Analytical and Numerical Study on a Parametric Pendulum with the Step-Wave Modulation of Length and Forcing

2019 ◽  
Vol 19 (05) ◽  
pp. 1941006
Author(s):  
Paweł Olejnik ◽  
Michal Fečkan ◽  
Jan Awrejcewicz

A parametric pendulum excited by a discrete wave-modulated step function of length is subjected to a mathematical analysis and numerical modeling. We observe an existence of almost periodic solutions of ordinary differential equations with linear boundary value conditions. An exemplary oscillator subject to both an almost periodic step elongation and forcing synchronizes with the forcing, tending to almost periodic motions like stable limit cycles. Conditions for that synchronization as well as trajectories of numerical solutions on time history plots and phase planes are shown to confirm correctness of the analytical derivations and dedicated numerical modeling.

2021 ◽  
Vol 11 (7) ◽  
pp. 3190
Author(s):  
Edmundo Schanze ◽  
Gilberto Leiva ◽  
Miguel Gómez ◽  
Alvaro Lopez

Engineering practitioners do not usually include soil–structure interactions in building design; rather, it is common to model and design foundations as embedded joints with joint–based reactions. In some cases, foundation structures are modeled as rigid bodies, embedding the first story into lower vertical elements. Given that the effects of underground floors on the seismic response are not generally included in current building design provisions, it has been little explored in the literature. This work compares and analyzes models to study the effects of different underground stories modeling approaches using earthquake vibration data recorded for the 16–story Alcazar building office in downtown Viña del Mar (Chile). The modeling expands beyond an embedded first story structure to soil with equivalent springs, representing soil–structure interaction (SSI), with varying rigid soil homogeneity. The building was modeled in a finite element software considering only dead load as a static load case because the structure remained in the framing stage when the monitoring system was operating. The instruments registered 72 aftershocks from the 2010 Maule Earthquake, and this study focused on 11 aftershocks of different hypocenters and magnitudes to collect representative information. The comparisons between empirical records and models in this study showed a better fit between the model and the real vibration data for the models that do consider the SSI using horizontal springs attached to the retaining walls of the underground stories. In addition, it was observed that applying a stiffness reduction factor of 0.7 to all elements in deformation verification models for average–height buildings was suitable to analyze the behavior under small earthquakes; better results are obtained embedding the structure in the foundation level than embedding in the street level; the use of horizontal springs with Kuesel’s model with traction for the analysis of the structure yields appropriate results; it is necessary to carefully select the spring constants to be used, paying special attention to the vertical springs. Even though the results presented herein indicate that the use of vertical springs to simulate the SSI of the base slab can result in major differences concerning the real response, it is necessary to obtain more data from instrumentation across a wider variety of structures to continue to evaluate better design and modeling practices. Similarly, further analyses, including nonlinear time–history and high–intensity events, are needed to best regulate building design.


Vibration ◽  
2021 ◽  
Vol 4 (2) ◽  
pp. 422-445
Author(s):  
Md Riasat Azim ◽  
Mustafa Gül

Railway bridges are an integral part of any railway communication network. As more and more railway bridges are showing signs of deterioration due to various natural and artificial causes, it is becoming increasingly imperative to develop effective health monitoring strategies specifically tailored to railway bridges. This paper presents a new damage detection framework for element level damage identification, for railway truss bridges, that combines the analysis of acceleration and strain responses. For this research, operational acceleration and strain time-history responses are obtained in response to the passage of trains. The acceleration response is analyzed through a sensor-clustering-based time-series analysis method and damage features are investigated in terms of structural nodes from the truss bridge. The strain data is analyzed through principal component analysis and provides information on damage from instrumented truss elements. A new damage index is developed by formulating a strategy to combine the damage features obtained individually from both acceleration and strain analysis. The proposed method is validated through a numerical study by utilizing a finite element model of a railway truss bridge. It is shown that while both methods individually can provide information on damage location, and severity, the new framework helps to provide substantially improved damage localization and can overcome the limitations of individual analysis.


1989 ◽  
Vol 209 ◽  
pp. 285-308 ◽  
Author(s):  
R. J. Bodonyi ◽  
W. J. C. Welch ◽  
P. W. Duck ◽  
M. Tadjfar

A numerical study of the generation of Tollmien-Schlichting (T–S) waves due to the interaction between a small free-stream disturbance and a small localized variation of the surface geometry has been carried out using both finite–difference and spectral methods. The nonlinear steady flow is of the viscous–inviscid interactive type while the unsteady disturbed flow is assumed to be governed by the Navier–Stokes equations linearized about this flow. Numerical solutions illustrate the growth or decay of the T–S waves generated by the interaction between the free-stream disturbance and the surface distortion, depending on the value of the scaled Strouhal number. An important result of this receptivity problem is the numerical determination of the amplitude of the T–S waves.


1983 ◽  
Vol 105 (4) ◽  
pp. 862-869 ◽  
Author(s):  
R. S. Amano ◽  
M. K. Jensen ◽  
P. Goel

An experimental and numerical study is reported on heat transfer in the separated flow region created by an abrupt circular pipe expansion. Heat transfer coefficients were measured along the pipe wall downstream from an expansion for three different expansion ratios of d/D = 0.195, 0.391, and 0.586 for Reynolds numbers ranging from 104 to 1.5 × 105. The results are compared with the numerical solutions obtained with the k ∼ ε turbulence model. In this computation a new finite difference scheme is developed which shows several advantages over the ordinary hybrid scheme. The study also covers the derivation of a new wall function model. Generally good agreement between the measured and the computed results is shown.


Author(s):  
Albert C. J. Luo ◽  
Bo Yu

In this paper, galloping vibrations of a lightly iced transmission line are investigated through a two-degree-of-freedom (2-DOF) nonlinear oscillator. The 2-DOF nonlinear oscillator is used to describe the transverse and torsional motions of the galloping cables. The analytical solutions of periodic motions of galloping cables are presented through generalized harmonic balanced method. The analytical solutions of periodic motions for the galloping cable are compared with the numerical solutions, and the corresponding stability and bifurcation of periodic motions are analyzed by the eigenvalues analysis. To demonstrate the accuracy of the analytical solutions of periodic motions, the harmonic amplitudes are presented. This investigation will help one better understand galloping mechanism of iced transmission lines.


2010 ◽  
Vol 132 (5) ◽  
Author(s):  
Seok-Ki Choi ◽  
Seong-O Kim ◽  
Hoon-Ki Choi

A numerical study for the evaluation of heat transfer correlations for sodium flows in a heat exchanger of a fast breeder nuclear reactor is performed. Three different types of flows such as parallel flow, cross flow, and two inclined flows are considered. Calculations are performed for these three typical flows in a heat exchanger changing turbulence models. The tested turbulence models are the shear stress transport (SST) model and the SSG-Reynolds stress turbulence model by Speziale, Sarkar, and Gaski (1991, “Modelling the Pressure-Strain Correlation of Turbulence: An Invariant Dynamical System Approach,” J. Fluid Mech., 227, pp. 245–272). The computational model for parallel flow is a flow past tubes inside a circular cylinder and those for the cross flow and inclined flows are flows past the perpendicular and inclined tube banks enclosed by a rectangular duct. The computational results show that the SST model produces the most reliable results that can distinguish the best heat transfer correlation from other correlations for the three different flows. It was also shown that the SSG-RSTM high-Reynolds number turbulence model does not deal with the low-Prandtl number effect properly when the Peclet number is small. According to the present calculations for a parallel flow, all the old correlations do not match with the present numerical solutions and a new correlation is proposed. The correlations by Dwyer (1966, “Recent Developments in Liquid-Metal Heat Transfer,” At. Energy Rev., 4, pp. 3–92) for a cross flow and its modified correlation that takes into account of flow inclination for inclined flows work best and are accurate enough to be used for the design of the heat exchanger.


Author(s):  
Saeed Onsorynezhad ◽  
Amin Abedini ◽  
Fengxia Wang

In this work, an impact based frequency up-conversion mechanism is studied via discontinuous dynamics analysis. The mechanism consists of a moving stopper and a piezoelectric beam. The repeated free vibration of the piezoelectric beam achieved through the impaction between the stopper and the beam, With the stopper excited by a sawtooth wave. Due to the impact, the system contains complex discontinuous dynamics, hence to better understand the energy harvesting performance of the piezoelectric beam, we seek the simple periodic motions of the system. As the system parameter varies, the output voltage and power of the piezoelectric beam with periodic motions is obtained. These results were also compared with those obtained when the piezoelectric beam is directly subjected to the same sawtooth wave. The piezoelectric beam was modeled as a mass-spring-damper system, and the linear piezoelectric constitutive equations have been used to obtain the lumped model of the piezoelectric beam. In this study, numerical solutions of the generated power and voltage were obtained via discontinuous dynamics analysis. When the excitation frequency is low, the effect of frequency-up-conversion is demonstrated by comparing the generated power of two cases: piezoelectric beam excited via impact and beam directly subject to the sawtooth wave. The stable and unstable periodic motions and bifurcation trees of the impact parameters are predicted analytically versus varying excitation frequency for period-1 and period-2.


2018 ◽  
Vol 174 ◽  
pp. 04003 ◽  
Author(s):  
Tomasz Maleska ◽  
Damian Beben

The design codes and calculation methods related to the corrugated steel plate (CSP) bridges and culverts say only on the minimum soil height. This value is connected with the bridge span and shell height. In the case of static and dynamic loads (like passing the vehicles), such approach seems to be reasonable. However, it is important to know how the CSP bridges with high the soil covers behave under the seismic loads. This paper is presented the result of numerical study of CSP bridge with different high cover under seismic excitation. The analysed CSP railway bridge in the cross section has two closed pipe-arches. The span of shells is 4.40 m and the height of shells is 2.80 m. The load-carrying structure was constructed as two shells assembled from CSP sheets, designed with a depth of 0.05 m, pitch of 0.15 m, and plate thickness of 0.003 m. The real soil cover depth over the CSP structure (including ballast, blanket and backfill) equals 2.40 m. In this study two heights of soil cover were analysed (2.40 m and 5.00 m). Numerical analysis was conducted using the DIANA program based on finite element method (FEM). A linear model with El Centro records and Time History was used to analyse the problem.


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