Analysis of guided waves with a nonlinear boundary condition caused by internal resonance using the method of multiple scales

Wave Motion ◽  
2018 ◽  
Vol 77 ◽  
pp. 28-39 ◽  
Author(s):  
Kosuke Kanda ◽  
Toshihiko Sugiura
Keyword(s):  
Boundary Condition ◽  
Internal Resonance ◽  
Guided Waves ◽  
Nonlinear Boundary ◽  
Nonlinear Boundary Condition ◽  
Multiple Scales ◽  
Method Of Multiple Scales

Two-Mode Interaction of a Beam with a Nonlinear Boundary Condition

1999 ◽  
Vol 121 (1) ◽  
pp. 84-88 ◽  
Author(s):  
Won Kyoung Lee ◽  
Myeong Hwan Yeo
Keyword(s):  
Boundary Condition ◽  
Nonlinear Boundary ◽  
Nonlinear Boundary Condition ◽  
Multiple Scales ◽  
Initial Conditions ◽  
Excitation Frequency ◽  
Linear Partial Differential Equation ◽  
Harmonic Excitation ◽  
Mode Interaction ◽  
Modal Interactions

In order to investigate modal interactions in a subharmonic resonance of a beam with a nonlinear boundary condition, we consider a beam constrained by a nonlinear spring to a harmonic excitation. The resonance conditions considered are ωn ≈ 3ωm and Ω ≈ 3ωn, where 3ωm and 3ωn are the natural frequencies and Ω is the excitation frequency. This nonlinear problem is governed by a linear partial differential equation, initial conditions and a nonlinear and inhomogeneous boundary condition. The method of multiple scales is used to transform the problem into a system of autonomous ordinary differential equations for amplitude and phase variables. The steady-state responses and their stability are determined by use of this system. In order to check the validity of the analytical solution we solve the initial and boundary value problem by means of a finite difference analysis.

Sign in / Sign up

Export Citation Format

Share Document