The paper presents the response of a three-layered annular plate with damaged laminated facings to the loads acting in their planes. The presented problem concerns the analysis of the combination of global plate failure in the form of buckling with the local micro defects, like fibre or matrix cracks, located in the laminas. The plate structure consists of thin laminated, fibre-reinforced composite facings and a thicker foam core. The matrix and fibre cracks of facings laminas can be transversally symmetrically or asymmetrically located in plate structure. Critical static and dynamic stability analyses were carried out solving the problem numerically and analytically. The numerical results show the static and dynamic stability state of the composite plate with different combinations of damages. The final results are compared with those for undamaged structure of the plate and treated as quasi-isotropic ones. The analysed problem makes it possible to evaluate the use of the non-ideal composite plate structure in practical applications.

The paper presents dynamic responses of annular plate composed of three layers. The middle layer of the plate has electrorheological properties expressed by the Bingham body model. The plate is loaded in the plane of facings with time-dependent forces. The electrorheological effect is observed in the area of supercritical plate behaviour. The influence of both material properties and geometrical dimensions of the core on plate behaviour is examined. The problem is solved analytically and numerically using the orthogonalization method and the finite difference method. Comparison of the results obtained using the finite difference and the finite element methods for a plate in critical state is shown. The numerical calculations are carried out for axisymmetric and asymmetric plate modes. The presented diagrams show the plate reaction to the changes in values of plate parameters and indicate that the supercritical control of plate work is possible.

An attempt is made in the current research to obtain the fundamental buckling torque and the associated buckled shape of an annular plate. The plate is subjected to a torque on its outer edge. An isotropic homogeneous plate is considered. The governing equations of the plate in polar coordinates are established with the aid of the Mindlin plate theory. Deformations and stresses of the plate prior to buckling are determined using the axisymmetric flatness conditions. Small perturbations are then applied to construct the linearised stability equations which govern the onset of buckling. To solve the highly coupled equations in terms of displacements and rotations, periodic auxiliary functions and the generalised differential quadrature method are applied. The coupled linear algebraic equations are a set of homogeneous equations dealing with the buckling state of the plate subjected to a unique torque. Benchmark results are given in tabular presentations for combinations of free, simply-supported, and clamped types of boundary conditions. It is shown that the critical buckling torque and its associated shape highly depend upon the combination of boundary conditions, radius ratio, and the thickness ratio.

The paper presents the dynamic behaviour of three-layer annular plates with damaged facings. The plate is composed of thin laminated, fibre-reinforced composite facings and thicker, foam core. Failure of the plate facings is modelled as fibre or matrix cracks. The plate loaded in the plane of facings with quickly increasing radially compressed forces loses its dynamic stability. Evaluation of the critical state of the plate with failures was carried out using both analytical and numerical solutions. The comparison of results between plates with material properties treated as isotropic, quasi-isotropic and composite has been conducted. Presented tables and figures create the image of dynamic responses of examined composite plates with structure failures.

Three-layered, annular plate with viscoelastic core is subjected to loads acting in the plane of the plate facings. One formulates the dynamic, stability problem concerning the action of time-dependent compressive stress on a plate with imperfection. This problem has been solved. One created the basic system of differential equations in which the approximation finite difference method was used for calculations. The essential analysis of the problem was concentrated on evaluation of the influence of the plate imperfection rate and the rate of plate loading growth on the results of calculation of critical parameters at the moment of loss of plate stability. It determines the analysed problem of sensitivity of the plate to imperfection and loading. In the evaluation of the dynamics of this problem, the dynamic factor defined as the quotient of the critical, dynamic load to the static one was used. The idea of dynamic factor and the type of the accepted criterion of the loss of plate stability were taken from the Volmir's work. The observations were confirmed by comparable results of calculations of plate models built in finite element method using the ABAQUS system. The analysis of the stress state in an exemplary plate model calculated in FEM demonstrated the importance of the strength condition in total evaluation of the plate work. One achieved satisfactory correctness of results in both methods.