1979•Transactions of the Architectural Institute of JapanOpen access
A CLASSIFICATION OF NONLINEAR VIBRATIONS : The Periodic Solution Problems of Nonlinear Equations of Motion-Part 2.
Youichi Minakawa
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Abstract
Nonlinear vibrations which take place in the equations of motion expressed by normal modes are classified into three types here. The method of harmonic balance is applied to analyse periodic solutions of the equations of motion. Then, the nonlinear vibration problems are expressed by algebraic equations which are composed of the Fourier coefficients. The unknowns of the algebraic equations are classified by applying the procedure described in Part 1. Sience the unknowns express the Fourier coefficients that represent nonlinear vibrations, nonlinear vibrations are classified into three types, accompanying type, branching type (1) and branching type (2). Then in order to study the stability of the periodic solutions corresponding to undisturbed motion, a complex eigenvalue problem is derived by applying the method of harmonic balance to the variational equations.
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