An infinite element algorithm for vibration of elastic and viscoelastic multilayered half spaces | |
| Author | Liu, Ya-chun |
| Call Number | AIT Diss. no.ST-92-01 |
| Subject(s) | Viscoelasticity Vibration--Mathematical models |
| Note | A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Engineering, School of Engineering and Technology |
| Publisher | Asian Institute of Technology |
| Series Statement | Dissertation ; no. ST-92-01 |
| Abstract | Far-field displacement functions of isotropic elastic and viscoelastic multilayered spaces undergoing vibration are obtained analytically in closed forms. Essentially, there are three simple fundamental problems: a homogeneous half space, a homogeneous full space, and two different half spaces perfectly bonded together. In the second fundamental problem, the homogeneous full space is treated as two half spaces of the same properties perfectly bonded together. According to their dimensions, the problems are grouped as; two-dimensional or plane problems, and three-dimensional problems. The plane problems can be divided further into in-plane and antiplane problems. There are two special cases in three-dimensional problems, i.e. axisymmetric (or torsion free) problems, and pure torsion problems. Fourier transforms with respect to an in-plane coordinate are employed for plane problems, and Hankel transforms with respect to the radial cylindrical coordinate are for three-dimensional problems. Employing proper contours in the complex plane, applying the residue theorem and an accurate method for approximating infinite integrals in the far field, the Cauchy's principal value of each infinite integral is obtained in a closed form. There is, at the most, only one surface wave in the first or the third fundamental problem; and none in the second one. Such a surface wave is of Rayleigh type, and nondispersive for any elastic case. There is no surface wave in the antiplane and pure torsion problems. The surface wave and the body waves can be discretized and identified from one another. There are two types of body waves, i.e. pressure and shear waves. Each wave can be put as outgoing and having geometric attenuation (i.e. radiation) and material attenuation. Such radiation does not exist in the surface wave of a plane problem, and there is no material attenuation in an elastic problem. The three fundamental problems are supposed to represent, respectively, the following parts of a multilayered half space: the surface, the interior of each and every layer, and each interface between every pair of adjacent layers of different properties. Such far field dis-placement functions can serve as rational and efficient shape functions of infinite elements, into which the far field of a multilayered half space is discretized. There are two types of infinite elements; horizontal elements in the horizontal layers in the upper part of such a multilayered half space, and radiating elements inside the underlying half space. By introducing a new reference coordinate system properly, shape functions of radiating infinite elements are put in the same forms as those of horizontal infinite elements. These infinite elements are capable of transmitting Rayleigh, shear and pressure waves; and satisfy the compatibility, completeness, finiteness and attenuation conditions. An efficient scheme to integrate numerically the stiffness and mass matrices of the elements is presented. With such infinite elements in the far field, the size of the near field being discretized into conventional finite elements can be kept small, the problems have relatively fewer degrees of freedom, and an analyst is provided with an inexpensive solution scheme. Finally, the com-pliance and impedance functions for vibration of rigid plates on half spaces, and rigid bodies partially embedded in half spaces, are found to agree closely with analytical results obtained by others. |
| Year | 1992 |
| Corresponding Series Added Entry | Asian Institute of Technology. Dissertation ; no. ST-92-01 |
| Type | Dissertation |
| School | School of Engineering and Technology |
| Department | Department of Civil and Infrastucture Engineering (DCIE) |
| Academic Program/FoS | Structural Engineering (STE) /Former Name = Structural Engineering and Construction (ST) |
| Chairperson(s) | Karasudhi, Pisidhi ; |
| Examination Committee(s) | Balasubramaniam, A.S. ;Worsak Kanok-Nukulchai ;Pichai Nimityongskul; |
| Scholarship Donor(s) | The Government of Australia; |
| Degree | Thesis (Ph.D.) - Asian Institute of Technology, 1992 |