Analysis and numerical results for the free axisymmetric and non-axisymmetric vibrations of functionally graded annular plates elastically supported on the ring support have been presented on the basis of classical plate theory. The quasi-Green's function has been employed to solve to boundary value problem of free vibration of functionally graded annular plate with free outer edge and clamped, simply supported and free inner edges. Additional properties of the quasi-Green's function were presented and discussed for the functionally graded annular plate. The influence of volume fraction index, core radius, selected boundary conditions, position and stiffness of ring supports on natural frequencies of an annular plate has been comprehensively studied. Singularities as the core and support radii shrink to zero are calculated for different values of volume fraction index and stiffness of the support. The quasi-Green's function method allows us to obtain universal non-linear multiparametric characteristic equations functional dependent on radius of core, volume fraction index, position and stiffness of any amount of elastic supports or other discrete elements without necessity considering new boundary value problem or find scaling factors. Additionally, the continuity conditions between the supports and plate can be omitted in the obtained solutions of boundary value problem. The presented investigation has not been reported previously. The exact frequencies of vibration presented in non-dimensional form can serve as benchmark values for researchers and engineers to validate their numerical methods applied in many fields of engineering such us mechanical, aeronautical or production engineering.

Free vibration analysis of elastically supported functionally graded annular plates via quasi-Green's function method

Quasi-Green’s function approach to free vibration analysis of elastically supported functionally graded circular plates

Green's function for frequency analysis of thin annular plates with nonlinear variable thickness

The lateral-torsional buckling behavior of functionally graded (FG) non-local beams with a tapered I-section is here investigated using an innovative methodology. The material properties are supposed to vary continuously along the longitudinal direction according to a homogenization procedure, based on a power-law function, whereas the nanobeam is modeled within the framework of a Vlasov thin-walled beam theory. The flexural-torsional governing equations of the problem are derived based on the Eringen's nonlocal elasticity theory and the energy method. The system of lateral stability equations is, thus, reduced to a fourth-order differential equation in terms of the twist angle by uncoupling the equilibrium differential equations. The buckling loads are finally determined using the differential quadrature method (DQM), which is here applied as numerical tool to solve directly the differential equations of the problem in a strong form. A systematic investigation checks for the influence of some parameters such as the power-law index, tapering ratios, loading height parameter, boundary conditions and non-local parameter, on the lateral stability resistance of the tapered I-nanobeams. The numerical outcomes of this paper can be used as benchmarks for further studies on nanoscale tapered thin-walled beams.

Nonlocal elasticity theory for lateral stability analysis of tapered thin-walled nanobeams with axially varying materials

Free vibration analysis of discrete-continuous functionally graded circular plate via the Neumann series method

This paper deals with stability of circular plate with foundation and elastic edge against translation and rotation. Exact solution is utilized for development of governing equation for the problem under consideration. This paper reveals the subsistence of mode switching and it varies with foundation parameter. Fundamental buckling may not relate to axisymmetric as earlier implicated. The buckling load parameter rises monotonically with the foundation parameter. Percent of increase in load-carrying ability with foundation is calculated. A wide range of data is generated based on the dominance of rotational, translational, and foundation parameters on the stability of the system.

Buckling of circular plate with foundation and elastic edge

Study on JWL equation of state for the numerical simulation of near-field and far-field effects in underwater explosion scenario

This article presents the exact elastic buckling of annular plates with elastically restrained edges against rotation and translation at inner and outer periphery. The classical plate theory is used to derive the governing differential equation for annular plate with elastically restrained edge support system. The buckling mode may not be axisymmetric as previously assumed. In certain cases, an asymmetric mode would yield a lower (critical) buckling load. This is due to switching of mode. This work presents the critical buckling load parameters for axisymmetric and asymmetric buckling modes. Extensive data is tabulated so that pertinent conclusions can be arrived at on the influence of rotational and translational restraints, Poisson's ratio and other boundary conditions on the buckling of uniform isotropic annular plates. The numerical results obtained are in good agreement with the previously published data. In this article, the characteristic equations are exact; therefore, the results can be calculate...

Buckling of Annular Plates with Elastically Restrained External and Internal Edges

This work presents the existence of buckling mode switching with respect to the radius of concentric rigid ring support. The buckling mode may not be axisymmetric as previously assumed. In general, the plate may buckle in an axisymmetric mode but when the radius of the ring support becomes small, the plate may buckle in an asymmetric mode. The optimum radius of the concentric rigid ring support for maximum buckling load is also determined. Introducing internal rigid ring support, when placed at an optimal position increases the elastic buckling load capacity by 149.39 percent. The numerical results obtained are in good agreement with the previously published data.

Lokavarapu Bhaskara Rao

Papers

Buckling of circular plate with foundation and elastic edge

Study on JWL equation of state for the numerical simulation of near-field and far-field effects in underwater explosion scenario

Buckling of Annular Plates with Elastically Restrained External and Internal Edges

Fundamental buckling of circular plates with elastically restrained edges and resting on concentric rigid ring support

Frequency analysis of annular plates with inner and outer edges elastically restrained and resting on Winkler foundation