scholarly journals Nonlinear Behaviour of Concrete Buttress Dams under High-Frequency Excitations Taking into Account Topographical Amplifications

2021 ◽  
Vol 2021 ◽  
pp. 1-22
Author(s):  
Roghayeh Abbasiverki ◽  
Richard Malm ◽  
Anders Ansell ◽  
Erik Nordström
Keyword(s):  
Finite Element ◽  
Wave Propagation ◽  
High Frequency ◽  
Free Field ◽  
Low Frequency ◽  
Nonlinear Behaviour ◽  
One Dimensional ◽  
Field Modelling ◽  
Stream Direction ◽  
Modelling Approach

Concrete buttress dams could potentially be susceptible to high-frequency vibrations, especially in the cross-stream direction, due to their slender design. Previous studies have mainly focused on low-frequency vibrations in stream direction using a simplified foundation model with the massless method, which does not consider topographic amplifications. This paper therefore investigates the nonlinear behaviour of concrete buttress dams subjected to high-frequency excitations, considering cross-stream vibrations. For comparison, the effect of low-frequency excitations is also investigated. The influence of the irregular topography of the foundation surface on the amplification of seismic waves at the foundation surface and thus in the dam is considered by a rigorous method based on the domain-reduction method using the direct finite element method. The sensitivity of the calculated response of the dam to the free-field modelling approach is investigated by comparing the result with analyses using an analytical method based on one-dimensional wave propagation theory and a massless approach. Available deconvolution software is based on the one-dimensional shear wave propagation to transform the earthquake motion from the foundation surface to the corresponding input motion at depth. Here, a new deconvolution method for both shear and pressure wave propagation is developed based on an iterative time-domain procedure using a one-dimensional finite element column. The examples presented showed that topographic amplifications of high-frequency excitations have a significant impact on the response of this type of dam. Cross-stream vibrations reduced the safety of the dam due to the opening of the joints and the increasing stresses. The foundation modelling approach had a significant impact on the calculated response of the dam. The massless method produced unreliable results, especially for high-frequency excitations. The free-field modelling with the analytical method led to unreliable joint openings. It is therefore recommended to use an accurate approach for foundation modelling, especially in cases where nonlinearity is considered.

Numerical analysis of kinematic response of single piles

2000 ◽  
Vol 37 (6) ◽  
pp. 1368-1382 ◽  
Author(s):  
Kevin J Bentley ◽  
M Hesham El Naggar
Keyword(s):  
Finite Element ◽  
Human Life ◽  
Free Field ◽  
Time History ◽  
Benchmark Problems ◽  
Soil Parameters ◽  
Nonlinear Behaviour ◽  
Pile Head ◽  
Element Mesh ◽  
Single Piles

Recent destructive earthquakes have highlighted the need for increased research into the revamping of design codes and building regulations to prevent further catastrophic losses in terms of human life and economic assets. The present study investigated the response of single piles to kinematic seismic loading using the three-dimensional finite element program ANSYS. The objectives of this study were (i) to develop a finite element model that can accurately model the kinematic soil–structure interaction of piles, accounting for the nonlinear behaviour of the soil, discontinuity conditions at the pile–soil interface, energy dissipation, and wave propagation; and (ii) to use the developed model to evaluate the kinematic interaction effects on the pile response with respect to the input ground motion. The static performance of the model was verified against exact available solutions for benchmark problems including piles in elastic and elastoplastic soils. The geostatic stresses were accounted for and radiating boundaries were provided to replicate actual field conditions. Earthquake excitation with a low predominant frequency was applied as an acceleration–time history at the base bedrock of the finite element mesh. To evaluate the effects of the kinematic loading, the responses of both the free-field soil (with no piles) and the pile head were compared. It was found that the effect of the response of piles in elastic soil was slightly amplified in terms of accelerations and Fourier amplitudes. However, for elastoplastic soil with separation allowed, the pile head response closely resembled the free-field response to the low-frequency seismic excitation and the range of pile and soil parameters considered in this study.Key words: numerical modelling, dynamic, lateral, piles, kinematic, seismic.

Sensitivity to Interaural Temporal Disparities of Low- and High-Frequency Neurons in the Superior Olivary Complex. I. Heterogeneity of Responses

1997 ◽  
Vol 78 (3) ◽  
pp. 1222-1236 ◽  
Author(s):  
Ranjan Batra ◽  
Shigeyuki Kuwada ◽  
Douglas C. Fitzpatrick
Keyword(s):  
Fine Structure ◽  
High Frequency ◽  
Complex I ◽  
General Trend ◽  
Free Field ◽  
Low Frequency ◽  
Superior Olivary Complex ◽  
Field Range ◽  
Multiple Units ◽  
Additional Phase

Batra, Ranjan, Shigeyuki Kuwada, and Douglas C. Fitzpatrick. Sensitivity to interaural temporal disparities of low- and high-frequency neurons in the superior olivary complex. I. Heterogeneity of responses. J. Neurophysiol. 78: 1222–1236, 1997. Interaural temporal disparities (ITDs) are a cue for localization of sounds along the azimuth. Listeners can detect ITDs in the fine structure of low-frequency sounds and also in the envelopes of high-frequency sounds. Sensitivity to ITDs originates in the main nuclei of the superior olivary complex (SOC), the medial and lateral superior olives (MSO and LSO, respectively). This sensitivity is believed to arise from bilateral excitation converging on neurons of the MSO and ipsilateral excitation converging with contralateral inhibition on neurons of the LSO. Here we investigate whether the sensitivity of neurons in the SOC to ITDs can be adequately explained by one of these two mechanisms. Single and multiple units ( n = 124) were studied extracellularly in the SOC of unanesthetized rabbits. We found units that were sensitive to ITDs in the fine structure of low-frequency (<2 kHz) tones and also units that were sensitive to ITDs in the envelopes of sinusoidally amplitude-modulated high-frequency tones. For both categories there were “peak-type” units that discharged maximally at a particular ITD across frequencies or modulation frequencies. These units were consistent with an MSO-type mechanism. There were also “trough-type” units that discharged minimally at a particular ITD. These units were consistent with an LSO-type mechanism. There was a general trend for peak-type units to be located in the vicinity of the MSO and for trough-type units to be located in the vicinity of the LSO. Units of both types appeared to encode ITDs within the estimated free-field range of the rabbit (±300 μs). Many units had varying degrees of irregularities in their responses, which manifested themselves in one of two ways. First, for some units there was no ITD at which the response was consistently maximal or minimal across frequencies. Instead there was an ITD at which the unit consistently responded at some intermediate level. Second, a unit could display considerable jitter from frequency to frequency in the ITD at which it responded maximally or minimally. Units with irregular responses had properties that were continuous with those of other units. They therefore appeared to be variants of peak- and trough-type units. The irregular responses could be modeled by assuming additional phase-locked inputs to a neuron in the MSO or LSO. The function of irregularities may be to shift the ITD sensitivity of a neuron without requiring changes in the anatomic delays of its inputs.

Fundamental Understanding of Wave Propagation in a Beam Using PZT Actuators and Sensors

2013 ◽  
Author(s):  
Vishnu Prasad Venugopal ◽  
Gang Wang
Keyword(s):  
Finite Element ◽  
Wave Propagation ◽  
Finite Elements ◽  
Timoshenko Beam ◽  
High Frequency ◽  
Beam Structure ◽  
Frequency Wave ◽  
Coupled Equations ◽  
High Frequency Wave ◽  
Spectral Finite Element

Embedded smart actuators/sensors, such as piezoelectric types, have been used to conduct wave transmission and reception, pulse-echo, pitch-catch, and phased array functions in order to achieve in-situ nondestructive evaluation for different structures. By comparing to baseline signatures, the damage location, amount, and type can be determined. Typically, this methodology does not require analytical structural models and interrogation algorithm is carefully designed with little wave propagation knowledge of the structure. However, the wave excitation frequency, waveform, and other signal characteristics must be comprehensively considered to effectively conduct diagnosis of incipient forms of damage. Accurate prediction of high frequency wave response requires a prohibitively large number of conventional finite elements in the structural model. A new high fidelity approach is needed to capture high frequency wave propagations in a structure. In this paper, a spectral finite element method (SFEM) is proposed to characterize wave propagations in a beam structure under piezoelectric material (i.e., PZT) actuation/sensing. Mathematical models are developed to account for both Uni-morph and bi-morph configurations, in which PZT layers are modeled as either an actuator or a sensor. The Timoshenko beam theory is adopted to accommodate high frequency wave propagations, i.e., 20–200 KHz. The PZT layer is modeled as a Timoshenko beam as well. Corresponding displacement compatibility conditions are applied at interfaces. Finally, a set of fully coupled governing equations and associated boundary conditions are obtained when applying the Hamilton’s principle. These electro-mechanical coupled equations are solved in the frequency domain. Then, analytical solutions are used to formulate the spectral finite element model. Very few spectral finite elements are required to accurately capture the wave propagation in the beam because the shape functions are duplicated from exact solutions. Both symmetric and antisymmetric mode of lamb waves can be generated using bimorph or uni-morph actuation. Comprehensive simulations are conducted to determine the beam wave propagation responses. It is shown that the PZT sensor can pick up the reflected waves from beam boundaries and damages. Parametric studies are conducted as well to determine the optimal actuation frequency and sensor sensitivity. Such information helps us to fundamentally understand wave propagations in a beam structure under PZT actuation and sensing. Our SFEM predictions are validated by the results in the literature.

scholarly journals Longitudinal wave propagation in a one-dimensional quasi-periodic waveguide

2019 ◽  
Vol 475 (2231) ◽  
pp. 20190392
Author(s):  
Vladislav S. Sorokin
Keyword(s):  
Wave Propagation ◽  
Wave Attenuation ◽  
Periodic Structures ◽  
Low Frequency ◽  
Periodic Waveguide ◽  
One Dimensional ◽  
Vibration Attenuation ◽  
Direct Separation ◽  
Longitudinal Wave Propagation ◽  
Spatial Modulations

The paper deals with the analysis of wave propagation in a general one-dimensional (1D) non-uniform waveguide featuring multiple modulations of parameters with different, arbitrarily related, spatial periods. The considered quasi-periodic waveguide, in particular, can be viewed as a model of pure periodic structures with imperfections. Effects of such imperfections on the waveguide frequency bandgaps are revealed and described by means of the method of varying amplitudes and the method of direct separation of motions. It is shown that imperfections cannot considerably degrade wave attenuation properties of 1D periodic structures, e.g. reduce widths of their frequency bandgaps. Attenuation levels and frequency bandgaps featured by the quasi-periodic waveguide are studied without imposing any restrictions on the periods of the modulations, e.g. for their ratio to be rational. For the waveguide featuring relatively small modulations with periods that are not close to each other, each of the frequency bandgaps, to the leading order of smallness, is controlled only by one of the modulations. It is shown that introducing additional spatial modulations to a pure periodic structure can enhance its wave attenuation properties, e.g. a relatively low-frequency bandgap can be induced providing vibration attenuation in frequency ranges where damping is less effective.

The Wavelet Spectral Finite Element-based user-defined element in Abaqus for wave propagation in one-dimensional composite structures

SIMULATION ◽  
2017 ◽  
Vol 93 (5) ◽  
pp. 397-408 ◽  
Author(s):  
Ashkan Khalili ◽  
Ratneshwar Jha ◽  
Dulip Samaratunga
Keyword(s):  
Finite Element ◽  
Wave Propagation ◽  
Composite Structures ◽  
Impact Damage ◽  
Shear Deformation Theory ◽  
Frequency Wave ◽  
One Dimensional ◽  
Finite Element Software ◽  
Model Complex ◽  
Spectral Finite Element

A Wavelet Spectral Finite Element (WSFE)-based user-defined element (UEL) is formulated and implemented in Abaqus (commercial finite element software) for wave propagation analysis in one-dimensional composite structures. The WSFE method is based on the first-order shear deformation theory to yield accurate and computationally efficient results for high-frequency wave motion. The frequency domain formulation of the WSFE leads to complex-valued parameters, which are decoupled into real and imaginary parts and presented to Abaqus as real values. The final solution is obtained by forming a complex value using the real number solutions given by Abaqus. Four numerical examples are presented in this article, namely an undamaged beam, a beam with impact damage, a beam with a delamination, and a truss structure. A multi-point constraint subroutine, defining the connectivity between nodes, is developed for modeling the delamination in a beam. Wave motions predicted by the UEL correlate very well with Abaqus simulations. The developed UEL largely retains the computational efficiency of the WSFE method and extends its ability to model complex features.

scholarly journals A High-Frequency Model of a Circular Beam with a T-Shaped Cross Section

Acoustics ◽  
2019 ◽  
Vol 1 (1) ◽  
pp. 295-336
Author(s):  
Andrew Hull ◽  
Daniel Perez
Keyword(s):  
Finite Element ◽  
Wave Propagation ◽  
Cross Section ◽  
High Frequency ◽  
Algebraic Equations ◽  
Frequency Range ◽  
Linear Algebraic Equations ◽  
Circular Beam ◽  
The Web ◽  
Shaped Cross Section

This paper derives an analytical model of a circular beam with a T-shaped cross section for use in the high-frequency range, defined here as approximately 1 to 50 kHz. The T-shaped cross section is composed of an outer web and an inner flange. The web in-plane motion is modeled with two-dimensional elasticity equations of motion, and the left portion and right portion of the flange are modeled separately with Timoshenko shell equations. The differential equations are solved with unknown wave propagation coefficients multiplied by Bessel and exponential spatial domain functions. These are inserted into constraint and equilibrium equations at the intersection of the web and flange and into boundary conditions at the edges of the system. Two separate cases are formulated: structural axisymmetric motion and structural non-axisymmetric motion and these results are added together for the total solution. The axisymmetric case produces 14 linear algebraic equations and the non-axisymmetric case produces 24 linear algebraic equations. These are solved to yield the wave propagation coefficients, and this gives a corresponding solution to the displacement field in the radial and tangential directions. The dynamics of the longitudinal direction are discussed but are not solved in this paper. An example problem is formulated and compared to solutions from fully elastic finite element modeling. It is shown that the accurate frequency range of this new model compares very favorably to finite element analysis up to 47 kHz. This new analytical model is about four magnitudes faster in computation time than the corresponding finite element models.

Stress Wave Propagation Analysis in One-Dimensional Micropolar Rods with Variable Cross-Section Using Micropolar Wave Finite Element Method

2018 ◽  
Vol 10 (04) ◽  
pp. 1850039 ◽  
Author(s):  
Mohsen Mirzajani ◽  
Naser Khaji ◽  
Muneo Hori
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Wave Propagation ◽  
Cross Section ◽  
Variable Cross Section ◽  
Stress Wave Propagation ◽  
Rotational Degree ◽  
Variable Cross ◽  
One Dimensional ◽  
Element Method

The wave finite element method (WFEM) is developed to simulate the wave propagation in one-dimensional problem of nonhomogeneous linear micropolar rod of variable cross-section. For this purpose, two kinds of waves with fast and slow velocities are detected. For micropolar medium, an additional rotational degree of freedom (DOF) is considered besides the classical elasticity’s DOF. The proposed method is implemented to solve the wave propagation, reflection and transmission of two distinct waves and impact problems in micropolar rods with different layers. Along with new solutions, results of the micropolar wave finite element method (MWFEM) are compared with some numerical and/or analytical solutions available in the literature, which indicate excellent agreements between the results.

scholarly journals Simulation of non-hydrostatic gravity wave propagation in the upper atmosphere

2014 ◽  
Vol 32 (4) ◽  
pp. 443-447 ◽  
Author(s):  
Y. Deng ◽  
A. J. Ridley
Keyword(s):  
Wave Propagation ◽  
Gravity Wave ◽  
High Frequency ◽  
General Circulation ◽  
Low Frequency ◽  
Circulation Model ◽  
Horizontal Resolution ◽  
Upper Atmosphere ◽  
Cutoff Wavelength ◽  
Frequency Wave

Abstract. The high-frequency and small horizontal scale gravity waves may be reflected and ducted in non-hydrostatic simulations, but usually propagate vertically in hydrostatic models. To examine gravity wave propagation, a preliminary study has been conducted with a global ionosphere–thermosphere model (GITM), which is a non-hydrostatic general circulation model for the upper atmosphere. GITM has been run regionally with a horizontal resolution of 0.2° long × 0.2° lat to resolve the gravity wave with wavelength of 250 km. A cosine wave oscillation with amplitude of 30 m s−1 has been applied to the zonal wind at the low boundary, and both high-frequency and low-frequency waves have been tested. In the high-frequency case, the gravity wave stays below 200 km, which indicates that the wave is reflected or ducted in propagation. The results are consistent with the theoretical analysis from the dispersion relationship when the wavelength is larger than the cutoff wavelength for the non-hydrostatic situation. However, the low-frequency wave propagates to the high altitudes during the whole simulation period, and the amplitude increases with height. This study shows that the non-hydrostatic model successfully reproduces the high-frequency gravity wave dissipation.

scholarly journals Wave Propagation in Rocks – Investigating the Effect of Rheology

2020 ◽  
Author(s):  
Tamás Fülöp
Keyword(s):  
Wave Propagation ◽  
High Frequency ◽  
Space Dimension ◽  
Low Frequency ◽  
Elastic Behaviour ◽  
Frequency Limit ◽  
Dispersion Error ◽  
Rock Types ◽  
Velocity Prediction ◽  
Symplectic Schemes

Rocks exhibit beyond-Hookean, delayed and damped elastic, behaviour (creep, relaxation etc.). In many cases, the Poynting–Thomson–Zener (PTZ) rheological model proves to describe these phenomena successfully. A forecast of the PTZ model is that the dynamic elasticity coefficients are larger than the static (slow-limit) counterparts. This prediction has recently been confirmed on a large variety of rock types. Correspondingly, according to the model, the speed of wave propagation depends on frequency, the high-frequency limit being larger than the low-frequency limit. This frequency dependence can have a considerable influence on the evaluation of various wave-based measurement methods of rock mechanics. As experience shows, commercial finite element softwares are not able to properly describe wave propagation, even for the Hooke model and simple specimen geometries, the seminal numerical artefacts being instability, dissipation error and dispersion error, respectively. This has motivated research on developing reliable numerical methods, which amalgamate beneficial properties of symplectic schemes, their thermodynamically consistent generalization (including contact geometry), and spacetime aspects. The present work reports on new results obtained by such a numerical scheme, on wave propagation according to the PTZ model, in one space dimension. The simulation outcomes coincide nicely with the theoretically obtained phase velocity prediction.

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