On the Large Amplitude Forced Vibration Analysis of Composite Sectorial Plates

The nonlinear steady state large amplitude forced vibration response of a laminated composite annular sector plate is presented. The nonlinear governing equation of motion of the laminated composite annular sector plate has been obtained using kinematics of first-order shear deformation theory (FSDT) and employing Hamilton’s principle. The governing equations of motion have been solved in a time domain using a modified shooting method and arc-length/pseudo-arc length continuation technique. The influence of the boundary condition, sector angle, and annularity ratio on the linear as well as nonlinear steady state forced vibration response has been investigated. The strain/stress variation across the thickness of the annular sector plate is presented to explain the reason for a decrease/increase in hardening nonlinear behaviour. The periodic variation of the non-linear steady state stress has also been obtained to throw light into the factors influencing the unequal stress half cycles and multiple cyclic stress reversals, which is detrimental to the fatigue design of laminated composite annular sectorial plates. The frequency spectra of the steady state stress reveals large even and odd higher harmonic contributions for different cases due to changes in the restoring force dynamics. The modal interaction/exchange during a cycle is demonstrated using a deformed configuration of the laminated annular sector plate.

A unified solution for in-plane vibration analysis of composite laminated sector and annular plate with elastic constraints

A semi-analytical method for in-plane vibration analysis of a composite laminated annular and sector plate with elastic constraints is presented. The theoretical model is on the basis of a variational method and a multi-segment technique. Displacement variables are expanded by the Jacobian orthogonal polynomial. Boundary conditions and continuity conditions between segments are characterized by penalty parameters. On this basis, a series of numerical examples are given. The results show that the method has good convergence speed and accuracy. Finally, the parametric study of geometric and material parameters is carried out to provide important support for solving the in-plane characteristics of this kind of composite structure.

The Transverse Shear Effect of a New Strain Based Sector Finite Elements for Plate Bending Problems

In this paper, we present the transverse shear effect on the plate bending. The element used is a sector finite element called SBSP (Strain Based Sector Plate-Kirchhoff Theory-), it used for the numerical analysis of circular thin plate bending., and it based on the strain approach. This element has four nodes and three degrees of freedom per node. Through the numerical applications with different loading cases and boundary conditions; This makes the present element robust, better suitable for computations.

Exploring the Experiences of People with Obesity Using Portion Control Tools—A Qualitative Study

Large portion sizes increase consumption and eating smaller portions is recommended as a weight control strategy. However, many people report difficulties enacting this advice. This study examined the experience of individuals using two commercially available portion-control tools to try to manage their weight. In a crossover design, 29 adults with obesity (18 women) who had attended a previous weight loss intervention in the community were invited to use two portion-control tool sets over a period of four weeks (two weeks each) and to complete a semi-structured questionnaire about their experience. The tools were a guided crockery set (sector plate, calibrated bowl, and calibrated glass) and a set of calibrated serving spoons (one for starch, one for protein, and one for vegetables). Data were analyzed using thematic framework analysis. A key theme was related to the educational benefits of the tools, such as generating awareness, guidance, and gaining an independent ability to judge appropriate portions. Other key themes were tool usability, acceptability, and feasibility of usage. Barriers identified by participants included unclear markings/instructions and the inconvenience of using the tool when eating away from home. Overall, the tools were perceived to be educationally useful, easy to use, and potentially effective for learning to control portions, which suggested that these instruments could help in weight management interventions alongside other strategies. Elements of the tool design could influence the ability of participants to adhere to using the tool, and hence allow the educational effect to be mediated.

Thermoelastic Coupling Vibration and Stability Analysis of Rotating Annular Sector Plates

This study investigates the thermoelastic coupling vibration and stability of rotating annular sector plates. Based on Hamilton’s principle and thermal conduction equation with deformation effect, the differential equation of transverse vibration for a rotating annular sector plate is established. The differential equation of vibration and corresponding boundary conditions are discretized by the differential quadrature method. Then, the thermoelastic coupling transverse vibrations under three different boundary conditions are calculated. The change curve of the first three order dimensionless complex frequencies of the rotating annular sector plate with the dimensionless angular speed are analyzed in the case of the thermoelastic coupling and uncoupling. The effects of the dimensionless angular speed, the ratio of inner to outer radius, the sector angle, and the dimensionless thermoelastic coupling coefficient on transverse vibration and stability of the annular sector plate are discussed. Finally, we obtained the type of instability and corresponding critical speed of the rotating annular sector plate in the case of the thermoelastic coupling and uncoupling.