Adhesively bonded joints have been investigated for several decades. In most analytical studies, the Bernoulli-Euler beam theory is employed to describe the behaviour of adherends. In the current work, three analytical models are developed for adhesively bonded joints using the Timoshenko beam theory for elastic material and a Bernoulli-Euler beam model for viscoelastic materials. One model is for the peeling test of an adhesively bonded joint, which is described using a Timoshenko beam on an elastic foundation. The adherend is considered as a Timoshenko beam, while the adhesive is taken to be a linearly elastic foundation. Three cases are considered: (1) only the normal stress is acting (mode I); (2) only the transverse shear stress is present (mode II); and (3) the normal and shear stresses co-exist (mode III) in the adhesive. The governing equations are derived in terms of the displacement and rotational angle of the adherend in each case. Analytical solutions are obtained for the displacements, rotational angle, and stresses. Numerical results are presented to show the trends of the displacements and rotational angle changing with geometrical and loading conditions. In the second model, the peeling test of an adhesively bonded joint is represented using a viscoelastic Bernoulli-Euler beam on an elastic foundation. The adherend is considered as a viscoelastic Bernoulli-Euler beam, while the adhesive is taken to be a linearly elastic foundation. Two cases under different stress history are considered: (1) only the normal stress is acting (mode I); and (2) only the transverse shear stress is present (mode II). The governing equations are derived in terms of the displacements. Analytical solutions are obtained for the displacements. The numerical results show that the deflection increases as time and temperature increase. The third model is developed using a symmetric composite adhesively bonded joint. The constitutive and kinematic relations of the adherends are derived based on the Timoshenko beam theory, and the governing equations are obtained for the normal and shear stresses in the adhesive layer. The numerical results are presented to reveal the normal and shear stresses in the adhesive.

A control metric, the weighted sum of spatial gradients (WSSG), has been developed for use in active structural acoustic control (ASAC). Previous development of WSSG [1] showed that it was an effective control metric on simply supported plates, while being simpler to measure than other control metrics, such as volume velocity. The purpose of the current work is to demonstrate that the previous research can be generalized to plates with a wider variety of boundary conditions and on less ideal plates. Two classes of plates have been considered: clamped flat plates, and ribbed plates. On clamped flat plates an analytical model has been developed for use in WSSG that assumes the mode shapes are the product of clamped-clamped beam mode shapes. The boundary condition specific weights for use in WSSG have been derived from this formulation and provide a relatively uniform measurement field, as in the case of the simply supported plate. Using this control metric, control of radiated sound power has been simulated. The results show that WSSG provides comparable control to volume velocity on the clamped plate. Results also show, through random placement of the sensors on the plate, that similar control can be achieved regardless of sensor location. This demonstrates that WSSG is an effective control metric on a variety of boundary conditions. Ribbed plates were considered because of their wide use in aircraft and ships. In this case, a finite-element model of the plate has been used to obtain the displacement field on the plate under a variety of boundary conditions. Due to the discretized model involved, a numerical, as opposed to analytical, formulation for WSSG has been developed. Simulations using this model show that ASAC can be performed effectively on ribbed plates. In particular WSSG was found to perform comparable to or better than volume velocity on all boundary conditions examined. The sensor insensitivity property was found to hold within each section (divided by the ribs) of the plate, a slightly modified form of the flat plate insensitivity property where the plates have been shown to be relatively insensitive to sensor location over the entire surface of the plate. Improved control at natural frequencies can be achieved by applying a second control force. This confirms that ASAC is a viable option for the control of radiated sound power on non-ideal physical systems similar to ribbed plates.