Affiliations: Acoustics Research Laboratory, Department of
Mechanical Engineering, Iran University of Science and Technology, Narmak,
Tehran, Iran | Department of Mechanical Engineering, Damavand Branch,
Islamic Azad University, Damavand, Iran
Note: [] Corresponding author: Seyyed M. Hasheminejad, Acoustics Research
Laboratory, Department of Mechanical Engineering, Iran University of Science
and Technology, Narmak, Tehran 16846-13114, Iran. Tel.: 98912 7371354; Fax:
9821 77240488; E-mail: hashemi@iust.ac.ir
Abstract: A three-dimensional elasticity-based continuum model is developed
for describing the free vibrational characteristics of an important class of
isotropic, homogeneous, and completely free structural bodies (i.e., finite
cylinders, solid spheres, and rectangular parallelepipeds) containing an
arbitrarily located simple inhomogeneity in form of a spherical or cylindrical
defect. The solution method uses Ritz minimization procedure with triplicate
series of orthogonal Chebyshev polynomials as the trial functions to
approximate the displacement components in the associated elastic domains, and
eventually arrive at the governing eigenvalue equations. An extensive review of
the literature spanning over the past three decades is also given herein
regarding the free vibration analysis of elastic structures using Ritz
approach. Accuracy of the implemented approach is established through proper
convergence studies, while the validity of results is demonstrated with the aid
of a commercial FEM software, and whenever possible, by comparison with other
published data. Numerical results are provided and discussed for the first few
clusters of eigen-frequencies corresponding to various mode categories in a
wide range of cavity eccentricities. Also, the corresponding 3D mode shapes are
graphically illustrated for selected eccentricities. The numerical results
disclose the vital influence of inner cavity eccentricity on the vibrational
characteristics of the voided elastic structures. In particular, the activation
of degenerate frequency splitting and incidence of internal/external mode
crossings are confirmed and discussed. Most of the results reported herein are
believed to be new to the existing literature and may serve as benchmark data
for future developments in computational techniques.
