• Structural Engineering and Mechanics
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• v.7 no.5
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• pp.503-512
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• 1999

Practicing a hole or an orifice through a plate or a slab constitutes a very frequent engineering situation due to operational reasons imposed on the structural system. From a designer's viewpoint it is important to know the effect of this modification of the mechanical system upon its elastodynamic characteristics. The present study deals with the determination of the lower natural frequencies of the structural element described in the title of the paper using a variational approach and expressing the displacement amplitude of the plate in terms of the double Fourier series which constitutes the classical, exact solution when the structure is simply supported at its four edges.

• Steel and Composite Structures
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• v.45 no.5
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• pp.621-640
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• 2022

In the present article, the vibration response of a geometrically imperfect bi-directional functionally graded plate (2D-FGP) with geometric discontinuities and micro-structural defects (porosities) has been investigated. A porosity model has been developed to incorporate the effective material properties of the bi-directional FGP which varies in two directions i.e. along the axial and transverse direction. The geometric discontinuity is also introduced in the plate in the form of a circular cut-out at the center of the plate. The structural kinematic formulation is based on the non-polynomial trigonometric higher-order shear deformation theory (HSDT). Finite element formulation is done using C° continuous Lagrangian quadrilateral four-noded element with seven degrees of freedom per node. The equations of motion have been derived using a variational approach. Convergence and validation studies have been documented to confirm the accuracy and efficiency of the present formulation. A detailed investigation study has been done to evaluate the influence of the circular cut-out, geometric imperfection, porosity inclusions, partial supports, volume fraction indexes (along with the thickness and length), and geometrical configurations on the vibration response of 2D-FGP. It is concluded that after a particular cut-out dimension, the vibration response of the 2D FGP exhibits non-monotonic behavior.