In this paper, a plane pendulum model is proposed to investigate the lateral vibration of a suspension bridge under crowd excitation. The plane model consists of two strings and a rigid body, which represent cables and the bridge deck, respectively. The lateral force induced by crowd is expressed as a cosine function with random phase. Comparing with other existing pedestrian-footbridge interaction models, the proposed model has two features: one is that the structural characteristics of the suspension bridge are taken into account. The other is that the expression of the lateral force induced by crowd has a unified form for different lateral bridge amplitudes. By numerically analyzing the solution stability of the plane model, we exhibit the whole changing process how a suspension bridge increases its lateral amplitude from small to large. It is shown that the worst case occurs when the lateral natural frequency of the bridge is half the lateral step frequency of the pedestrians. Based on the analysis results, the plane pendulum model can be easily used to explain why the central span of the London Millennium Bridge has large lateral oscillations at about 0.48&#x2009;Hz.

Lijun Ouyang

Bin Ding

Tingting Li

Bin Zhen

A Suspension Footbridge Model under Crowd-Induced Lateral Excitation

The stochastic averaging is applied to derive the random responses of the SDOF vibro-impact system with one-side wall under additive and multiplicative broadband noise, where the impact is described by the modified Hertzian contact model. Compared with the popular simplified “classical model” (i.e., <span class="nowrap"><svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-3.400761pt" id="M1" height="12.1541pt" version="1.1" viewBox="-0.0498162 -8.75334 47.1457 12.1541" width="47.1457pt"><g transform="matrix(.013,0,0,-0.013,7.262,-.222)"><path id="g117-11" d="M-161 571C-161 600 -183 623 -212 623C-238 623 -262 600 -262 571C-262 544 -238 520 -212 520C-183 520 -161 544 -161 571Z"/></g><g transform="matrix(.013,0,0,-0.013,0,0)"><path id="g113-121" d="M536 404C536 423 520 448 491 448C445 448 398 404 308 283L286 338C255 416 242 448 217 448C182 448 138 402 92 341L111 321C149 368 169 378 178 378C188 378 198 363 214 320L254 212C185 117 138 65 107 65C98 65 85 69 82 75C79 82 73 86 65 86C44 86 23 60 23 39C23 7 44 -12 71 -12C119 -12 168 33 265 177L306 61C321 17 347 -12 373 -12C413 -12 465 33 507 96L491 119C459 84 432 60 413 60C395 60 378 92 358 148L321 250C341 279 369 310 389 332C417 363 439 382 456 382C466 382 475 376 481 368C486 361 492 358 496 358C513 358 536 381 536 404Z"/></g><g transform="matrix(.0091,0,0,-0.0091,7.202,3.132)"><path id="g54-33" d="M556 236V289H56V236H556Z"/></g><g transform="matrix(.013,0,0,-0.013,16.94,0)"><path id="g117-34" d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z"/></g><g transform="matrix(.013,0,0,-0.013,28.203,0)"><path id="g113-115" d="M393 379C402 394 400 411 393 422C384 437 365 448 348 448C301 448 237 372 186 285H182L193 335C210 408 205 448 178 448C150 448 80 402 29 344L45 321C80 355 114 373 122 373C128 373 130 365 124 330C106 228 76 98 50 -5L57 -12C82 -5 112 3 132 6L172 203C196 256 234 304 254 329C275 355 293 367 306 367C318 367 330 360 342 348C347 343 355 343 365 350S386 367 393 379Z"/></g><g transform="matrix(.013,0,0,-0.013,40.953,-.222)"><use xlink:href="#g117-11"/></g><g transform="matrix(.013,0,0,-0.013,33.691,0)"><use xlink:href="#g113-121"/></g><g transform="matrix(.0091,0,0,-0.0091,40.893,3.132)"><path id="g54-36" d="M556 236V289H337V504H275V289H56V236H275V-4H337V236H556Z"/></g></svg>),</span> the whole impact process is captured by the modified Hertzian contact model without any assumptions. One example is given to illustrate the proposed technique. The comparison between the analytical results and those from Monte Carlo simulations manifests the accuracy of the proposed technique. It should be pointed out that the technique proposed in this paper is powerful for the cases of weak excitation and big enough bandwidth of the broadband noise. Finally, the influences of various parameters are also discussed in detail.

S. W. Guan

Q. Ling

M. Xu

Stochastic Responses for the Vibro-Impact System under the Broadband Noise

Since the load of electrohydraulic servo shaking table is an elastic load, there is a mutual coupling effect that exists between the experimental object and the shaking table, forming the resonance to weaken the dynamic characteristics, and producing resonant peak and resonant valley in the bandwidth required by the system, in which the amplitude is often larger than the stability range of acceleration&#x2019;s amplitude. In this paper, the mathematical modeling of hydraulic power mechanism in a two-mass dynamic system is established based on electrohydraulic servo shaking table, yielding the frequency characteristic curve in accordance with the transfer function of the model. A multifrequency adaptive notch filter based on the least mean square algorithm is proposed to suppress the resonance, and the suppression effect of the resonance is simulated and verified in line with various values of load stiffness. Finally, the power spectrum is used to demonstrate the effectiveness of the multifrequency adaptive notch filter in the resonant suppression.

Tao Wang

Jinchun Song

Study on the Resonant Suppression of Electrohydraulic Servo Shaking Table of a 2-Mass Dynamic System

Tapered thin-walled structures have been widely used in wind turbine and rotor blade. In this paper, a spectral finite element model is developed to investigate tapered thin-walled beam structures, in which torsion related warping effect is included. First, a set of fully coupled governing equations are derived using Hamilton&#x2019;s principle to account for axial, bending, and torsion motion. Then, the differential transform method (DTM) is applied to obtain the semianalytical solutions in order to formulate the spectral finite element. Finally, numerical simulations are conducted for tapered thin-walled wind turbine rotor blades and validated by the ANSYS. Modal frequency results agree well with the ANSYS predictions, in which approximate 30,000 shell elements were used. In the SFEM, one single spectral finite element is needed to perform such calculations because the interpolation functions are deduced from the exact semianalytical solutions. Coupled axial-bending-torsion mode shapes are obtained as well. In summary, the proposed spectral finite element model is able to accurately and efficiently to perform the modal analysis for tapered thin-walled rotor blades. These modal frequency and mode shape results are important to carry out design and performance evaluation of the tapered thin-walled structures.

Yiping Shen

Zhijun Zhu

Songlai Wang

Gang Wang

Dynamic Analysis of Tapered Thin-Walled Beams Using Spectral Finite Element Method

Ground deformation observation is wildly concerned in the field of earthquake engineering. This paper proposes a high-precision displacement measurement technology based on both computer vision and numerical simulation. During the earthquake, the vision-based testing system collects visual data of the target installed on the location to be observed. The visual data streams can be quantified to the dynamic relative displacement value automatically, by employing mathematical vision algorithms and then by taking the relative displacement as an intermediate quantity, which is brought into the numerical model for iteration. When the test result is close to the simulated one, the absolute ground displacement data could be obtained approximately. A series of experiments have been carried out to suggest that the proposed method presents an innovative and low-cost solution to ground measurement in high accuracy. The method not only realizes the real-time ground deformation observation; moreover, it also provides a wider range of reliable data support to understand deformation mechanism, investigate seismic source information, and recognize the ground motion characteristics.

Chen Su

Zhao Sicheng

Dai Zhijun

Li Xiaojun

Zhou Yue

Visual Identity-Based Earthquake Ground Displacement Testing Method

In this paper, it is described how the matrix mixing model updating technique can be combined with the local correspondence (LC) mode shape expansion algorithm, to give a new finite element (FE) model updating method. The matrix mixing method uses that the inverse mass and stiffness matrices can be expressed as a linear combination of outer products of FE mode shape vectors, where the low-frequency part of these sums are substituted with expanded test modes. The approach is meant to update FE models in one-step and is exact, except for the following two approximations: the mode shape smoothing and the mass scaling of the expanded experimental mode shapes. A simulation study illustrates the errors from the two approximations and shows the ability of the technique to improve the modal assurance criterion (MAC) values so that they get very close to unity. Finally, the performance of the proposed updating method is assessed by means of an application example in which the FE model is updated based on the test modes of a real structure.

Martin &#x00D8;. &#x00D8;. Jull

Sandro D. R. Amador

Anders Skafte

Jannick B. Hansen

Manuel L. Aenlle

Rune Brincker

One-Step FE Model Updating Using Local Correspondence and Mode Shape Orthogonality

About this journal

<p><em>Shock and Vibration</em> publishes papers on all aspects of shock and vibration, especially in relation to civil, mechanical and aerospace engineering applications, as well as transport, materials and geoscience.&nbsp;</p>


Journal profile

Meet the editorial board

<p>Chief Editor&nbsp;Dr Tai Thai&nbsp;is based at the University of Melbourne and his current research focuses on high strength materials for sustainable construction of buildings, bridges and other infrastructure.</p>


Editor spotlight

Submit to Special Issue

We currently have a number of Special Issues open for submission. Special Issues highlight emerging areas of research within a field, or provide a venue for a deeper investigation into an existing research area.

Special Issues

Author guidelines

Editorial board

Databases and indexing

Shock and Vibration - Table of contents 2019

title

Shock and Vibration publishes papers on all aspects of shock and vibration, especially in relation to civil, mechanical and aerospace engineering applications, as well as transport, materials and geoscience. 

Shock and Vibration