Steady-state Vibration Responses of a Beam with a Nonlinear Boundary Condition

비선형 경계조건을 가진 보의 정상상태 진동응답

  • Lee, Won-Kyoung (Dept.of Mechanical Engineering, Yeungnam University) ;
  • Yeo, Myeong-Hwan (Dept.of Mechanical Engineering, Graduate School of Yeungnam University)
  • 이원경 (영남대학교 기계공학부) ;
  • 여명환 (영남대학교 대학원 기계공학부)
  • Published : 1997.01.01


An analysis is presented for the response of a beam constrained by a nonlinear spring to a harmonic excitation. The system is governed by a linear partial differential equation with a nonlinear boundary condition. The method of multiple scales is used to reduce the nonlinear boundary value problem to a system of autonomous ordinary differential equations of the amplitudes and phases. The case of the third-order subharmonic resonance is considered in this study. The autonomous system is used to determine the steady-state responses and their stability.


Nonlinear Boundary Condition;Beam Vibration;Method of Multiple Scales;Subharmonic Resonance