248 T. Mace et al. Fig. 25.1 Novel setup, utilizing (a) contacting surface for the excitation and (b) tip masses to enforce a quasi-pinned boundary condition the nonlinearity in the system can lead to an interaction with the shaker, thereby altering the observed damping behaviour. This study proposes an improved damping extraction technique, with the goal of measuring small levels of damping whilst minimizing the damping introduced from extraneous sources. 25.2 A Novel Method to Extract Damping The specimen support technique adopted for this study was originally proposed by Bishop et al. [4], and involves the attachment of a mass at both ends of a beam-like specimen. This alters the modeshape of the specimen in the ‘free–free’ configuration, moving the nodes of every mode towards the tips of the specimen. This improves the predictability of the node location, allowing the suspension of the specimen from locations where the damping contribution from the string suspension can be minimized. An analytical beam model was developed to determine the minimum tip-mass to beam-mass ratio, ‘mr’, considering an Euler-Bernoulli beam with both one-dimensional lumped masses and inertias at both ends. This revealed that a mr of 10was required in order to enforce an approximate ‘quasi-pinned’ condition. The specimen used in this study was an aluminium plate (764 mm×58mm×1 mm) requiring tip masses of 1.22 kg at either end. The location of the clamp at the nodal line of the system, the coupled rotation with the beam mode shape, and large bolt torques at the clamps thereby ensured minimal impact of the added frictional interface. In order to enable a single harmonic, free decay measurement from initial large amplitudes, a new excitation approach was needed that allowed large amplitude levels via a rigid connection, but also enabled free decay for the damping extraction. The final system, that represents a significant improvement over the one presented in [2] consisted of an electromagnetic shaker, but, in lieu of a permanent connection via a stinger, the specimen was connected to the shaker via a c-shaped bracket and vertical rod, which maintained contact with the beam (Fig. 25.1). A small rubber wedge was attached to localize the contact point and reduce chatter. A small preload was introduced between the shaker and the beam to ensure adequate contact. Due to the shaker attachment, only a half-sine forcing function could be introduced to the system, but the resonance excitation frequency ensured that force and response stayed accurately aligned. Once the desired displacement amplitude was reached, decoupling of the exciter and specimen was achieved by introducing a voltage offset into the shaker’s input signal, resulting in a displacement offset of the drive rod that was larger than the initial preloading displacement. Timing of the detachment was thereby crucial in order to ensure a gentle release of the system without introducing an appreciable transient. In a first instant, time domain data was captured with an accelerometer due to its simplicity. Future measurements will use non-contact measurements to minimize the impact of the accelerometer cabling on the damping. The damping of the system was then subsequently be extracted at different response levels using the logarithmic decrement method. 25.3 Results An initial roving hammer test was conducted using 22 points across the length of the beam in order to validate the modeshape prediction of the analytical model and to experimentally obtain the resonant frequencies. Figure 25.2 indicates the excellent correlation between the predicted and experimentally obtained modeshapes, verifying the functionality of the analytical
RkJQdWJsaXNoZXIy MTMzNzEzMQ==