Characteristics of defect states in periodic railway track structure

To overcome the ill-conditioned matrix problem of the traditional transfer matrix method, the Floquet transform method and supercell technology are used to study the defect states of the periodic track structure. By solving the equations of the supercell directly, the propagation characteristics of elastic waves in the track structure with defects are analyzed. The existence of defects destroys the periodicity of track structure, thus resulting in the formation of defect states within the band gaps. Moreover, the elastic wave is localized near the defect position at the frequency of the defect state. The formation mechanism of the defect state in track structure can be explained by the local resonance at the defect. With the expansion of the defect range, the number of local resonance modes that can be formed near the defect increases, thus generating multiple defect states. Furthermore, the defect state enhances the vibration of the structure adjacent to the defect. Therefore, the vibration transmission coefficient in a finite-length range can be used to detect the defect characteristics in the track structure, and the defect degree can be evaluated by the peak frequency of the vibration transmission coefficient within the band gap.

Vibration transmission across fractured beam-to-column junctions of reinforced concrete

To detect human survivors trapped in buildings after earthquakes by using structure-borne sound it is necessary to have knowledge of vibration transmission in collapsed and fragmented reinforced-concrete buildings. In this paper, Statistical Energy Analysis (SEA) is used to model the vibration transmission in seismic damaged reinforced concrete beam-to-column junctions where the connection between the beam and the column is made only via the steel reinforcement. An ensemble of 30 randomly damaged beam-to-column junctions was generated using a Monte Carlo simulation with FEM. Experimental SEA (ESEA) is then considered with two or three subsystems to determine the CLFs between the beam and the column with either bending modes or the combination of all mode types. It is shown that bending modes dominate the dynamic response and that the uncertainty of predicting the CLFs using FEM with ESEA is sufficiently low that it should be feasible to estimate the coupling even when the exact angle between the beam and the column is unknown. In addition, the use of two rather than three subsystems for the junction significantly decreases the number of negative coupling loss factors with ESEA.

Predicting vibration transmission across junctions using diffuse field reciprocity

Predicting the sound insulation of an engineering system is a complex problem since not only the direct path through a separating element but also the flanking transmission paths can largely influence the sound insulation of the system. When conventionally analyzing flanking transmission, a diffuse field is assumed in the walls and floors, which are modelled as plates. The junction connecting the walls and floors is assumed to be of infinite extent and the transmission of vibration across the junction is calculated by integrating over all possible angles of incidence. Due to the limitations of the conventional approach, a new approach based on diffuse field reciprocity is proposed. The diffuse field reciprocity relationship relates the vibration transmission to the direct field of a diffuse subsystem to the direct field dynamic stiffness of the subsystem, i.e., the dynamic stiffness of the equivalent infinite subsystem as observed at the junction. The direct field dynamic stiffness matrices of thin, isotropic, elastic plates can be analytically derived. For more complex walls or floors a possible approach is to calculate the direct field dynamic stiffness using finite elements and perfectly matched layers. The perfectly matched layer surrounding the finite element model absorbs the wave propagating outwards from the bounded domain, thus simulating an infinite subsystem.

Effects of Strongbacks and Strappings on Vibrations of Timber Truss Joist Floors

It is well known that the vertical vibrations of lightweight timber floors would cause discomfort to the occupants. As a new kind of flooring system, the metal-plate-connected timber truss joist floors were developed due to their larger spans and easier crossing of pipes and cables after sawn timber and I-joist floors. In this paper, the vibration modes and transfer functions of sixteen metal-plate-connected timber truss joist floors over a nominal span of 6 m were determined experimentally to measure the changes in vibration frequencies and transmissions obtained after the installation of strongbacks and strappings. The results showed that the fundamental natural frequencies of the metal-plate-connected timber truss joist floors at a 400 mm joist spacing were about 15 Hz, while the frequencies of the floors at a 600 mm joist spacing were about 12.5 Hz. The bracing elements of the strongbacks and strappings mainly enhanced the system stiffness in the across-joist direction of the flooring system, but they did not govern the fundamental natural frequencies of the floors and just changed the spacing of adjacent natural frequencies. The bracing elements as secondary elements of the floors also altered the vibration transmission paths in the across-joist direction. The frequencies where the stronger vibration transfers happened in the direction perpendicular to floor joists were generally above 15 Hz. Proper installation measurements of bracing elements in practical control need to be taken to alleviate the vibration response intensity at the targeted locations and frequencies.