关键词: 竖直振动, 重力, 静变形, 线性, 非线性

Abstract: The effects of the weight on vertical vibrations are analyzed. The Lagrangian equation is applied to a multi-degree-of-freedom time-independent conservative linear systems with the gravitational potential energy as a linear function of generalized coordinates to demonstrate that the weight can be canceled by the static deformation effect and then ignored together provided that the static equilibrium configuration is chosen as the origin the the generalized coordinates. A vertically vibrating one-degree-of-freedom nonlinear system is treated as an example to reveal that the weight changed both the linearized system and the nonlinear terms and thus cannot be ignored. The investigation outcomes clarify the validity conditions of relevant conclusions in domestical and international textbooks on vibrations.

Key words: vertical vibration, weight, static equilibrium, linearity, nonlinearity