In this study we present the interactions of the fundamental frequencies of a nanomanufacturing coupled system by exploring the natural frequencies of the subsystems. These nanomanufacturing subsystems function in concert, e.g., a cantilever beam with spring-mass. The individual subsystems are studied under free vibration to generate the natural and buckling frequencies. These subsystems, when under free vibration, generate unique local natural frequencies that interact to form a unique global natural frequency. This allows for greater control and improved sensitivity for scanning and shaping nano surfaces, by allowing selective variation of the local frequency of one system to influence the global system frequencies. In this investigation, a nanobeam with arbitrary boundary conditions is used to model the system and the effects on the parameters of interest are studied. Euler–Bernoulli theory is applied in conjunction with Eringen’s theory of nonlocal continuum theory to model the small-scale effects due to the size of the beam under consideration. The coupled equations are solved using separation of variables for the local and global frequencies. The nanobeam is restrained with an adjustable torsional spring and pin at one end. The boundary condition at the free end is a spring-mass system with axial load. Altering the torsional, transverse spring stiffness and mass increases or decreases the natural frequencies. The motions of the beam and the tip-mass generates a frequency response during contact interactions. The tip response frequency is used to determine the maximum displacements (penetration depth) and accelerations (contact forces) in a sample during nanomanufacturing.

In this study we investigate the motion of a torsionally restrained beam used in tapping mode atomic force microscopy (TM-AFM), with the aim of manufacturing at nano-scale. TM-AFM oscillates at high frequency in order to remove material or shape nano structures. Euler-Bernoulli theory and Eringen’s theory of non-local continuum are used to model the nano machining structure composed of two single degree of freedom systems. Eringen’s theory is effective at nano-scale and takes into account small-scale effects. This theory has been shown to yield reliable results when compared to modelling using molecular dynamics.The system is modelled as a beam with a torsional boundary condition at one end; and at the free end is a transverse linear spring attached to the tip. The other end of the spring is attached to a mass, resulting in a single degree of freedom spring-mass system. The motion of the tip of the beam and tip mass can be investigated to observe the tip frequency response, displacement and contact force. The beam and spring–mass frequencies contain information about the maximum displacement amplitude and therefore the sample penetration depth and this allows

No abstract

The fundamental frequencies of an elastically restrained nanobeam with a tip mass are studied based on the nonlocal Euler-Bernoulli beam theory. The nanobeam has a torsional spring at one end and a translational spring at the other end where a tip mass is attached. The aim is to model a tapping mode atomic force microscope (TM-AFM), which can be utilized in imaging and the manufacture of Nano-scale structures. A TM-AFM uses high frequency oscillations to remove material, shape structures or scan the topology of a Nano-scale structure. The nonlocal theory is effective at modelling Nano-scale structures, as it takes small scale effects into account. Torsional elastic restraints can model clamped and pinned boundary conditions, as their stiffness values change between zero and infinity. The effects of the stiffness of the elastic restraints, tip mass and the small-scale parameter on the fundamental frequency are investigated numerically.