# Accession Number:

## AD0673235

# Title:

## THE USE OF CONSOLIDATED EXPANSIONS IN SOLVING FOR THE STATISTICAL PROPERTIES OF A NONLINEAR OSCILLATOR.

# Descriptive Note:

## Doctoral thesis,

# Corporate Author:

## JOHNS HOPKINS UNIV BALTIMORE MD DEPT OF MECHANICS

# Personal Author(s):

# Report Date:

## 1967-10-01

# Pagination or Media Count:

## 187.0

# Abstract:

We consider a nonlinear harmonic oscillator driven by random, Gaussian noise. The oscillator is damped and has linear and cubic terms in the restoring force. The Fourier transform of the solution of this equation, usually referred to as the Duffing equation, is expanded in a series in the coefficient of the cubic term. This series is then squared to give a series for the spectrum of the response. Each term in this series is expressed in terms of the solution of the linearized harmonic oscillator i.e. without the cubic term. Since the forcing function is Gaussian, the solution of the linearized harmonic oscillator is Gaussian. Thus each term in the series for the response spectrum can be expressed as a function of the spectrum of the linear oscillator using the properties of a Gaussian random function. The numerical results indicate that the consolidated equations provide a substantial improvement over other methods used to solve this type of problem. Author

# Descriptors:

- (*HARMONIC GENERATORS
- RESPONSE)
- (*NONLINEAR SYSTEMS
- MATHEMATICAL ANALYSIS)
- STATISTICAL PROCESSES
- NOISE
- NONLINEAR DIFFERENTIAL EQUATIONS
- DISTRIBUTION FUNCTIONS
- TURBULENCE
- SPECTRUM SIGNATURES
- NUMERICAL METHODS AND PROCEDURES
- COMPUTER PROGRAMMING
- ANALOG COMPUTERS
- PROBABILITY DENSITY FUNCTIONS
- NAVIER STOKES EQUATIONS
- INTEGRAL EQUATIONS
- THESES

# Subject Categories:

- Electrical and Electronic Equipment