of the two parameters is studied. The effectiveness of the present model is discussed by comparing the results with those obtained by applying the Gradient Elasticity theory. Finally, the normalised natural frequencies for the second, third and fourth modes of vibrations are presented and discussed for each study case.