Abstract
The aim of this paper is to study the propagation of torsional surface waves in non-homogeneous isotropic layer of finite thickness placed over a homogeneous viscoelastic half-space, when both density and rigidity of the non-homogeneous medium are assumed to vary exponentially with
depth. The frequency equations are obtained by using simple method of separation of variables. Further, it is seen that when viscoelastic parameter and non-homogeneity parameter is neglected, the dispersion equation gives the dispersion equations of Love waves in homogeneous, elastic and isotropic layer placed over homogeneous viscoelastic medium. The problem has been solved numerically and the effects of various inhomogeneities of the medium on torsional waves have been illustrated graphically.
Key Words
torsional waves; viscoelastic media; inhomogeneities; internal friction
Address
Rajneesh Kakar: Principal, DIPS Polytechnic College, Hoshiarpur-146001, India; Kishan Chand Gupta: Faculty of Applied Sciences, BMSCE, Muktsar-152026, India
Abstract
Phononic system composed of periodical elastic structures exhibit band gap phenomenon, and all elastic wave cannot propagate within the band gap. In this article, we consider one-dimensional binary materials which are periodically arranged as a 20-layered medium instead of infinite layered system for phononic system. The layered medium with finite dimension is subjected to a uniformly distributed sinusoidal loading at the upper surface, and the bottom surface is assumed to be traction free. The transient wave propagation in the 20-layered medium is analyzed by Laplace transform technique. The analytical solutions are presented in the transform domain and the numerical Laplace inversion (Durbin\'s formula) is performed to obtain the transient response in time domain. The numerical results show that when a sinusoidal loading with a specific frequency within band gap is applied, stress response will be significantly
decayed if the receiver is away from the source. However, when a sinusoidal force with frequency is out of band gap, the attenuation of the stress response is not obvious as that in the band gap.
Key Words
phononic system; band gap; multilayered; transient wave; laplace transform; durbin
Address
Yi-Hsien Lin and Chien-Ching Ma: Department of Mechanical Engineering, National Taiwan University, Taipei, Taiwan 10617, R.O.C.
Abstract
A five parameter viscoelastic model is developed to study harmonic waves propagating in the non-homogeneous viscoelastic filaments of varying density. The constitutive relation for five parameter model is first developed and then it is applied for harmonic waves in the specimen. In this study, it is assumed that density, rigidity and viscosity of the specimen i.e., rod are space dependent. The specimen is non-homogeneous, initially unstressed and at rest. The method of non-linear partial differential equation has been used for finding the dispersion equation of harmonic waves in the rods. A simple method is presented for reflections at the free end of the finite non-homogeneous viscoelastic rods. The harmonic wave propagation in viscoelastic rod is also presented numerically with MATLAB.
Key Words
harmonic waves; viscoelastic media; friedlander series; inhomogeneous; varying density
Address
Rajneesh Kakar: DIPS Polytechnic College, Hoshiarpur-146001, India; Kanwaljeet Kaur and Kishan Chand Gupta: Applied Sciences, BMSCE, Muktsar-152026, India
Abstract
A wide literature review on Static Soil-Structure Interaction (SSI) is done to highlight the key impacts of soil complexity on structural members of framed structures. Attention is paid to the developed approaches, i.e., conventional and Finite Element Method (FEM), to emphasize on deficiencies and merits of the proposed methods according to their applicability, accuracy and power to model and idealization of the superstructures as well as the soil continuum. Proposed hypothesis are much deeply discussed herein for better understanding which is normally neglected in literature review papers due to the large number of references and limit of space.
Key Words
review paper; static soil-structure-interaction; winkler model; finite element analysis; shallow foundation
Address
Mohammad Dalili S., Huat B.B.K. and M.S. Jaafar: Civil Engineering Department, Faculty of Engineering, Universiti Putra Malaysia, 43400 UPM-Serdang, Malaysia; A. Alkarni: College of Engineering, Geotechnical Engineering Faculty, King Saud University, Riyadh, Saudi Arabia
