Closed form solution of nonlinear oscillation of a cantilever beam using λ-symmetry linearization criteria.

A mechanical system, in general, undergoes vibrational motion when the system is subjected to a tension or an external force. One of the examples of such a system is a cantilever beam when it is exposed to a bending action. When the tension is released, the cantilever beam suffers from the oscillations until the strain energy is totally released through the damping characteristics of the cantilever beam. Depending on the stiffness and damping factors of the beam, the vibrational motion can be non-linear; in which case, the analytical solution becomes challenging formulating the flexural characteristics of the beam. Although numerical solution for the non-linear problem is possible, the analytical solution provides useful information between the mechanical response and the cantilever beam characteristics. In the present study, the analytical solution of the non-linear equations governing the motion of the cantilever beam is presented. The governing equation is linearized incorporating the Lie-Tresse linearization method. The closed form solution for the displacement of the cantilever beam is reduced to a linear solution after introducing the appropriate beam characteristics. The dynamic behavior of the flexural motion due to non-linear and linear cantilever beams are compared.

Environmental Dust Particles Repelling from A Hydrophobic Surface under Electrostatic Influence.

Environmental dust particles repelling from a hydrophobic surface under the electrostatic influence are considered and the dynamics of the dust particles are analyzed incorporating the high speed camera. The velocity of the repelled dust particles are formulated using the force balance incorporating the forces associated with the electrostatic repulsion, particle adhesion, particle drag, and the inflight particles interaction under the charge influence. The functionalized silica particles are deposited on the glass surface towards achieving a hydrophobic wetting state on the surface. An electronic circuitry is designed and built while generating the electrostatic effect, in the pulse form, on the dust particles located on the surface of the hydrophobic plate. Findings revealed that functionalized silica particles deposited surface results in hydrophobic wetting state with contact angle in the order of 158° ± 2° and contact angle hysteresis of 2° ± 1°. The electrostatic impulsive force generated on the plate surface enables to repel most of the sizes of the dust particles; however, some of the small dust particles remain as the residues on the surface after the electrostatic influence. The dust particle velocity predicted from the analytical formulation agrees with that obtained from the high speed camera data. The pinning force of the small size particles (0.6 µm≤), due to adhesion on the surface, is found to be larger than the average size particles (∼1.2 µm), which in turn, suppresses these particles repelling from the surface under the electrostatic influence. The residues of the dust particles on the as received glass surface after dust repelling are more than those residues on the hydrophobic surface. This behavior is associated with the dust particles adhesion on the surface. Consequently, hydrophobic wetting state on the plate surface improves the dust particle repelling from the surface.

Laser processing of Ti6Al4V alloy: wetting state of surface and environmental dust effects.

Laser processing of Ti6Al4V alloy surface, via repetitive pulses, is realized incorporating the nitrogen assisting gas. The texture characteristics of the surface and wetting state are analyzed. The free energy of the laser treated surface is estimated. The influence of the dust particles on the treated and untreated surfaces is examined. The solution formed due to water condensate on the dust particles is evaluated. The adhesion of the mud dried solution on the treated and untreated surfaces is assessed through determining the tangential force required for the removal of the solution from the surface. The findings demonstrate that the high power laser repetitive pulse heating results in formation of the hieratically distributed micro/nano pillars on the workpiece surface. The wetting state of the processed surface remains hydrophilic because of the large gap size between the micro/nano pillars. The free energy of the laser textured surface is similar to that obtained for the TiN coated surfaces, which is because of the nitride compounds developed during the processing. The dried liquid solution strongly adheres at the surface and the force needed for removing the dried liquid solution is almost four times of the friction force at the surface. The liquid solution gives rise to locally scattered shallow pit sites on as received surface. This phenomenon does not occur for the laser treated surface, which is related to the passive layer developed on the surface.

Chemo-Mechanical Characteristics of Mud Formed from Environmental Dust Particles in Humid Ambient Air.

Mud formed from environmental dust particles in humid ambient air significantly influences the performance of solar harvesting devices. This study examines the characterization of environmental dust particles and the chemo-mechanics of dry mud formed from dust particles. Analytical tools, including scanning electron microscopy, atomic force microscopy, energy dispersive spectroscopy, particle sizing, and X-ray diffraction, are used to characterize dry mud and dust particles. A micro/nano tribometer is used to measure the tangential force and friction coefficient while tensile tests are carried out to assess the binding forces of dry mud pellets. After dry mud is removed, mud residuals on the glass surface are examined and the optical transmittance of the glass is measured. Dust particles include alkaline compounds, which dissolve in water condensate and form a mud solution with high pH (pH = 7.5). The mud solution forms a thin liquid film at the interface of dust particles and surface. Crystals form as the mud solution dries, thus, increasing the adhesion work required to remove dry mud from the surface. Optical transmittance of the glass is reduced after dry mud is removed due to the dry mud residue on the surface.