杆、梁结构振动能量密度的简化解法

A simplified method for solving energy density of rods and beams

以能量密度为变量,研究了杆、梁结构受激励分别产生纵向振动和弯曲振动时的控制方程,获得了一维结构振动能量密度的简化解法.该简化方法为船舶基本结构的高频振动噪声分析提供方便准确的方法,它只需要比传统的模态法较少的参数,且不需要关于结构共振响应的信息.计算分析表明,在高频时,由简化方法得到的近似解与精确解吻合很好.文中进一步验证了Nefske＆Sung提出的振动噪声结构的能量流与热流的相似性,即当阻尼较小时,一维结构中的振动能量流具有与热传导中热流类似的特性.

The governing equations for both longitudinal vibration in rods and transverse flexural vibration of beams were derived from the classical displacement solutions taking energy density as variable. An approximate solution of energy density was investigated.The method was used to analyze structure-borne sound of ship basic structures at high frequency.It's a convenient and accurate method.Fewer parameters are required to approximate the energy solution than are required to model the characteristic wave behavior of structural vibration by using traditional displacement formulations. The advantage of energy formulation over displacement formulation is that the relationships between power and energy density are independent of the resonant state of rods or beams. It is found that the simplified and exact solutions are in very close agreement at high frequency. The thermal analogy proposed by Nefske and Sung to model mechanical power in structural acoustic systems is investigated further. When assumptions based on small structural damping were used, the flow of mechanical energy through a one-dimensional structure took on some of the attributes of thermal power flow in a heat conduction problem.