Free Vibration Of Isotropic Plates Research Articles

Free vibration of isotropic plates with various cutout configurations using finite elements and design of experiments

This work represents a finite element analysis of free vibration of isotropic plates with different cutout shapes, areas, locations and aspect ratios. Modal analysis was carried out using the ANSYS APDL software to evaluate the fundamental frequencies. ANSYS model was validated in the first stage and showed good agreement with the selected literature works. Furthermore, the selected cutout parameters were investigated to assess which parameter is more effective on the frequency. It is found that these parameters was overlapping, therefore Design of Experiments was conducted. Results revealed that the aspect ratio of the cutouts is the most significant factor on the fundamental frequency.

Non-linear free vibration of isotropic plates with internal resonance

The geometrically non-linear free vibration of thin isotropic plates is investigated using the hierarchical finite element method (HFEM). Von Kármán's non-linear strain–displacement relationships are employed and the middle plane in-plane displacements are included in the model. The equations of motion are developed by applying the principle of virtual work and the harmonic balance method (HBM), and the solutions are determined using a continuation method. The convergence properties of the HFEM and of the HBM are analyzed. Internal resonances are discovered. The variation of the plate's mode shape with the amplitude of vibration and during the period of vibration is demonstrated.

Influences of large amplitudes, transverse shear deformation and rotatory inertia on free lateral vibrations of transversely isotropic plates—A new approach

In this paper, using an improved Reissner's variational theorem [E. Reissner, J. math. Phys., 90–95 (1950)] along with Banerjee's hypothesis, [B. Banerjee and S. Dutta, Int. J. Non-Linear Mech. 16, 47–52 (1981)] a new set of governing equations which include the effects of transverse shear deformation and rotatory inertia is derived for the large amplitude free vibrations of isotropic plates. The case of a simply supported square plate has been discussed in detail. Numerical results have been computed showing the effect of the transverse shear deformation and compared with other known results.