Size-dependent nonlinear secondary resonance of micro-/nano-beams made of nano-porous biomaterials including truncated cube cells

• Published in: Acta mechanica 2019-03, Vol.230 (3), p.1077-1103
• Main Authors: Sahmani, Saeid, Fotouhi, Mohamad, Aghdam, Mohammad Mohammadi
• Format: Article
• Language: English
• Subjects: Analysis; Beams (radiation); Bifurcations; Biological products; Biomedical materials; Cellular structure; Classical and Continuum Physics; Control; Deformation mechanisms; Differential equations; Dynamical Systems; Engineering; Engineering Fluid Dynamics; Engineering Thermodynamics; Equations of motion; Excitation; Frequency response; Galerkin method; Heat and Mass Transfer; Mechanical properties; Nonlinear response; Original Paper; Pore size; Porosity; Shear deformation; Solid Mechanics; Theoretical and Applied Mechanics; Tissue engineering; Vibration
• ISSN: 0001-5970; 1619-6937
• DOI: 10.1007/s00707-018-2334-9

Porous biomaterials have been utilized in cellular structures in order to mimic the function of bone as a branch of tissue engineering approach. With the aid of nano-porous biomaterials in which the pore size is at nanoscale, the capability of biological molecular isolation becomes more efficient. In the present study, first the mechanical properties of nano-porous biomaterials are estimated on the basis of a truncated cube cell model including a refined hyperbolic shear deformation for the associated lattice structure. After that, based upon a nonlocal strain gradient beam model, the size-dependent nonlinear secondary resonance of micro-/nano-beams made of the nano-porous biomaterial is predicted corresponding to both subharmonic and superharmonic excitations. The nonclassical governing differential equation of motion is constructed via Hamilton’s principle. By employing the Galerkin technique together with the multiple-timescale method, the nonlocal strain gradient frequency response and amplitude response of the nonlinear oscillation of micro-/nano-beams made of a nano-porous biomaterial under hard excitation are achieved. It is shown that in the superharmonic case, increasing the pore size leads to an enhancement of the nonlinear hardening spring-type behavior of the jump phenomenon and the height of limit point bifurcations. In the subharmonic case, higher pore size causes an increase in the gap between two branches associated with the high-frequency and low-frequency solutions.