INTERACTION OF TWO SEMI-CYLINDRICAL CANYONS EXCITED BY SH WAVES

2020 ◽  
Vol 7 (1) ◽  
Author(s):  
Abdul Hayir ◽  
Sinan Emre Cankaya
Keyword(s):  
Transfer Function ◽  
Infinite Series ◽  
Order Term ◽  
Closed Form Solution ◽  
Form Solution ◽  
Propagation Path ◽  
Earthquake Ground Motion ◽  
Dimensionless Frequency ◽  
Sh Waves ◽  
Incident Waves

The spectral analysis of strong earthquake ground motion needs detailed understanding of transfer function properties and source radiation along the wave propagation path. The main goal of this study is to evaluate the interaction of two semi-cylindrical canyons, which are subjected to the horizontally polarized shear-wave (SH-wave) and to find the transfer function properties of two canyons. In this study, the interaction of two semi-cylindrical canyons subjected to SH waves are considered and evaluated for a general angle of wave incidence. The method of Wave Function Expansion is derived, and the infinite series solution is obtained. Due to the complexity and convergence of infinite series including Bessel functions, the numerical results are limited. The convergence of the solution for the high frequencies requires the high order term. Moreover, the difficulties of this study come from convergence of the solution owing to interaction of two canyons having various dimensions and material properties. The closed-form solution of the problem shows that the surface topography can have prominent effects on incident waves when the wavelengths of incident motion are short compared to the radius of a canyon. The parameters, dimensions of the canyons, distance between two canyons, and the amplifications of the displacement amplitudes are obtained with respect to the incident angles of the waves and dimensionless frequency.

Interaction of a shear wall with the soil for incident plane SH waves

1972 ◽  
Vol 62 (1) ◽  
pp. 63-83
Author(s):  
M. D. Trifunac
Keyword(s):  
Incidence Angle ◽  
Closed Form Solution ◽  
Shear Wall ◽  
Elastic Half Space ◽  
Form Solution ◽  
Angle Of Incidence ◽  
Sh Waves ◽  
Incident Plane ◽  
Interaction Equation ◽  
Plane Sh Waves

Abstract The closed-form solution of the dynamic interaction of a shear wall and the isotropic homogeneous and elastic half-space, previously studied only for vertically-incident SH waves, is generalized to any angle of incidence. It is shown that the interaction equation is independent of the incidence angle, while the surface-ground displacements heavily depend on it. For the two-dimensional model studied, it is demonstrated that disturbances generated by waves scattering and diffracting around the rigid foundation mass are not a local phenomenon but extend to large distances relative to the characteristic foundation length.

Torsional response of structures for SH waves: The case of hemispherical foundations

1976 ◽  
Vol 66 (1) ◽  
pp. 109-123
Author(s):  
J. E. Luco
Keyword(s):  
Closed Form Solution ◽  
Form Solution ◽  
Basic Step ◽  
Sh Waves ◽  
Torsional Response ◽  
Obliquely Incident ◽  
Incident Plane ◽  
Interaction Problem ◽  
Plane Sh Wave ◽  
Plane Sh Waves

abstract A study is made of the harmonic torsional response of an elastic structure placed on a rigid hemispherical foundation which is supported on an elastic medium and is subjected to the action of obliquely incident plane SH waves. As a basic step in the solution of the torsion interaction problem, a closed-form solution is obtained for the torsional response of a rigid hemispherical foundation excited externally by a harmonic torque and through the soil by an obliquely incident plane SH wave. Comparisons between the results for a hemispherical foundation with those for a circular plate allow the estimation of the effects that the embedment of the foundation has on the torsional response of the superstructure.

Probabilistic Representation and Transmission of Nonstationary Processes in Multi-Degree-of-Freedom Systems

1998 ◽  
Vol 65 (2) ◽  
pp. 398-409 ◽  
Author(s):  
S. F. Masri ◽  
A. W. Smyth ◽  
M.-I. Traina
Keyword(s):  
Random Process ◽  
Structural Control ◽  
Extreme Values ◽  
Free Field ◽  
Closed Form Solution ◽  
Form Solution ◽  
Degree Of Freedom ◽  
Statistical Characteristics ◽  
Earthquake Ground Motion ◽  
Process Data

A relatively simple and straightforward procedure is presented for representing non-stationary random process data in a compact probabilistic format which can be used as excitation input in multi-degree-of-freedom analytical random vibration studies. The method involves two main stages of compaction. The first stage is based on the spectral decomposition of the covariance matrix by the orthogonal Karhunen-Loeve expansion. The dominant eigenvectors are subsequently least-squares fitted with orthogonal polynomials to yield an analytical approximation. This compact analytical representation of the random process is then used to derive an exact closed-form solution for the nonstationary response of general linear multi-degree-of-freedom dynamic systems. The approach is illustrated by the use of an ensemble of free-field acceleration records from the 1994 Northridge earthquake to analytically determine the covariance kernels of the response of a two-degree-of-freedom system resembling a commonly encountered problem in the structural control field. Spectral plots of the extreme values of the rms response of representative multi-degree-of-freedom systems under the action of the subject earthquake are also presented. It is shown that the proposed random data-processing method is not only a useful data-archiving and earthquake feature-extraction tool, but also provides a probabilistic measure of the average statistical characteristics of earthquake ground motion corresponding to a spatially distributed region. Such a representation could be a valuable tool in risk management studies to quantify the average seismic risk over a spatially extended area.

Active Sound Attenuation in Finite-Length Ducts Using Close-Form Transfer Function Models

1995 ◽  
Vol 117 (2) ◽  
pp. 143-154 ◽  
Author(s):  
Jwu-Sheng Hu
Keyword(s):  
Transfer Function ◽  
Finite Length ◽  
Repetitive Control ◽  
Closed Form Solution ◽  
Form Solution ◽  
Sensors And Actuators ◽  
Transmission Zeros ◽  
Control Scheme ◽  
Close Form ◽  
Function Models

In this paper, the problem of active sound cancellation in finite-length ducts is investigated. The closed-form solution of a one-dimensional wave equation is obtained as the plant model. The controllability, observability, and transmission zeros are discussed based on the transfer function model. For ducts with totally reflective boundaries, stabilization can be achieved by using a speaker (actuator) and a microphone (sensor). Cases of collocated and noncollocated sensors and actuators are presented. A repetitive control algorithm was developed to drive the actuator so that harmonic noises in a duct are attenuated. For a duct with partially reflective boundaries, the application of repetitive control prevents sound from leaking out of the duct at a chosen end. A simulation study demonstrating the effects of this feedback control scheme is also presented.

On a Closed-Form Solution of Prandtl's System of Equations

2013 ◽  
Vol 40 (2) ◽  
pp. 106-114
Author(s):  
J. Venetis ◽  
Aimilios (Preferred name Emilios) Sideridis
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
System Of Equations

Plane Wave Resonance in the Tire Air Cavity as a Vehicle Interior Noise Source

1995 ◽  
Vol 23 (1) ◽  
pp. 2-10 ◽  
Author(s):  
J. K. Thompson
Keyword(s):  
Closed Form Solution ◽  
Form Solution ◽  
Interior Noise ◽  
Cavity Resonance ◽  
Test Results ◽  
Vehicle Interior ◽  
Air Cavity ◽  
Vehicle Interior Noise ◽  
Wave Resonance ◽  
Resonance Frequencies

Abstract Vehicle interior noise is the result of numerous sources of excitation. One source involving tire pavement interaction is the tire air cavity resonance and the forcing it provides to the vehicle spindle: This paper applies fundamental principles combined with experimental verification to describe the tire cavity resonance. A closed form solution is developed to predict the resonance frequencies from geometric data. Tire test results are used to examine the accuracy of predictions of undeflected and deflected tire resonances. Errors in predicted and actual frequencies are shown to be less than 2%. The nature of the forcing this resonance as it applies to the vehicle spindle is also examined.

Capacity Analysis for Correlated Multi-Hop MIMO Channels under Colored Noise

2015 ◽  
Vol 1 ◽  
pp. 41
Author(s):  
Nguyen N. Tran ◽  
Ha X. Nguyen
Keyword(s):  
Computational Complexity ◽  
Mutual Information ◽  
Closed Form Solution ◽  
Optimal Solution ◽  
Form Solution ◽  
Maximization Problem ◽  
Capacity Analysis ◽  
Mimo Channels ◽  
Average Mutual Information ◽  
Channel Output

A capacity analysis for generally correlated wireless multi-hop multi-input multi-output (MIMO) channels is presented in this paper. The channel at each hop is spatially correlated, the source symbols are mutually correlated, and the additive Gaussian noises are colored. First, by invoking Karush-Kuhn-Tucker condition for the optimality of convex programming, we derive the optimal source symbol covariance for the maximum mutual information between the channel input and the channel output when having the full knowledge of channel at the transmitter. Secondly, we formulate the average mutual information maximization problem when having only the channel statistics at the transmitter. Since this problem is almost impossible to be solved analytically, the numerical interior-point-method is employed to obtain the optimal solution. Furthermore, to reduce the computational complexity, an asymptotic closed-form solution is derived by maximizing an upper bound of the objective function. Simulation results show that the average mutual information obtained by the asymptotic design is very closed to that obtained by the optimal design, while saving a huge computational complexity.

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