טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
Ph.D Thesis
Ph.D StudentBar on Benny
SubjectSurface Effects on Mechanical Properties of Heterogeneous
Nano Beams
DepartmentDepartment of Mechanical Engineering
Supervisor Professor Emeritus Eli Altus
Full Thesis textFull thesis text - English Version


Abstract

This work analyzes surface effects in nano scale beam-like elements. Both effects of surface residual stresses and surface modulus are accounted. A mechanical model for heterogeneous nano-beam is first introduced. The model considers local effect of surface residual and modulus variations on the beam cross section, including a new geometrical parameter of an equivalent surface thickness. The nano-beam is described as a laminated structure including a “bulk layer” coated by two “surface layers”, dictates by an equivalent single layer kinematics. Effects of surface non-uniformities in nano-beams are exhibited by local surface force and moment, as well as variations in the axial and bending stiffness in the beam's cross sections. A validation of the continuum model is conducted via atomistic simulations. The simulations include an ensemble of atoms in FCC structure, interacting by a second neighbor Lennard-Jones pair potential. Two types of atoms are considered, for describing non-uniform surface configurations. The effective continuum mechanical and geometric properties of the bulk and surface layers are first extracted from a set of calibration simulations. Governing equations are than solved analytically for cantilever beam including surface non-uniformity and exhibit fine correspondence with results from the atomistic simulations. The validation of the continuum model can be generalized for any surface heterogeneity, by using the superposition principle. On the next stage, local effects of adsorption induced nano sensors are analyzed. Statistical local surface interactions are derived from the Langmuir interaction model and their corresponding stochastic surface stresses are introduced. Two types of nano-beam sensors are studied: cantilever beam with pure surface bending effect and clamped beam with mixed surface force and bending moment effects. Advantages of each type are discussed. The deflection statistics are found analytically and validated by Monte-Carlo simulations. An analytical relation between the adsorption/desorption rates and the maximum deflection variance is found. Finally, the effect of local non-uniformity in surface residual stresses on the resonance frequency of hinged beam is analyzed. By considering weak geometrical non-linearity, it is found that a local variation in the surface residual stresses cause a shift in the frequency response curve, corresponding to their location along the beam. The analytical results are validated by finite elements simulations. This effect can be used for design of novel small scale sensors.