Dixon Lane-Meadow Creek, CA, United States
Dixon Lane-Meadow Creek, CA, United States

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El-Raheb M.,Satellite Consulting Inc.
International Journal of Solids and Structures | Year: 2012

Treated is the asymmetric static and dynamic response of a stack of layered thick disks from external load. Variables of the three-dimensional equations are separated assuming approximate simple supports along the cylindrical perimeter, yielding non-orthogonal eigenfunctions. This also couples the truncated set of radial wave numbers. Applying a radial transform to all variables eliminates radial dependence producing a diagonal eigenproblem in all coupled axial wave numbers. Comparing 3-D and 2-D asymmetric models of industrial glass disks reveals that the 3-D resonances are close to their 2-D counterparts adopting the Mindlin model. A Fourier analysis of a specific asymmetric line-load from pressure or thermal expansion produces a scale factor to static stress from a limited number of asymmetric solutions each with a different circumferential wave number. © 2011 Elsevier Ltd. All rights reserved.


El-Raheb M.,Satellite Consulting Inc.
Journal of Sound and Vibration | Year: 2011

Analyzed is transient response of an elastic beam from decelerating boundaries. It is shown that passive attenuation of peak transient deceleration is possible by coupling the beam to a tuned one-degree-of-freedom (1-dof) oscillator. For a fixed oscillator mass, optimum spring stiffness yields the lowest deceleration response. Furthermore, over a finite range of spring stiffness, the second coupled system mode disappears yielding an additional sharp reduction in transient deceleration response. The disappearance of the second mode is independent of boundary conditions from the weakest simple supports to the strongest clamped ends. © 2011 Elsevier Ltd.


El-Raheb M.,Satellite Consulting Inc.
Journal of Sound and Vibration | Year: 2011

Analyzed is the dynamics of an elastic L-shaped ring coupled to an elastic frame joined at discrete locations of the ring perimeter. The approximate ring model is evaluated adopting a two-dimensional model of a short shell joined to a narrow annular disk along one of its boundaries thus forming the L-shaped cross-section. Coupling the ring to an internal frame is accomplished by segmenting the ring. The frame impedance matrix relating forces and displacements at terminations is then applied at junctions of ring segments corresponding to these terminations. © 2011 Elsevier Ltd. All rights reserved.


El-Raheb M.,Satellite Consulting Inc.
International Journal of Solids and Structures | Year: 2011

Analyzed is transient response of an elastic disk from its decelerating boundary. Eigenfunctions of the bear disk are used as Galerkin trial functions to the disk with discrete masses and impedances in the form of a one-degree-of-freedom (1-dof) oscillator. The oscillator mass models a module connected to the disk and the spring models the connecting isolation stiffness. For a fixed oscillator mass, except for very weak springs, stiffness mostly raises transmissibility of deceleration from disk to mass. © 2011 Elsevier Ltd. All rights reserved.


El-Raheb M.,Satellite Consulting Inc
Computers and Structures | Year: 2011

Analyzed are the modal properties of a hexagon lattice formed of equilateral triangles. Cyclic symmetry is utilized to reduce the size of the problem to that of repeated segments. Four distinct sets of eigenvalues are determined for the independent symmetric components of the displacement vector along the two sides of a segment. In the physical domain, the dynamic stiffness matrix of the cyclic segment is determined analytically by solving for the state vectors from unit displacements independently applied at junction nodes. The cyclic model is validated with analytical results from the complete hexagon. The effect of curvature on modal properties is evaluated by comparing generalized quantities of flat and curved geometries. © 2011 Elsevier Ltd. All rights reserved.

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