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R.H. Gutierrez

Bio: R.H. Gutierrez is an academic researcher from National Scientific and Technical Research Council. The author has contributed to research in topics: Fundamental frequency & Transverse plane. The author has an hindex of 15, co-authored 99 publications receiving 847 citations.


Papers
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Journal ArticleDOI
TL;DR: In this paper, an approximate solution of the title problem is obtained by using the Rayleigh-Schmidt approach, which yields accurate engineering results which in the case of a uniform cantilever beam are in very good agreement with To's eigenvalues.

67 citations

Journal ArticleDOI
TL;DR: The main advantages of the differential quadrature method are its inherent complexity and the fact that easily programmable algorithmic expressions can be obtained as discussed by the authors, however, it was developed by Bellman in the 1970s but only recently has been applied in the solution of technically important problems.
Abstract: The main advantages of the differential quadrature method are its inherent concep­ tual simplicity and the fact that easily programmable algorithmic expressions are obtained. It was developed by Bellman in the 1970s but only recently has been applied in the solution of technically important problems. Essentially, it consists of the ap­ proximate solution of the differential system by means of a polynomial-collocation approach at afinite number of points selected by the analyst. This article reports some numerical experiments on vibrating Timoshenko beams of nonuniform cross­ section. © 1993 John Wiley & Sons, Inc.

62 citations

Journal ArticleDOI
TL;DR: In this article, a general method is presented for dealing with supports having translational and rotational flexibilities which vary in an arbitrary manner around the boundary, which can be represented as accurately as desired by expanding them into trigonometric series in the polar angle.
Abstract: The free vibrations of circular plates having flexible edge supports have been studied by several researchers for the restricted case when the supports are represented by springs having constant stiffness. In the present paper a general method is presented for dealing with supports having translational and rotational flexibilities which vary in an arbitrary manner around the boundary. It is shown that the varying stiffnesses can be represented as accurately as desired by expanding them into trigonometric series in the polar angle. The exact solution in polar coordinates of the differential equation of motion for the plate is then substituted into the elastic boundary conditions. The resulting infinite characteristic determinant is solved by successive truncation. As an example the case of a plate having a simply supported edge (infinite translational stiffness) with rotational stiffness varying according to L0 + L1 cos θ (L0 and L1 being constants) is considered. Numerical results are obtained by the meth...

51 citations

Journal ArticleDOI
TL;DR: In this paper, the lower natural frequencies of vibration of the structural system described the title have been determined and are presented for a significant range of values of the governing mechanical and geometric parameters for two types of configurations of structural interest: discontinuous variation of the thickness and continuous, linear variation.

44 citations

Journal ArticleDOI
TL;DR: In this paper, the fundamental frequency of vibration of rectangular plates with edges elastically restrained against rotation was determined by a single integral stiffener placed along one of its center lines, assuming that the value of the parameter f/h (stiffener deph/plate thickness) is moderate.

33 citations


Cited by
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Journal ArticleDOI
TL;DR: The differential quadrature method (DQM) as discussed by the authors is a numerical solution technique for initial and/or boundary problems, which was developed by the late Richard Bellman and his associates in the early 70s.
Abstract: The differential quadrature method is a numerical solution technique for initial and/or boundary problems. It was developed by the late Richard Bellman and his associates in the early 70s and, since then, the technique has been successfully employed in a variety of problems in engineering and physical sciences. The method has been projected by its proponents as a potential alternative to the conventional numerical solution techniques such as the finite difference and finite element methods. This paper presents a state-of-the-art review of the differential quadrature method, which should be of general interest to the computational mechanics community.

1,217 citations

Book
16 Dec 2008
TL;DR: Vibration of Plates as discussed by the authors provides a comprehensive, self-contained introduction to vibration theory and analysis of two-dimensional plates, including boundary characteristically orthogonal polynomials (BCOPs).
Abstract: Plates are integral parts of most engineering structures and their vibration analysis is required for safe design. Vibration of Plates provides a comprehensive, self-contained introduction to vibration theory and analysis of two-dimensional plates. Reflecting the author's more than 15 years of original research on plate vibration, this book presents new methodologies and demonstrates their effectiveness by providing comprehensive results. The text also offers background information on vibration problems along with a discussion of various plate geometries and boundary conditions, including the new concepts of Boundary Characteristic Orthogonal Polynomials (BCOPs).

465 citations

Journal ArticleDOI
W.L. Li1
TL;DR: In this paper, a simple and unified approach for the vibration analysis of a generally supported beam is presented, where the flexural displacement of the beam is sought as the linear combination of a Fourier series and an auxiliary polynomial function.

295 citations

Journal ArticleDOI
TL;DR: The eigenvalue problem for the Laplace operator in two dimensions is classical in mathematics and physics as mentioned in this paper, and computational methods for estimating the eigenvalues are still of much current interest, particularly in applications to acoustic and electromagnetic waveguides.
Abstract: The eigenvalue problem for the Laplace operator in two dimensions is classical in mathematics and physics. Nevertheless, computational methods for estimating the eigenvalues are still of much current interest, particularly in applications to acoustic and electromagnetic waveguides. Although our primary interest is with the computational methods, there are a number of theoretical results on the behavior of the eigenvalues and eigenfunctions that are useful for understanding the methods and, in addition, are of interest in themselves. These results are discussed first and then the various computational methods that have been used to estimate the eigenvalues are reviewed with particular emphasis on methods that give error bounds. Some of the more powerful techniques available are illustrated by applying them to a model problem.

253 citations

Journal ArticleDOI
TL;DR: In this article, the free and forced vibration of a laminated functionally graded beam of variable thickness under thermally induced initial stresses is studied within the framework of Timoshenko beam theory, where the beam consists of a homogeneous substrate and two inhomogeneous functionally graded layers whose material composition follows a power law distribution in the thickness direction.
Abstract: The free and forced vibration of a laminated functionally graded beam of variable thickness under thermally induced initial stresses is studied in this paper within the framework of Timoshenko beam theory. The beam consists of a homogeneous substrate and two inhomogeneous functionally graded layers whose material composition follows a power law distribution in the thickness direction in terms of the volume fractions of the material constituents. Both the axial and rotary inertia of the beam are considered in the present analysis. It is assumed that the beam may be clamped, hinged, or free at its ends and is subjected to one-dimensional steady heat conduction in the thickness direction before undergoing dynamic deformation. To include the effect of temperature change, the initial stress state is determined through a thermo-elastic analysis before the free and forced vibration analyses. The differential quadrature method that makes use of Lagrange interpolation polynomials is employed as a numerical solution tool to solve both the thermo-elastic equilibrium equation and dynamic equation. Numerical results are presented in both tabular and graphical forms for various laminated functionally graded beams, showing that vibration frequencies, mode shapes and dynamic response are significantly influenced by the thickness variation, temperature change, slenderness ratio, volume fraction index, the thickness of the functionally graded layer, and the end support conditions.

223 citations