The dynamic stiffness method is developed for the dynamics of a beam structure carrying multiple spring−mass systems. Based on classical Bernoulli–Euler beam theory, three types of vibrations, namely, bending, longitudinal and torsional motions, are formulated in terms of dynamic stiffness matrix. Similar to finite element technique, the local dynamic stiffness matrices for individual beams and spring−mass systems are assembled into global dynamic stiffness matrices so as to address vibration transmission from machines to flexible beamlike foundations. Using our proposed method, the vibration transmission within a beam frame, carrying multiple spring−mass systems is addressed. Through numerical analysis, the calculated vibration responses agree well with those from finite element method, which demonstrates that dynamic stiffness formulation has great potential in modeling the dynamics of built-up beam structures that supports machinery, especially in characterizing vibration isolation due to wave reflections, wave conversions, and other underlying mechanisms.

动态刚度方法是为承载多个弹簧质量系统的梁结构的动力学而开发的。根据经典的伯努利-欧拉梁理论，根据动态刚度矩阵，可以表示三种类型的振动，即弯曲，纵向和扭转运动。与有限元技术相似，将单个梁和弹簧质量系统的局部动态刚度矩阵组装为整体动态刚度矩阵，以解决从机器到柔性梁状基础的振动传递。使用我们提出的方法，解决了承载多个弹簧质量系统的梁框架内的振动传递问题。通过数值分析，计算得到的振动响应与有限元方法的吻合很好，