Abstract
This paper describes vibration analysis using finite element method for an elastic frame connected by nonlinear concentrated springs having elastic principal axes in arbitrary directions. The restoring forces of the springs have cubic nonlinearity. Finite element for the nonlinear springs are expressed and are connected to the elastic frame modeled by linear solid finite elements in consideration of complex modulus of elasticity. Further, the discretized equations in physical coordinate are transformed into the nonlinear ordinary coupled equations using normal coordinate corresponding to linear natural modes. This transformation yields computation efficiency. The calculated results by the proposed method are verified. Moreover, nonlinear and chaotic responses are generated.
