Shell08 – Cantilever Plate Eigenvalue Problem ✔!!!!

Problem Description

In this example a cantilever square plate is analyzed to find the periods of the first five plate-bending modes of vibration. This model periods are compared with hand calculated results based on data presented in Harris and Crede 1976.
The plate is 24 inches square and 1 inch thick. A mass per unit area of 7.35E-07 k-sec2/in3 is assigned to the plate. This is the only mass that exists in the problem.
The example is solved using three different meshes in three different models. Models A, B and C have 10x10, 20x20 and 40x40 meshes respectively. The model is created using a single area object and this meshing is applied using the automatic area meshing feature available in this model.
The plate is modeled in the XZ plane. Because only plate bending modes of vibration are desired, only the Uy, Rx, and Rz degrees of freedom are activated in the model, thus restricting its behavior to plate bending. The Uy and Rx degrees of freedom are restrained at joints 1 and 2.
The automatic area meshing feature has a special option to add a restraint to a degree of freedom at a new joint (created by the meshing) along the edge of the area object if both adjacent corners of the area object have that degree of freedom restrained. This special option is used in this example, thus providing restraint along the entire base of the plate.

Tested Features

•  Eigenvalue analysis using shell elements
•  Area object mass assignment
•  Area object automatic mesh
•  Area object stiffness modifiers

App

Object Link: https://openbrim.org/objid4wv0oszhepsj0zorf2nekc.project

Library

Object Link: https://openbrim.org/objideervl2sm7suxesuxvm2dec.libobj