Therefore, the approximate solutions were obtained using the superposition method suggested for. The exact solutions satisfying both equations of motion and boundary conditions are not available. The coupled vibration was analyzed for a piezoelectric array element of two-dimensional structure whose vibration can be described by two coupled differential equations with coupled boundary conditions.
#Logo smartz crack cracked
It is found that the dynamic analysis of cracked beam based on impedance elements yields an efficient expression for the vibration of the cracked smart beam. The obtained resonant frequencies of cracked beam agree with the results of other methods and known experiment results.
In the numerical examples, the dynamic analysis of smart beam containing single-edge and double-edge open crack is given to illustrate the application of this modeling method by assembling the two different impedance elements. Considering the continuum conditions between impedance elements, the continuum conditions at the location of cracks represented by massless spring and mechanical boundary conditions, the relation between the input electric admittance of piezoelectric patches and the crack parameters is built by solving these elements' linear impedance equations, also the electromechanical dynamic characteristic of cracked smart beam is obtained conveniently. The beams were divided into finite impedance elements, consisting of two typical impedance elements, impedance elements of bi-piezoelectric crystals and impedance ones of elastic beams expressed by 4 × 4 and 5 × 5 impedance matrix respectively. The smart beams, with cracks driven by a pair of distributed bi-piezoelectric actuators, were analyzed dynamically.
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