Interaction of the fundamental frequencies of a torsional cantilever nanobeam and spring mass system single degree of freedom (SDOF) under axial load, including buckling

Abstract

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.

Amplitude resonance response and feedback control of cantilever beams with tip-mass under aerodynamic load

“…Many studies have been carried out on cantilever beams with tuned mass in order to study the influence of tip mass on the dynamics (Payam and Fathipour 2015), invest the energy harvesting (Homayouni-Amlashi et al 1919, Izadgoshasb et al 2018, Ahn et al 2018, Abdollahzadeh 2019 of the system or the influence of the parameters (Payam and Fathipour 2015, Pratiher and Dwivedy 2011, Labdzki et al 2018, Kim et al 2012, Meesala and Hajj 2019a, Warminski et al 1919 of the system on its natural frequency (Mahmoud 2019, Li et al 2013, Payam and Fathipour 2013 and control (Moutlana and Adali 2015, Belhaq and Fahsi 2009, Moutlana and (2-4 December), 2013, Pratiher 2012). Among them, in 2012, Kim et al (2012) study the behaviour of a nonlinear cantilever beam with tuned mass and subjected to an axial force and an electrostatic excitation.…”

“…It is therefore necessary to use technical control. So in 2012, Pratiher (2012) has examined the vibration control of a transversely excited cantilever beam with tip mass, he shows that the feedback control law can successfully be used to effectively suppress the vibrations and bifurcation control, Moutlana and Adali (2015) in 2015 has investigated the piezoelectric control of the (AFM) cantilever beam. among the existing technical control, the time-delay feedback is one of the mostly resent and unavoidable technical which were used by many authors and Liu et al (2019), they found that, an optimal choice of control parameter can consequently reduce vibrations.…”