**1. Introduction**

Railway sleepers and bearers are typically made of timber, concrete, steel, and other composite materials. In traditional railway tracks, timber is normally used as railway sleepers and bearers. Due to the diverse environmental concern of noble wood leading to the high deterioration rate of timber sleepers, the need of using other materials has grown. Currently, the development and improvement of railway structure, which is economically competitive for meeting the requirements of the industry, is a key challenge for track engineers. One of the major concerns in the railway industry is the replacement of deteriorated and damaged timber sleepers in existing railway tracks [1]. Recently, polymer and composite sleepers with mostly fiber materials have been developed [2] and designed

to mimic timber behavior [3,4]. This is conducted presently on a basis of a like-for-like replacement in terms of equivalent static performances (i.e., similarities of static strength, modulus of elasticity, stiffness, etc.). For example, a fiber composite system is composed of a lightweight polymer matrix with strong fibers added into the matrix [2]. These fibers can well resist forces because of their extreme strength and can be used only in the longitudinal and/or transverse direction. The static strength and elastic modulus of composites are found to be equivalent to hard timber. Recently, practitioners have strong concerns whether dynamic properties should rather be considered due to the fact that railway tracks are generally exposed to dynamic loading conditions. It is also well-known that concrete and steel are likely to have nearly no damping coefficient when compared to timber, which has an outstanding damping coefficient [5–8]. In recent reviews [9,10], it has been found that steel bearers behaved well in the short-term, but tended to have higher turnout settlements and severe ballast breakage in the long-term. In contrast, concrete tends to be an extremely good counterpart to enhance track and turnout stability in a longitudinal, vertical, and lateral direction [11,12]. However, concrete is relatively much heavier than timber and it is impractical to use concrete bearers as timber barer replacement. A major benefit of using polymer and composite sleepers and bearers is their flexibility, which results in an extreme ability to withstand vibrations induced by dynamic forces in a railway track system [13,14]. Moreover, polymer and composite sleepers and bearers are durable, simple to make, are presently cost-attractive, and need low to nearly no maintenance. Therefore, their improved lifecycle is useful for areas that are very difficult to maintain, for instance, turnouts (or referred to as 'switches and crossings'), bridges, and tunnels. Another benefit is that the utilization of the polymer and composite sleepers and bearers can handle the constant rise of concern throughout the existing environment in the present industry, because of its durability and its nearly 100% recyclability [15].

Composite railway sleepers and bearers are one of the most attractive structural elements in a railway infrastructure, acting as crosstie beams, which are placed under the rails to support track loading [16]. Their key functions are not only to transfer and distribute dynamic train loads to track substructure, but also to ensure safe rail gauge that permits the train to travel securely [17–19]. The vibration of Fiber-reinforced Foamed Urethane (FFU) composite sleepers and bearers in a railway turnout system is a key factor causing failure of FFU composite sleepers and bearers and excessive railway track maintenance costs. As such, the performance of Fiber-reinforced Foamed Urethane (FFU) composite sleepers and bearers over the entire service life and their failure modes under vibration cannot be fully identified to establish a design standard for these composite sleepers and bearers. It is important to comprehend the dynamic modal parameters of the composite sleepers and bearers to develop and design a realistic dynamic model of a railway track for predicting its responses under vibration. The essential information of the dynamic parameters can be used for dynamic performance benchmarking when a new material is manufactured for railway applications. Furthermore, the information is critical in the development of a predictive vibration-based condition assessment of the components. On this ground, it is necessary to monitor and inspect the vibration behavior of FFU composite sleepers and bearers during operation in order to prioritize and plan effective maintenance management. Note that the inspection of railway sleepers and bearers is currently carried out by visual observation. Monitoring of dynamic properties can provide an alternative technique in structural integrity assessment for track engineers.

It is noted that the use of common damage detection techniques (visual observation) is inefficient to identify any component damage in real-time and they cannot perform to completely reduce track possessions (i.e., track maintenance time). In many engineering applications, one of the reliable inspection techniques widely used in modal analysis is based on an instrumented hammer impact excitation. Modal analysis is a useful tool for comprehending the vibration characteristics of mechanical structures. This tool converts the vibration waves of excitation and response identified on a complicated structure into a range of predictive modal parameters [20]. One with the most perspectives of structural dynamics is the modal domain, which provides modal parameters (such as natural frequencies, dynamic stiffness, and dynamic damping). A structure deforms or vibrates in particular shapes, so-called 'mode shapes', when the structure is excited at its natural frequencies. It will move back and forth in a complex combination, which includes all the mode shapes under common operation conditions [20].

In a modal testing process, a Frequency Response Function (FRF) is a transfer function used for impact hammer analysis in order to determine the resonant frequencies and mode shapes, as well as damping of a vibrating structure [21]. During the design phase, the dynamic modal parameters obtained from the FRF are an important factor to consider before manufacturing a real structure to find and eliminate potential problems early [21]. In 2006, Kaewunruen and Remennikov carried out an investigation into the modal analysis of pre-stressed concrete sleepers for evaluating dynamic behaviors of the sleepers, using the impact hammer excitation technique at a particular frequency series of 0–1600 Hz [21,22]. According to their study, the PROSIG modal analysis suite was used to measure the frequency response functions (FRFs). They also used the STAR Modal analysis package to determine the natural frequencies and corresponding modal shapes of each sleeper from the FRFs. Obviously, the impact hammer excitation technique is one of the most attractive non-destructive force excitation methods to identify dynamic modal parameters of a structure under vibration. These modal parameters are helpful for the development of a realistic dynamic model of railway composite sleepers and bearers capable of predicting its dynamic responses.

In terms of mechanical properties of a common material, two independent constants called elastic modulus, E, and shear modulus, G, define the elastic properties for linearly elastic isotropic solids. The design of engineered structures has been significantly concerned about these two elastic properties. For the above reason, many experimental methods to identify E and G have been developed. These methods consist of two sets, which are static and dynamic techniques. According to studies in [23–25], the researchers were the first to determine the elastic properties of isotropic materials, based on non-destructive vibration testing. They established the formulae to calculate dynamic E and G from the natural frequencies in bending and twisting modes of cylinder and prisms, based on the Timoshenko beam theory. In fact, the base of the ASTM criterion [26] test method to characterize dynamic elastic properties was set by those researchers, using the impulse excitation technique [27]. To date, several researchers have investigated the estimation of the elastic properties of laminated composites [28–33], timber materials [34,35], or concrete materials [36], which are non-isotropic and/or inhomogeneous, using vibration-based approaches. It is important to note that the standard tests for dynamic properties gain significant supports from scientific and engineering communities in present days.

For railway applications, it is well-known that a common turnout induces high impact loads on the structural members because of its blunt geometry and mechanical connections between closure rails and switch rails. Therefore, the turnout system requires improved structural members, which use an alternative material like the FFU material, having an identical timber-like behavior. For that reason, the FFU material in switches and crossings offers its high-impact attenuation, high damping property, high UV resistance, lightweight, and long-lifecycle. The static properties of FFU bearers are presented in Table 1. However, neither of the dynamic properties of FFU bearers have been investigated before, nor are available in open literature.

In this paper, the experimental and numerical dynamic parameters of FFU composite beams in free-free conditions have been identified. The free-free condition is scientifically ideal for performance benchmarking or comparison of test results. This condition excludes uncertainties that can affect the test results, such as type of ballast, type of support, and type of fastening system. This condition is very critical when the like-for-life performance of an individual component is being assessed. In this study, two FFU composite beams have been tested using an impact hammer excitation technique over the frequency range of interest: 0 to 2100 Hz. Frequency response functions (FRFs) have been measured using the Modal Analysis Suite package to identify natural frequencies and the corresponding mode shapes, as well as damping values for the full-scale beams. The experimental results provide the correlations between modal parameters and structural damage. Then, the experimental natural

frequencies are used to determine the dynamic elastic moduli of the beam in different bending modes. Therefore, the vibration parameters of FFU composite beams are inevitably required for the development of a realistic dynamic model of a railway track capable of predicting its responses to impact loads stemmed from irregularities of the rail, wheel burns, and so on.


**Table 1.** Static properties of Fiber-reinforced Foamed Urethane (FFU) material.
