Accession Number:

ADA230533

Title:

An Evolution Operator Solution for a Nonlinear Beam Equation

Descriptive Note:

Doctoral thesis

Corporate Author:

AIR FORCE INST OF TECH WRIGHT-PATTERSON AFB OH SCHOOL OF ENGINEERING

Personal Author(s):

• Crockett, Carl E.

Report Date:

1990-12-01

Pagination or Media Count:

152.0

Abstract:

A nonlinear partial differential equation, motivated by the transverse vibration of a beam, is shown to have a unique solution. The existence theory, which is in the setting of semigroups and evolution operators, is a composite and synthesis of theorems of Kato. The formulation of the problem and the verification that the formulation leads to a solution are new. The introductory chapter provides background on the topic generally. Chapter 2 provides detailed formulations for the constant coefficient case. Chapter 3 describes nonautonomous cases. The general theorem is presented here. In Chapter 4, a more general case is considered. Namely, Kelvin Voigt damping with a coefficient which depends on the solution. This introduces a nonlinearity to the problem which makes it of the form frequently called quasilinear. This is a stronger form of nonlinearity than semilinear. Results of a numerical example are presented.

Descriptors:

• *NONLINEAR DIFFERENTIAL EQUATIONS
• *PARTIAL DIFFERENTIAL EQUATIONS
• *BEAMS(STRUCTURAL)
• THESES
• NONLINEAR SYSTEMS
• SOLUTIONS(GENERAL)
• THEOREMS
• MATHEMATICAL ANALYSIS
• EVOLUTION(GENERAL)
• DIFFERENTIAL EQUATIONS
• EQUATIONS
• OPERATORS(PERSONNEL)
• TRANSVERSE
• DAMPING
• FORMULATIONS
• VIBRATION
• COEFFICIENTS

Subject Categories:

• Numerical Mathematics
• Unmanned Spacecraft
• Manned Spacecraft

Distribution Statement:

APPROVED FOR PUBLIC RELEASE