A set of some 30 Benchmark tests of finite elements in free vibration is presented. The tests cover most popular element types and solution procedures. Full details of each test are given in a standard one-page format, comprising geometrical arrangements, boundary conditions, two sets of ‘target’ frequencies (theoretical or numerical) and a schematic presentation of mode shapes.

This document provides details of some benchmark tests of finite element assemblies in free vibration. It was commissioned by the NAFEMS Steering Committee and produced by W.S Atkins Engineering Sciences under the direction of the Dynamics Working Group.

The object of the document is to provide in succinct form a set of tests, which collectively may be used to assess the accuracy of linear elastic finite element assemblies undergoing undamped free vibration. Only isotropic, stress free assemblies are considered and attention is focused on the most popular types of finite element in commercial use.

The tests are of two types; firstly those to assess the performance of particular element types and secondly those dealing with various aspects of the eigen-solution method and the algorithms used.

The document is, quite deliberately, fairly concise. Essential details of each test are provided in a standard form in Section 3. It is intended that each test should be self-explanatory. However, some further information covering the organisation and background of the various tests is given in Section 2.

Contents

SUMMARY

ACKNOWLEDGEMENTS

CONTENTS

SYMBOLS AND ABBREVIATIONS

INTRODUCTION

ORGANISATION OF TESTS

• Test Numbering
• Solutions
• Element Assemblage Tests
• Beam Element Tests
• Plate Element Tests
• Continuum Element Tests
• Solution Algorithm Tests

DETAILS OF EACH TEST

REFERENCES