Study of flexural wave propagation through a cable stayed beam subjected to a moving load

A physical perspective of the propagation and attenuation of flexural waves is presented in this paper for the dynamic behaviors of cable stayed beams subjected to a moving load. Based on the method of reverberation-ray matrix (MRRM), the waveform solutions of the wave equations of a simplified beam-cable system subjected to a moving load (hereinafter referred to as a beam-cable system) are given, and the theory is verified by a numerical example. The dynamic response of cable stayed beams is decomposed into nine kinds of flexural waves, including traveling waves, near-field waves, and nondispersive waves, according to the wavenumber characteristics. Numerical examples are analyzed to demonstrate the propagation characteristics of flexural waves through cable stayed beams. Numerical results show that the flexural waves in the cable stayed beams are mainly low-frequency waves whose frequencies are less than 3 times the structural fundamental frequency, which can be used to further improve the computational efficiency of response analysis method based on MRRM, and the proportion of high-frequency components increases gradually with increasing structural stiffness. The near-field wave can be transformed into a traveling shear wave when its frequency is larger than the critical frequency, which decreases with increasing radius of gyration and decreasing elastic modulus of the beam. With the increase in the radius of gyration and the elastic modulus of the beam, the attenuation effect of the near-field wave weakens. The wave velocity and the wave dispersion effect have a positive correlation with the stiffness-related parameters of the beam-cable system. The study of the effect of the beam-cable system parameters on flexural wave propagation characteristics can be applied to achieve a better dynamic design for engineering structures.

Flexural band gaps and vibration control of a periodic railway track

Periodic structures exhibit unique band gap characteristics by virtue of which they behave as vibro-acoustic filters thereby allowing only waves within a certain frequency range to pass through. In this paper, lateral and vertical flexural wave propagation and vibration control of a railway track periodically supported on rigid sleepers using fastenings are studied in depth. The dispersion relations in both lateral and vertical directions are obtained using the Floquet-Bloch theorem and the resulting dispersion curves are verified using finite element models. Afterwards, tuned mass dampers (TMDs) with different mass ratios are designed to control vibrations of the examined rail in both the directions. Moreover, the influence of damping of rail and resonators on band gap characteristics is investigated. As a replacement to the conventional TMD, a novel possibility to control vibration relies on using another existing rail as a lateral distributed resonator (LDR). Although the effectiveness of LDR is lower than that of localized resonators, the former represents a simple and promising way to control vibrations. Efficacy of the proposed control methods is finally verified by applying a random Gaussian white noise input. The study presented here is useful to understand the propagation and attenuation behavior of flexural waves and to develop efficient and novel vibration control strategies for track structures.

Low-frequency broadband vibration attenuation of sandwich plate-type metastructures with periodic thin-wall tube cores

Sandwich structures are widely applied in modern industry such as aerospace, automobile as well as marine structures. However, the vibroacoustic properties of sandwich structures are adversely influenced by low effective mass. In this study, the flexural wave propagation characteristics and vibration mitigation performances of the periodic sandwich plate-type metastructures are investigated. The proposed sandwich plate-type metastructures are constituted of a sandwich plate with periodic thin-wall circular tube cores and periodically attached local stepped resonators. A finite element method combining Solid-Shell coupling numerical method and Bloch theory is presented to calculate the dispersion relations and the displacement fields of the eigenmodes of the infinite periodic sandwich plate-type metastructures. In addition, the acceleration frequency responses and vibration attenuation performances of finite periodic sandwich plate-type metastructures are numerically investigated and compared with the experimental measurements. Furthermore, the influences of geometric parameters on flexural wave band gaps are conducted. Results show that the sandwich plate-type metastructures can yield a low-frequency broad flexural wave band gap, in which the flexural wave propagation is conspicuously suppressed, resulting in significant flexural vibration attenuation. The flexural wave band gap and vibration attenuation performances can be effectively manipulated by designing geometric parameters of the sandwich plate-type metastructures.

Flexural Band Gaps and Vibration Control of a Periodic Railway Track

Periodic structures exhibit unique band gap characteristics by virtue of which they behave as vibro-acoustic filters thereby allowing only waves within a certain frequency range to pass through. In this paper, both lateral and vertical flexural wave propagation and vibration control of a periodic railway track are studied in depth. More precisely, a rail fastened on rigid sleeper blocks is modeled with an Euler-Bernoulli beam. The dispersion relations in both lateral and vertical directions are obtained using the Floquet-Bloch theorem and the resulting dispersion curves are verified using finite element (FE) models. Afterwards, tuned mass dampers (TMDs) with different mass ratios are designed to control vibrations of the examined rail along both lateral and vertical directions. Moreover, the influence of damping of rail and resonators on band structures is investigated. As a replacement to the conventional TMD, a novel possibility to control vibrations relies on using another rail as a lateral distributed resonator (LDR). Although the effectiveness of LDR is lower than that of localized resonators, the former represents a simple and promising way to control vibrations. Efficacy of the proposed control methods is finally verified using the results of transient simulation based on a random Gaussian white noise input.

Modelling flexural wave propagation by the nonlocal strain gradient elasticity with fractional derivatives

The flexural wave propagation in a microbeam is studied based upon the nonlocal strain gradient model with the spatial and time fractional order differentials in the present work. To capture the dispersive behaviour induced by the inherent nanoscale heterogeneity, the stress gradient elasticity and the strain gradient elasticity are often used to model the mechanical behaviour. The present model incorporates the two models and introduces the fractional order derivatives which can be understood as a generalization of integral order nonlocal strain gradient model. The Laplacian operator in the constitutive equation is replaced with the symmetric Caputo fractional differential in the present model. To illustrate the flexibility of the present model, the flexural wave propagation in a microbeam is studied. The fractional order in the present model as a new material parameter can be adjusted appropriately to describe the dispersive properties of the flexural waves. The numerical results based on the new nonlocal strain gradient elasticity with fractional order derivatives are provided for both Euler–Bernoulli beam and Timoshenko beam. The comparisons with the integer order nonlocal strain gradient model and the molecular dynamic simulation are performed to validate the flexibility of the fractional order nonlocal strain gradient model.