Keywords: FGM, piezoelectric, natural frequency, eigenvector, sensitivity analysis, feedback gain.

Dynamic behavior modification of a system may be defined as finding the necessary changes in physical or geometrical properties of a structure in order to achieve predefined shifts in natural frequencies of the structure. This is conventionally done using an ad hoc approach wherein the natural frequencies are iteratively calculated for different values of design variables until the result converges to the desired value. To avoid this time consuming iterative method, the optimisation problem can be formulated as an inverse eigenvalue problem.

Recent research proposed efficient and accurate methods for performing the inverse eigenvalue problem in conjunction with finite element (FE) analysis for beam elements [1], two dimensional elements [2], smart trusses [3] and functionally graded materials (FGM) plates with passive piezoelectric layers [4,5]. The main challenge in dynamic behavior modification of a structure is reducing the computational cost when changing the physical or geometrical characteristics of the structure. Additionally, when attempts are made to actively controll the structure's dynamic behaviour, such changes have to take effect in very short intervals of time.

This study deals with solving the inverse eigenvalue problem for an FGM plate which is actively controlled by piezoelectric sensor-actuator (S-A) pairs. In each patch attached to the plate, the input signal to the actuator is a linear function of the generated electric potential in its corresponding sensor. The dynamic characteristics of this structure can be modified by changing the controller gains in piezoelectric patches that can be performed instantaneously. In addition to the effect of controller gains, the effect of simultaneous change of the piezoelectric layer thickness and the controller gain in each patch on natural frequencies of the plate is also studied.

Sensitivity analysis on the natural frequencies is performed in a case study in order to find the most effective S-A pair and both the direct and inverse eigenvalue problems are studied. Finally, the appropriate sequence for the controller gains in order to achieve predefined changes in natural frequencies is calculated.

1

Djoudi, M.S., Bahai, H., "An inverse eigenvalue formulation for optimisaing the dynamic behaviour of pin-jointed structures", Journal of Sounds and Vibration, 253 (5):1039-50, 2002. doi:10.1006/jsvi.2001.4068

2

Aryana, F., Bahai, H., "Sensitivity analysis and modification of structural dynamic characteristics using second order approximation", Journal of Engineering Structures, 25, 1279-1287, 2003. doi:10.1016/S0141-0296(03)00078-6

3

Aryana, F., Mirzaeifar, R., "Vibration behavior modification of piezoelectric truss using finite element method", Proceedings of 13th annual (International) Mechanical Engineering Conference, Isfahan, 2005.

4

Aryana, F., Bahai, H., Mirzaeifar, R., Yeilaghi, A., "Modification of dynamic characteristics of FGM plates with integrated piezoelectric layers using first and second order approximations", International Journal for Numerical Methods in Engineering, In Press, 2006. doi:10.1002/nme.1927

5

Yeilaghi, A., Mirzaeifar, R., Ohadi, A.R., Eslami, M.R., "Vibration control of FGM plate with piezoelectric sensors and actuators using higher order shear deformation theory", Proceedings of the 8th Biennial ASME Conference on Engineering Systems Design and Analysis, Torino, Italy. Paper ESDA2006-95710, 2006.

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