Interface - The Journal of Wheel/Rail Interaction

MASS-SPRING SYSTEMS

Using High-Performance Mass-Spring-Systems to Reduce Noise and Vibration in Track
(continued)

In order to provide a high level of attenuation, a mass-spring system requires an oscillating system. This consists of a mass, represented by the concrete slab or ballasted trough, that is supported by a resilient layer, represented by a spring (see Figures 3 and 4). The mass-spring-system can be simplified and sufficiently represented by a rigid mass system in which the concrete slab is considered a rigid body with negligible influence on the natural frequencies of the slab. Since the lowest natural bending frequency (of short and long slabs) is usually far beyond (or below) the theoretical support frequency of the system, transmission of the bending frequency through the spring is ruled out.

Such a system with six degrees of freedom and six eigenfrequencies can further be simplified into a one degree-of-freedom model, as the excitation by the train is mainly in the vertical direction. Figure 5 shows the principle behavior of the simplified spring-mass model with excitation and inertia forces out of phase.

The balance of the sum of all forces is one of the main principles of statics. A force always corresponds to a reaction force of the same magnitude. The same principle applies to dynamic analysis. Therefore, in order to reduce the reaction force generated by a dynamic excitation force, it is necessary to introduce an additional force that works opposite to the excitation force. A periodically excited acceleration of the mass generates this counteracting force.

With an optimal choice of the system frequency, it is possible to achieve inertia forces that are very close to the relevant excitation forces that are generated by a train. The small difference in the forces left is still transmitted but can usually be neglected or even often not perceived. On the other hand, when both excitation and inertia force work in the same direction, the reaction force is actually increased, which yields a worsened effect. When both excitation and inertia force are in sync, the system is in resonance.

The relevant excitation spectra relating to vibration and ground-borne noise generated by railway traffic is usually between 10Hz and 200Hz. Vibrations with frequencies above this range are dissipated rapidly by materials such as soil or concrete, which carry the waves. Since all oscillating systems have a resonance frequency, it is essential to set this frequency (= tuning frequency) outside the relevant excitation spectrum area. In general, the wide range of frequencies excited by railway systems suggests that the tuning frequency should be set as low as possible. It is important to have projected excitation spectra for the train when planning a mass-spring-system.

The natural frequencies of neighboring buildings must also be considered in the design of the mass-spring system in order to prevent the occurrence of resonant vibrations that can disturb people or sensitive equipment. In the lower frequency range, natural frequencies of building slabs (depending on their design) usually range between 10 and 30 Hz, or lower. A mass-spring system with a tuning frequency that met a slab’s natural frequency would actually make the situation worse. As train excitation includes stochastic components, resonant building slab excitation may occur even if the excitation spectrum does not show low frequencies explicitly.

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