ON FREE VIBRATION ANALYSIS OF NON-LINEAR PIEZOELECTRIC CIRCULAR SHALLOW SPHERICAL SHELLS BY THE DIFFERENTIAL QUADRATURE ELEMENT METHOD

摘要

Piezoelectric materials are widely used as sensors and actuators in smart materials and structures due to their fast responses and some other advantages. As an actuator, it can be used to control structural shapes or to suppress undesired vibrations in certain degrees for some flexible lightweight structural elements or structures. In such cases, geometrical non-linearity should be considered in the theoretical formulations. Recently, the axisymmetric free vibration analysis were performed by using the semi-analytical and semi-numerical method for simply supported non-linear piezoelectric circular plates [1] and simply supported circular shallow spherical shells [2]. Since analytical solutions can only be obtained for some simple cases, numerical methods should be adopted to obtain responses of smart structural elements or smart structures under various loading conditions.