Modification of dynamic characteristics of FGM plates with integrated piezoelectric layers using first- and second-order approximations. (English) Zbl 1194.74106
Summary: This paper proposes a method for calculating the required changes in the physical properties of plates made of functionally graded materials (FGM) in order to achieve the desired eigenfrequency shifts in the structure. A finite element formulation based on the classical laminated plate theory (CLPT) is presented for an FGM plate with integrated piezoelectric layers. Using this formulation, an efficient method based on the first-order and second-order approximations in Taylor expansion is expressed to calculate the corresponding changes in the plate modal properties due to changes in parameters which characterize the structure’s dynamic behaviour. An initial sensitivity analysis is carried out to identify the regions within the structure where modifications are most effective on the structure’s dynamic characteristics. The proposed algorithm is applied to a case study with two different boundary conditions and the results are validated against exact solutions. The influence of structural modifications on dynamic response of the plate is also studied using the Newmark-\(\beta\) method.
MSC:
| 74H15 | Numerical approximation of solutions of dynamical problems in solid mechanics |
| 74H45 | Vibrations in dynamical problems in solid mechanics |
| 74K20 | Plates |
| 74F15 | Electromagnetic effects in solid mechanics |
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