Modal characteristics and passive vibration control of swept cantilevered beam-plates

This work is on the free vibration of swept (skewed, trapezoidal and tapered) cantilevered beam-plates and an investigation on the use of modal patterns for the design of viscoelastic damping treatments of the beam-plates. The generic name beam-plate is used to define beam-like and plate-like structures. The natural vibrations of swept cantilevered beam-plates play an important role in various structural applications such as aircraft wings and rocket fins. The natural frequencies and mode shapes of aluminium beam-plates of aspect ratios ranging from 1 to 10 with several leading and trailing edge sweep angles were predicted using the ABAQUS FE programme. To classify complex mode shapes, a new nodal pattern matching technique was established in which mode shapes with similar nodal pattern features were put into the same modal families that were identify by the number of nodal lines ('i') of the mode shapes along the lengthwise direction of the uniform beam-plate design. Then modal families were classified into modal groups which were identified by the number of nodal lines ('j') of the mode shapes along the breadthwise direction of the uniform beam-plate design, namely: predominantly bending (j =0), predominantly torsional (j=1), composite (j=2, 3...) and in-plane bending (n =1) modal groups. The modal assurance criterion (MAC) was used to validate the visual nodal pattern matching technique. The modal data was used to produce frequency parameter graphs which showed the variations of the dimensionless natural frequencies against aspect ratios and swept angles of the beam-plates. Then the data from these graphs were combined together to produce graphs which are referred to as frequency parameter charts. Experimental modal testing and analysis were performed on swept cantilevered beam-plates with aspect ratios 2, 4, 4.85 and 6 to validate the natural frequencies and mode shapes. The use of the frequency charts to identify mode types from measured FRF was illustrated. Thus, the charts facilitate the identification of mode types and prevent the need to perform a full experimental modal testing and analysis. Another major application of the mode shapes was to design constrained viscoelastic layer damping (CLD) treatments of beam-plates. CLD patches were cut according to the nodal patterns and used to suppress the vibrations of the beam-plates. It is shown that to control the first bending mode, CLD patch should be placed at the fixed end of the beam-plate which covers a passive nodal line. To control the second bending mode the CLD patch should be placed in the middle of the beam-plate and the later bending modes are best controlled if the patch is placed towards the free end of the beam-plate. It was concluded that to obtain higher damping then the size of the damping patch should be just big enough to cover all the active nodal lines in a deformed beam-plate.