Research On Dynamic Problems Of Intelligent Material Based On State Space Method

With the rapid development of science and technology, the material properties gradually transform the traditional function of carrying capacity into the multi-functional and intelligent directions. Piezoelectric intelligent materials show a application prospect in various fields. In civil engineering, piezoelectric materials play a vital role in structural monitoring, control, intelligent adjustment and other aspects. Laminated components formed by piezoelectric smart materials are the most common structure in a variety of structure. And the researches on the mechanical properties especially the studies on dynamic problems are also highly significant for designers.The present research mainly focuses on the dynamic problems of general elastic material single beams, general elastic material laminated beams, piezoelectric single beams and piezoelectric laminated beams. In case of neglecting physical strength, volume charge and volume current, with the help of the state space methods, the present research have deduced the state variable equations of piezoelectric materials based on the fundamental equations of elasticity and constitutive equations of piezoelectric materials. Combined with the boundary conditions, the exact solution of the free vibration frequency of state space have been obtained. And the exact solution of the simple support piezoelectric laminated beam has been further derived. This method is especially suitable for laminated beams, and it is not limited by thickness. Moreover, it can be widely used in solving the laminated component. This solution is simple, accurate and it is easy to apply.In the last part of the thesis, the elastic single beams, the elastic laminated beams, piezoelectric single beams and piezoelectric laminated beams in different span depth ratio have been calculated accurately by using the Matlab software. Acording to the results from the Matlab, the research has obtained the simulative results among the mechanical dynam, the mechanical physical quantity and electrical physical quantity. Additionally, the simulative results are compared to that of the ANSYS,Base on the contrastive results, it can be seen that the calculating results of two methods for different materials are very similar no matter the single beams or the laminated beams. Taking fully into account the different height to span ratio, the errors of the calculation results by method of the present research and that of the FEM simulation results are both in the allowable range. Therefore, based on state space theory, the calculation results of the present research of intelligent structure method are accurate both in the different materials single beams and the laminated beams. What’s more, this method is more appropriate for the laminated structure and computer programming.