NUMERICAL AND ASYMPTOTIC METHODS OF INTEGRATING THE BERNOULLI-EULER EQUATION

Abstract

At present, Mykelstad's method (BRL R-1070) is used to calculate the normal modes and natural frequencies of gun tubes and other beams of variable cross section. In this method, the actual beam is replaced by an equivalent discrete system of concentrated masses and massless springs. The use of a discrete system in place of a continuous system introduces a truncation error which is small in the lower modes, but which may amount to several per cent in the higher modes. It is believed that a higher-order method of numerical integration in which the step size may be varied at will should considerably reduce this error. (Author)

Document Details

Document Type
Technical Report
Publication Date
Aug 01, 1961
Accession Number
AD0266692

Entities

People

  • A.s. Elder

Organizations

  • Ballistic Research Laboratory

Tags

DTIC Thesaurus Topics

  • Equations
  • Euler Equations
  • Frequency
  • Mathematics
  • Numerical Integration
  • Resonant Frequency
  • Truncation

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Structural Dynamics.
  • ballistics.