Bending analysis of magnetoelectroelastic nanoplates resting on Pasternak elastic foundation based on nonlocal theory

Based on the nonlocal theory and Mindlin plate theory,the governing equations(i.e.,a system of partial differential equations(PDEs)for bending problem)of magnetoelectroelastic(MEE)nanoplates resting on the Pasternak elastic foundation are first derived by the variational principle.The polynomial particular solutions corresponding to the established model are then obtained and further employed as basis functions with the method of particular solutions(MPS)to solve the governing equations numerically.It is confirmed that for the present bending model,the new solution strategy possesses more general applicability and superior flexibility in the selection of collocation points.The effects of different boundary conditions,applied loads,and geometrical shapes on the bending properties of MEE nanoplates are evaluated by using the developed method.Some important conclusions are drawn,which should be helpful for the design and applications of electromagnetic nanoplate structures.

Modeling and solving for transverse vibration of gear with variational thickness

A analyzed model of gear with wheel hub, web and rim was derived from the Mindlin moderate plate theory. The gear was divided into three annular segments along the locations of the step variations. Traverse displacement, rotation angle, shear force and fiexural moment were equal to ensure the continuity along the interface of the wheel hub, web and rim segments. The governing differential equations for harmonic vibration of annular segments were derived to solve the gear vibration problem. The influence of hole to diameter ratios, segment thickness ratios, segment location ratios, Poisson ratio on the vibration behavior of stepped circular Mindlin disk were calculated, tabletted and plotted. Comparisons were made with the frequencies arising from the presented method, finite elements method, and structure modal experiment. The result correlation among these three ways is very good. The largest error for all frequencies is 5.46%, and less than 5% for most frequencies.

Non-Resonant Structure Design of Catenary Transformer in Ultrasonic Gear Honing

To solve the design problem of transformer composed of non-resonant structure in ultrasonic gear-honing, force coupling conditions for moderately thick annular plate （MTAP） and catenary horn are proposed, and the frequency equations of the transformer, which consist of an MTAP and a catenary horn, are derived based on Mindlin＇s theory. The design parameters of the transformer were obtained by solving the frequency equations with the help of MATLAB, and its mode and frequency were deduced by the modal analysis of finite element method （FEM）, which are consistent with the theoretical design demands. The transformer design can be extended from system with thin annular plate to that with MTAP as the theoretical method by the simulation analysis of various ratios of the thickness to radius.