Modeling vibration of infinite beams sensoring and actuated by piezoelectric elements

The structural health monitoring of large span or infinite structures such as pipe lines and rails is always an interesting topic for engineers in the industry fields. The vibration analysis of infinite beams sensoring and actuated by piezoelectric elements is set as the basic for these important scientific and technical problem. Introducing a spring-damp element to semi-infinite long beam and considering the boundary conditions at the beam end, the relations between the deformation velocities and driving internal forces are derived, then a 2 × 2 impedance matrix is obtained for representing the dynamic of a semi-infinite long elastic beam. The infinite smart beams supported by multiple piezoelectric stacks with certain distances are analyzed. They are modeled as combination of semi-infinite beam, piezoelectric stack and finite length beam, and their impedance equations and continuous conditions are formulated respectively, and one numerical computation procedure to solving the impedance matrix equations is presented finally. The infinite smart beams actuated by distributed dual piezoelectric bending actuators are also analyzed in this paper. This smart beam are modeled by combining semi-infinite beam, piezoelectric bending actuators and finite length beams, and numerical solutions for these similar problem are obtained as well. The semi-infinite and infinite beams with piezoelectric stacks and/or piezoelectric bending actuators are considered as numerical examples. The model of infinite beams proposed by Wang and Lai is adapted to modeling the above examples by FEM and the piezoelectric elements are also included in FE models. The comparison show that all results obtained by using the proposed approaches and by FEM are agreed each other very well. It is shown that the proposed models and approaches are efficient for vibration analysis of infinite beams sensoring and actuated by piezoelectric elements.