Keywords: smart beams, cross–ply beams, beam theory, free vibration, exact solutions, state–space approach, arbitrary boundary conditions, automotive structures, modelling, vehicle vibration, piezoelectric actuators, shear deformation
Modal characteristics of cross–ply laminated smart beams using various beam theories
Analytical models and solutions are obtained for the free vibration of cross–ply laminated beams with extension piezoelectric actuators. The piezoelectric actuators are bonded along the beam surface. The models are based on the higher–order shear deformation beam theory (HOBT), first–order shear deformation beam theory (FOBT) and the classical Euler–Bernoulli beam theory (CBT). The equations of motion and associated boundary conditions are derived for the beam models using Hamilton's principle. The state–space approach is used to find accurate natural frequencies and mode shapes for arbitrary combinations of boundary conditions. The exact analytical solutions obtained are illustrated numerically in a number of figures and tables revealing the effects of the number of layers, the actuators' thickness, the length to thickness ratio and the character of boundary conditions on the non–dimensional frequencies. Finally comparison of frequencies obtained by CBT, FOBT and HOBT is made to assess the importance of shear deformation.