Abstract
Free in-plane vibration of super-elliptical plates of uniform thickness was investigated by the Ritz method. A large variety of plate shapes ranging from an ellipse to a rectangle were examined. Two cases were considered: (1) a completely free, and (2) a point-supported plate. The geometrical boundary conditions were satisfied by the Lagrange multipliers. The results were compared with those of rectangular plates. Basically good agreement was obtained. Matching results were reported, and the discrepancies were highlighted.
Keywords
Rectangle
Ellipse
Vibration
Ritz method
Lagrange multiplier
Plane (geometry)
Geometry
Point (geometry)
Vibration of plates
Boundary value problem
Boundary (topology)
Mathematics
Structural engineering
Mathematical analysis
Physics
Engineering
Acoustics
Mathematical optimization
Subject Areas
Composite Structure Analysis and Optimization
·Mechanics of Materials ·Physical Sciences
Vibration and Dynamic Analysis
·Control and Systems Engineering ·Physical Sciences
Railway Engineering and Dynamics
·Mechanical Engineering ·Physical Sciences
Citations by Year
2017: 1
2021: 1
2022: 1
2024: 2
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