Experimental Investigation of the Differential Combination Resonance

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Summed and differential combination resonances, caused in cantilevered columns subjected to a pulsating Reut force, are experimentally investigated. Reut force is realized by impinging an air jet from the nozzle onto the attachment-plate mounted to the column at the free end. Pulsation of the air jet is carried out by means of an electromagnetic valve which is on-off-controlled by the signal from a function generator. The realized wave form is not a complete sinusoidal form. However, the periodicity of force is realized. The test column is a slender plastic plate of length 1000mm, depth 10mm and thickness 2mm. The attachment-plate is made of balsa. To change the direction of the line of action of an applied force, the attachment was covered with materials such as unwoven material for the roughest surface or a glass plate for the smoothest surface. It was confirmed that the direction coefficient was 0.006 for the case of nylon unwoven material and 0.90 for the case of glass plate. The vanishingly small direction coefficient resulted in differential combination resonances between the first and second mode. Summed combination resonance between the first and second modes was observed for the direction coefficient of 0.9. To confirm the type of resonances, experimental responses of the columns in each region were resolved into the first and second modes, using high-pass and low-pass filters with the cutting frequency 2.0Hz. Theoretical predictions of boundaries of parametric resonances are compared with the experimental results. The theory is supported qualitatively by the experiment.