Investigation of Dynamic Responses and Vibration Serviceability of Temporary Grandstands by a 3 DOF Interaction Model due to Swaying Motion

Excessive vibration of temporary grandstand by the crowd has lateral rhythmic motions, which attracted increasing attention in the recent years. This paper focuses on experiments where a temporary grandstand occupied by 20 participants is oscillated by a shaking table with a series of random waves and the crowd-induced rhythmic swaying motions at lateral direction, respectively. The dynamic forces that were induced by participants who have swayed at 0.5–1.8 Hz are recorded by a tri-axial human biomechanics force plate. A new relationship between the annoyance rate and structural acceleration at logarithmic coordinate is investigated and proposed, and the swaying load model is given. Based on these experimental results, a simplified three-degree-of-freedom lumped dynamic model of the joint human–structure system is reinterpreted. Afterwards, combined with a feasible range of crowd/structural dynamic parameters, a series of interaction models are analyzed, the vibration dose value (VDV) of the structure is obtained and discussed, and the notable parameters for interaction model are predicted. The experimental results show that the lateral serviceability limit is 1.29 m/s1.75 and the upper boundary is 2.32 m/s1.75. The dynamic response of model indicated that the VDV of structure will be decreased with increasing the mass of static crowd and damping ratio of the dynamic crowd. The max response of the model is α ≤ 0.6, f2 = 1.8 Hz or α > 0.6, f2 = 1.5 Hz or f1 = 2.5–3.5 Hz. It may be used as a reference value in vibration safety and serviceability assessment of TDGs, to estimate realistically the vibration response on the occasions when the crowds are swaying.

Method of the Laboratory Wave Generation for Two Dimensional Hydraulic Model Experiment in the Coastal Engineering Fields: Case of Random Waves

The experiments in coastal engineering are very complex and a lot of components should be concerned. The experience has an important role in the successful execution. Hydraulic model experiments have been improved with the development of the wave generator and the advanced measuring apparatus. The hydraulic experiments have the advantage, that is, the stability of coastal structures and the hydraulic characteristics could be observed more intuitively rather than the numerical modelings. However, different experimental results can be drawn depending on the model scale, facilities, apparatus, and experimenters. In this study, two-dimensional hydraulic experiments were performed to suggest the guide of the test wave(random wave) generation, which is the most basic and important factor for the model test. The techniques for generating the random waves with frequency energy spectrum and the range for the incident wave height [(HS)M/(HS)T = 1~1.05] were suggested. The proposed guide for the test wave generation will contribute to enhancing the reliability of the experimental results in coastal engineering.

Spatial Variation of Wave Force Acting on a Vertical Detached Breakwater Considering Diffraction

In this study, the analytical solution for diffraction near a vertical detached breakwater was suggested by superposing the solutions of diffraction near a semi-infinite breakwater suggested previously using linear wave theory. The solutions of wave forces acting on front, lee and composed wave forces on both side were also derived. Relative wave amplitude changed periodically in space owing to the interactions between diffracting waves and standing waves on front side and the interactions between diffracting waves from both tips of a detached breakwater on lee side. The wave forces on a vertical detached breakwater were investigated with monochromatic, uni-directional random and multi-directional random waves. The maximum composed wave force considering the forces on front and lee side reached maximum 1.6 times of wave forces which doesn’t consider diffraction. This value is larger than the maximum composed wave force of semi-infinite breakwater considering diffraction, 1.34 times, which was suggested by Jung et al. (2021). The maximum composed wave forces were calculated in the order of monochromatic, uni-directional random and multi-directional random waves in terms of intensity. It was also found that the maximum wave force of obliquely incident waves was sometimes larger than that of normally incident waves. It can be known that the considerations of diffraction, the composed wave force on both front and lee side and incident wave angle are important from this study.

SET-UP DUE TO RANDOM WAVES: INFLUENCE OF THE DIRECTIONAL SPECTRUM

The correct estimation of set-up is very important to evaluate coastal hazard and to design coastal structures. In this paper, we derived a mathematical expression for wave set-up in the context of random waves. The solution to this expression assumes straight, parallel depth contours and constant average flow parameters in the longshore direction. We then investigated the effect of different types of sea state taking account of different frequency spectrum and spreading function assumed in the expression on estimates of wave set-up. We found the set-up was highly influenced by the frequency spectrum used. Finally, we applied this expression to estimate set-up values at locations in Italy and in the United States using buoy data provided by ISPRA (Istituto Superiore per la Protezione e la Ricerca Ambientale) and NDBC (National Data Buoy Centre).

Random vibration analysis with radial basis function neural networks

Random vibrations occur in many engineering systems including buildings subject to earthquake excitation, vehicles traveling on a rough road and off-shore platform in random waves. Analysis of random vibrations for linear systems has been well studied. For nonlinear systems, particularly for multi-degree-of-freedom systems, however, there are still many challenges including analyzing the probability distribution of transient responses of the system. Monte Carlo simulation was considered the only viable method for this task. In this paper, We propose a method to construct semi-analytical transient solutions of the probability distribution of transient responses of nonlinear systems by using the radial basis function neural networks. The activation functions consist of normalized Gaussian probability density functions. Two examples are presented to show the effectiveness of the proposed solution method. The transient probability distributions and response moments of these examples are presented, which have not been reported in the literature before.

On the variance of the nodal volume of arithmetic random waves

Rudnick and Wigman (2008) conjectured that the variance of the volume of the nodal set of arithmetic random waves on the d-dimensional torus is O ⁢ ( E / 𝒩 ) {O(E/\mathcal{N})} , as E → ∞ {E\to\infty} , where E is the energy and 𝒩 {\mathcal{N}} is the dimension of the eigenspace corresponding to E. Previous results have established this with stronger asymptotics when d = 2 {d=2} and d = 3 {d=3} . In this brief note we prove an upper bound of the form O ⁢ ( E / 𝒩 1 + α ⁢ ( d ) - ϵ ) {O(E/\mathcal{N}^{1+\alpha(d)-\epsilon})} , for any ϵ > 0 {\epsilon>0} and d ≥ 4 {d\geq 4} , where α ⁢ ( d ) {\alpha(d)} is positive and tends to zero with d. The power saving is the best possible with the current method (up to ϵ) when d ≥ 5 {d\geq 5} due to the proof of the ℓ 2 {\ell^{2}} -decoupling conjecture by Bourgain and Demeter.

SMALL-SCALE EQUIDISTRIBUTION OF RANDOM WAVES GENERATED BY AN UNFAIR COIN FLIP

In this paper we study the small-scale equidistribution property of random waves whose coefficients are determined by an unfair coin. That is, the coefficients take value $+1$ with probability p and $-1$ with probability $1-p$ . Random waves whose coefficients are associated with a fair coin are known to equidistribute down to the wavelength scale. We obtain explicit requirements on the deviation from the fair ( $p=0.5$ ) coin to retain equidistribution.

Model Test about Reflection Coefficient for Perforated Wall Caisson according to Perforated Wall Shapes: Single Chamber Open Slit Caisson

In this study, the hydraulic model tests for the single chamber perforated wall caisson were performed to investigate the reflection coefficients according to the slit shapes. The perforated wall with vertical and horizontal slits was applied to the tests. The random waves were used for the test by using Bretschneider-Mitsuyasu frequency spectrum. The similar reflection coefficients were measured in the vertical and horizontal slit caisson within a similar perforation ratio and area. The reflection coefficient according to relative slit length(S/Hs) was analyzed and the minimum reflection coefficients were measured in relatively small S/Hs (=2.7). The results from horizontal slits showed similar trends with those from the vertical slit perforated wall.