Attenuation and Damping of Multireflected Transient Elastic Waves in a Pile

Early time transient waves multireflected in a finite pile, governed by a damped wave equation, are analyzed by a reverberation-ray matrix. The pile is surrounded by compacted soil, and the composite is modeled by elastic springs and viscous dampers distributed along the length and at the tip of an...

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Bibliographic Details
Published in:Journal of engineering mechanics 2011-08, Vol.137 (8), p.571-579
Main Authors: Pao, Yih-Hsing, Yu, Yun-Yan
Format: Article
Language:English
Subjects:
Acoustical measurements and instrumentation
Acoustics
Applied sciences
Attenuation
Buildings. Public works
Damping
Earthwork. Foundations. Retaining walls
Exact sciences and technology
Fourier series
Fundamental areas of phenomenology (including applications)
Geotechnics
Integrals
Mathematical analysis
Mathematical models
Physics
Piles
Reflection
Solid mechanics
Static elasticity (thermoelasticity...)
Structural and continuum mechanics
TECHNICAL PAPERS
Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...)
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Summary:Early time transient waves multireflected in a finite pile, governed by a damped wave equation, are analyzed by a reverberation-ray matrix. The pile is surrounded by compacted soil, and the composite is modeled by elastic springs and viscous dampers distributed along the length and at the tip of an elastic rod. Steady-state waves with complex frequencies and wave numbers that are generated by a source of harmonic time function at the top and reverberated between the top and bottom surface of the pile are sorted in matrix form into ray-groups, arriving at a receiver in successive orders of reflections from the bottom. The steady-state ray groups are synthesized into a series of nonsingular Fourier integrals that can be evaluated accurately with a fast Fourier-transform algorithm. The first integral (zeroth-order) has also been reduced by complex contour integration to the well-known closed-form solution in Bessel functions for a semi-infinite pile. Detailed time records of velocity response received at the top after three reflections are calculated to illustrate attenuation and damping; arrival times and amplitude-phase change on each reflection for various lateral and base supports. The calculated records resemble ultrasonic nondestructive testing data.
ISSN:0733-9399
1943-7889
DOI:10.1061/(ASCE)EM.1943-7889.0000259