scholarly journals Geometrical Optics applied to 1D Site Response of Inhomogeneous Soil Deposits

2020 ◽  
Author(s):  
Joaquin Garcia-Suarez ◽  
Domniki Asimaki ◽  
Elnaz E. Seylabi
Keyword(s):  
Wave Propagation ◽  
Natural Frequencies ◽  
Site Response ◽  
Geometrical Optics ◽  
Ray Theory ◽  
Resonance Amplitude ◽  
Analytical Results ◽  
Soil Deposits ◽  
Open Question ◽  
As If

The technique referred as Geometrical Optics entails considering the wave propagation in a heterogeneousmedium as if it happened with infinitely small wavelength. This classic simplification allows to obtain useful approximate analytical results in cases where complete description of the waveform behavior is virtually unattainable, hence its wide use in Physics. This approximation is also commonly termed Ray Theory, and it has already been thoroughly applied in Seismology. This text presents an application of Geometrical Optics to 1D Site Response (1DSR): it is used herein to, first, explainand elucidate the generality of some previous observations and results; second, to partially settle an open question in 1DSR, namely “what are the equivalent homogeneous properties that yield the same response, in terms of natural frequencies and resonance amplitude, for a certain inhomogeneous site?”, provided few assumptions.

Simplified Criteria to Select Ground Response Analysis Methods for Seismic Building Design: Equivalent Linear versus Nonlinear Approaches

2021 ◽  
Author(s):  
Mauro Aimar ◽  
Sebastiano Foti
Keyword(s):  
Seismic Waves ◽  
Site Response ◽  
Building Design ◽  
Soil Conditions ◽  
Response Analysis ◽  
Depth Range ◽  
Ground Response Analysis ◽  
Equivalent Linear ◽  
Acceleration Time Histories ◽  
Soil Deposits

ABSTRACT The possible amplification of seismic waves in soil deposits is crucial for the seismic design of buildings and geotechnical systems. The most common approaches for the numerical simulation of seismic site response are the equivalent linear (EQL) and the nonlinear (NL). Even though their advantages and limitations have been investigated in several studies, the relative field of applicability is still under debate. This study tested both methods over a wide population of soil models, which were subjected to a set of acceleration time histories recorded from strong earthquakes. A thorough comparison of the results of the EQL and the NL approaches was carried out, to identify the conditions in which the relative differences are significant. This assessment allowed for the definition of simplified criteria to predict when the two schemes are or are not compatible for large expected shaking levels. The proposed criteria are based on simple and intuitive parameters describing the soil deposit and the ground-motion parameters, which can be predicted straightforwardly. Therefore, this study provides a scheme for the choice between the EQL and the NL approaches that can be used even at the preliminary design stages. It appears that the EQL approach provides reliable amplification estimates in soil deposits with thickness up to 30 m, except for very deformable soils, but this depth range may be extended at long vibration periods. This result reveals a good level of reliability of the EQL approach for various soil conditions encountered in common applications, even for high-intensity shaking.

Axial Wave Propagation in Infinitely Long Periodic Curved Panels

2003 ◽  
Vol 125 (1) ◽  
pp. 24-30 ◽  
Author(s):  
C. Pany ◽  
S. Parthan
Keyword(s):  
Wave Propagation ◽  
Natural Frequencies ◽  
Propagation Constant ◽  
Infinite Length ◽  
Approximate Methods ◽  
Bending Vibration ◽  
Element Analysis ◽  
Curved Panel ◽  
Propagation Of Waves ◽  
Curved Panels

Propagation of waves along the axis of the cylindrically curved panels of infinite length, supported at regular intervals is considered in this paper to determine their natural frequencies in bending vibration. Two approximate methods of analysis are presented. In the first, bending deflections in the form of beam functions and sinusoidal modes are used to obtain the propagation constant curves. In the second method high precision triangular finite elements is used combined with a wave approach to determine the natural frequencies. It is shown that by this approach the order of the resulting matrices in the FEM is considerably reduced leading to a significant decrease in computational effect. Curves of propagation constant versus natural frequencies have been obtained for axial wave propagation of a multi supported curved panel of infinite length. From these curves, frequencies of a finite multi supported curved panel of k segments may be obtained by simply reading off the frequencies corresponding to jπ/kj=1,2…k. Bounding frequencies and bounding modes of the multi supported curved panels have been identified. It reveals that the bounding modes are similar to periodic flat panel case. Wherever possible the numerical results have been compared with those obtained independently from finite element analysis and/or results available in the literature.

Vibrations of rotating cylindrical shells with functionally graded material using wave propagation approach

2018 ◽  
Vol 232 (23) ◽  
pp. 4342-4356 ◽  
Author(s):  
Muzammal Hussain ◽  
M Nawaz Naeem ◽  
Aamir Shahzad ◽  
Mao-Gang He ◽  
Siddra Habib
Keyword(s):  
Wave Propagation ◽  
Natural Frequencies ◽  
Volume Fraction ◽  
Cylindrical Shells ◽  
Functionally Graded ◽  
Wave Number ◽  
Type I ◽  
Rotating Speed ◽  
Simply Supported ◽  
Fundamental Frequencies

Fundamental natural frequencies of rotating functionally graded cylindrical shells have been calculated through the improved wave propagation approach using three different volume fraction laws. The governing shell equations are obtained from Love’s shell approximations using improved rotating terms and the new equations are obtained in standard eigenvalue problem with wave propagation approach and volume fraction laws. The effects of circumferential wave number, rotating speed, length-to-radius, and thickness-to-radius ratios have been computed with various combinations of axial wave numbers and volume fraction law exponent on the fundamental natural frequencies of nonrotating and rotating functionally graded cylindrical shells using wave propagation approach and volume fraction laws with simply supported edge. In this work, variation of material properties of functionally graded materials is controlled by three volume fraction laws. This process creates a variation in the results of shell frequency. MATLAB programming has been used to determine shell frequencies for traveling mode (backward and forward) rotating motions. New estimations show that the rotating forward and backward simply supported fundamental natural frequencies increases with an increase in circumferential wave number, for Type I and Type II of functionally graded cylindrical shells. The presented results of backward and forward simply supported fundamental natural frequencies corresponding to Law I are higher than Laws II and III for Type I and reverse effects are found for Type II, depending on rotating speed. Our investigations show that the decreasing and increasing behaviors are noted for rotating simply supported fundamental natural frequencies with increasing length-to-radius and thickness-to-radius ratios, respectively. It is found that the fundamental frequencies of the forward waves decrease with the increase in the rotating speed, and the fundamental frequencies of the backward waves increase with the increase in the rotating speed. This investigation has been made with three different volume fraction laws of polynomial (Law I), exponential (Law II), and trigonometric (Law III). The presented numerical results of nonrotating isotropic and rotating functionally graded simply supported are in fair agreement with parts of other earlier numerical results.

Natural frequency modulation of a kinematically redundant planar parallel robot

2021 ◽  
pp. 095440622110524
Author(s):  
Jiawei Gu ◽  
Zhijiang Xie ◽  
Jian Zhang ◽  
Yangjun Pi
Keyword(s):  
Natural Frequency ◽  
Frequency Modulation ◽  
Natural Frequencies ◽  
Vibration Suppression ◽  
Excitation Frequency ◽  
Parallel Robot ◽  
Modulation Method ◽  
Kinematic Redundancy ◽  
Resonance Amplitude ◽  
Searching Method

When a parallel robot is equipped with kinematic redundancy, it has sufficient capabilities of natural frequency modulation through adjusting geometric configuration. To reduce resonance of a mechanism, this paper investigates the natural frequency modulation of a kinematically redundant planar parallel robot. A double-threshold searching method is proposed for controlling the inverse kinematics solution and keeping the natural frequencies away from the excitation frequency. The effectiveness of modulating the natural frequencies is demonstrated by comparing it with a non-modulation method. The simulation results indicate that, in all directions, the responses are coupled, and every order should be taken into consideration during natural frequency modulation. Compared to the non-modulation method, the proposed method can reduce the resonance amplitude to a certain extent, and the effect of vibration suppression is remarkable.

scholarly journals Gradient index phononic crystals and metamaterials

Nanophotonics ◽  
2019 ◽  
Vol 8 (5) ◽  
pp. 685-701 ◽  
Author(s):  
Yabin Jin ◽  
Bahram Djafari-Rouhani ◽  
Daniel Torrent
Keyword(s):  
Refractive Index ◽  
Wave Propagation ◽  
Acoustic Waves ◽  
Effective Properties ◽  
Periodic Structures ◽  
Phononic Crystals ◽  
Ray Theory ◽  
Acoustic Metamaterials ◽  
Propagation Of Waves ◽  
At Will

AbstractPhononic crystals and acoustic metamaterials are periodic structures whose effective properties can be tailored at will to achieve extreme control on wave propagation. Their refractive index is obtained from the homogenization of the infinite periodic system, but it is possible to locally change the properties of a finite crystal in such a way that it results in an effective gradient of the refractive index. In such case the propagation of waves can be accurately described by means of ray theory, and different refractive devices can be designed in the framework of wave propagation in inhomogeneous media. In this paper we review the different devices that have been studied for the control of both bulk and guided acoustic waves based on graded phononic crystals.

scholarly journals Free Vibration Characteristics of Cylindrical Shells Using a Wave Propagation Method

2001 ◽  
Vol 8 (2) ◽  
pp. 71-84 ◽  
Author(s):  
A. Ghoshal ◽  
S. Parthan ◽  
D. Hughes ◽  
M.J. Schulz
Keyword(s):  
Cylindrical Shell ◽  
Wave Propagation ◽  
Free Vibration ◽  
Periodic Structure ◽  
Natural Frequencies ◽  
Vibration Characteristics ◽  
Structural Element ◽  
Lower Bounding ◽  
Nodal Points ◽  
Wave Propagation Method

In the present paper, concept of a periodic structure is used to study the characteristics of the natural frequencies of a complete unstiffened cylindrical shell. A segment of the shell between two consecutive nodal points is chosen to be a periodic structural element. The present effort is to modify Mead and Bardell's approach to study the free vibration characteristics of unstiffened cylindrical shell. The Love-Timoshenko formulation for the strain energy is used in conjunction with Hamilton's principle to compute the natural propagation constants for two shell geometries and different circumferential nodal patterns employing Floquet's principle. The natural frequencies were obtained using Sengupta's method and were compared with those obtained from classical Arnold-Warburton's method. The results from the wave propagation method were found to compare identically with the classical methods, since both the methods lead to the exact solution of the same problem. Thus consideration of the shell segment between two consecutive nodal points as a periodic structure is validated. The variations of the phase constants at the lower bounding frequency for the first propagation band for different nodal patterns have been computed. The method is highly computationally efficient.

WAVE PROPAGATION IN A LIQUID LAYER

Geophysics ◽  
1959 ◽  
Vol 24 (4) ◽  
pp. 658-666 ◽  
Author(s):  
D. T. Liu
Keyword(s):  
Wave Propagation ◽  
Wave Equation ◽  
Pressure Wave ◽  
Wave Length ◽  
Water Layer ◽  
Fundamental Wave ◽  
Ray Theory ◽  
Seismic Record ◽  
Amplitude Response ◽  
Oscillatory Phenomenon

In many areas offshore, the conventional seismic record has the appearance of a series of sine waves or simple odd harmonic combinations of sine waves, with a fundamental wave length four times the water depth. Burg, et al., in a ray theory treatment, ascribe this oscillatory phenomenon to guided energy traveling in the water layer. A solution of the pressure wave equation for a point source in the water layer has been obtained. It allows one to examine not only the frequency dependence with the depth, but also the transient amplitude response with depth and time. It is concluded that in most actual situations, the phenomenon cannot be wholly explained by the assumed mechanism, because the theory indicates too rapid a decay of the energy.

Influence of Tie Beams of Pier on the Seismic Performance of a Continuous Rigid Frame Bridge with Twin-Legged Piers

2011 ◽  
Vol 368-373 ◽  
pp. 1105-1110
Author(s):  
Yun Jing Nie ◽  
Xu Yan ◽  
Tie Ying Li
Keyword(s):  
Seismic Response ◽  
Seismic Performance ◽  
Seismic Design ◽  
Dynamic Characteristics ◽  
Natural Frequencies ◽  
Continuous Rigid Frame Bridge ◽  
Analytical Results ◽  
Rigid Frame ◽  
Rigid Frame Bridge

In this paper, the influence of tie beams for piers is investigated on the dynamic characteristics and the seismic performance of a continuous rigid frame bridge with twin-legged piers. Modal analyses and the linear seismic response analyses are performed on a practical continuous rigid frame bridge with twin-legged piers with no tie beam, one tie beam and three tie beams of pier, using software Midas/civil. The findings indicate that installing tie beams of pier can increase the natural frequencies of this kind of bridge. Setting tie beams of pier is disadvantageous to the seismic performance of the bridge beam, but advantageous to improving the seismic performance of the twin-legged piers. The influence of tie beams of pier on the seismic performance on the whole structure is relevant to the pier height. These analytical results provide a reference for the seismic design and analysis of similar structures.

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