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Keywords: differential equations
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Journal Articles
Publisher: ASME
Article Type: Research Papers
J. Vib. Acoust. April 2012, 134(2): 021019.
Published Online: January 26, 2012
...C. C. Hong The thermal vibration study of magnetostrictive functionally graded material (FGM) plate under rapid heating is computed by using the generalized differential quadrature (GDQ) method. The dynamic equilibrium differential equations with displacements and shear rotations...
Journal Articles
Publisher: ASME
Article Type: Research Papers
J. Vib. Acoust. December 2011, 133(6): 061019.
Published Online: November 28, 2011
..., a special case of a cantilever microbeam is studied and modeled as a distributed-parameter system, which is attached to the PCB. These lumped-distributed and distributed-distributed models are discretized into ordinary differential equations, using the Galerkin method, which are then integrated numerically...
Journal Articles
Publisher: ASME
Article Type: Research Papers
J. Vib. Acoust. December 2011, 133(6): 061013.
Published Online: November 28, 2011
... or tensile) and other parameters of the PVC layers on the vibration characteristics of flexible structure have been investigated. The Hamilton principle in conjunction with finite element method is used to derive the differential equations of motion. Using proportional feedback controllers, the complex...
Journal Articles
Publisher: ASME
Article Type: Research Papers
J. Vib. Acoust. June 2011, 133(3): 031001.
Published Online: March 24, 2011
... is of great importance. In this paper, the free vibration of an inclined taut cable is further investigated by accounting for the factor of the weight component parallel to the cable chord. Two coupled linear differential equations describing two-dimensional in-plane motion of the cable are derived based...
Journal Articles
Publisher: ASME
Article Type: Research Papers
J. Vib. Acoust. August 2010, 132(4): 041007.
Published Online: May 25, 2010
...Peng Lan; Ahmed A. Shabana The goal of this study is to develop the dynamic differential equations of the first finite element based on the rational absolute nodal coordinate formulation (RANCF) and to demonstrate its use in the nonlinear dynamic and vibration analysis of flexible bodies...
Journal Articles
Publisher: ASME
Article Type: Research Papers
J. Vib. Acoust. August 2010, 132(4): 041001.
Published Online: May 20, 2010
... differential equation of motion. Frequency equations for an annular plate for two different combinations of edge conditions have been obtained employing Chebyshev collocation technique. Numerical results thus obtained have been presented in the form of tables and graphs. The effect of foundation parameter...
Journal Articles
Publisher: ASME
Article Type: Research Papers
J. Vib. Acoust. April 2010, 132(2): 021006.
Published Online: March 16, 2010
... were used to represent the active material while the inertia, viscous losses, and compressibility of the fluid were included using differential equations. Factors affecting system performance are identified and the inclusion of fluid inertia in the model is also justified. The starting point...
Journal Articles
Publisher: ASME
Article Type: Research Papers
J. Vib. Acoust. October 2009, 131(5): 051011.
Published Online: September 25, 2009
... leads to a homogeneous differential equation. This is similar to the definition of free vibration in the case of SDoF systems with constant parameters. The physical meaning associated with condition (i) is that it represents a case when the absolute velocity of the entering or exiting mass is negligible...
Journal Articles
Publisher: ASME
Article Type: Technical Briefs
J. Vib. Acoust. February 2009, 131(1): 014502.
Published Online: January 8, 2009
..., and show that this leads to a significantly improved quality. Our idea also works for operators of order greater than 1. damping differential equations integration mathematical operators numerical analysis vibrations fractional derivative numerical method Yuan–Agrawal method...
Journal Articles
Publisher: ASME
Article Type: Technical Briefs
J. Vib. Acoust. December 2008, 130(6): 064504.
Published Online: October 22, 2008
... quantification, which generally require an efficient and robust sensitivity calculation method. In this paper, the sensitivity of the milling process, which can be modeled by a set of time delay differential equations, to variations in the input parameters is calculated. The semi-analytical derivative...
Journal Articles
Publisher: ASME
Article Type: Research Papers
J. Vib. Acoust. October 2008, 130(5): 051006.
Published Online: August 13, 2008
..., namely, a formulation where the governing differential equation had constant coefficients. In the present study, when the foundation is narrower than the plate and its spatial footprint varies in time, the equation of motion presents time-varying coefficients, and motion is excited both parametrically...
Journal Articles
Publisher: ASME
Article Type: Research Papers
J. Vib. Acoust. August 2008, 130(4): 041005.
Published Online: July 1, 2008
..., a stiff differential equation with analytical results is adopted to be solved using the symplectic precise integration method, precise integration method, and general Runge–Kutta method. The Hamiltonian of this system is 72 H = 1 2 m 1 x ̇ 1 2 + 1 2 m 2 x ̇ 2 2...
Journal Articles
Publisher: ASME
Article Type: Research Papers
J. Vib. Acoust. February 2008, 130(1): 011004.
Published Online: November 12, 2007
... the governing differential equations of motion that describe the deformations of the beam element according to the trigonometric shear deformation theory, which include the sinusoidal variation of the axial displacement over the cross section of the beam. The application of the dynamic stiffness matrix...
Journal Articles
Publisher: ASME
Article Type: Technical Papers
J. Vib. Acoust. December 2007, 129(6): 784–802.
Published Online: March 14, 2007
.... This work demonstrates that the parameters of a system of ordinary differential equations may be adjusted via an evolutionary algorithm to produce excitations that improve the sensitivity and robustness to extraneous noise of state-space based damage detection features extracted from the structural response...
Journal Articles
Publisher: ASME
Article Type: Technical Briefs
J. Vib. Acoust. August 2006, 128(4): 532–534.
Published Online: February 21, 2006
...Igor V. Andrianov; Jan Awrejcewicz; Alexander A. Diskovsky A novel asymptotical approach to integrate differential equations governing quasi-regular structures, particularly suitable on the stage of construction design, is proposed. 02 12 2004 21 02 2006 periodic structures...
Journal Articles
Publisher: ASME
Article Type: Technical Papers
J. Vib. Acoust. June 2006, 128(3): 366–374.
Published Online: November 28, 2005
... degrees of freedom, viz., three translational components along the cylindrical coordinates and two rotational components of the normal to the middle surface. Then the strain and kinetic energy expressions are obtained in terms of these displacement fields. The differential equation governing the vibration...
Journal Articles
Journal Articles
Publisher: ASME
Article Type: Technical Papers
J. Vib. Acoust. April 2004, 126(2): 212–219.
Published Online: May 4, 2004
...L. Starek; D. J. Inman, Fellow ASME This paper summarizes the authors’ previous efforts on solving inverse eigenvalue problems for linear vibrating systems described by a vector differential equations with constant coefficient matrices and nonproportional damping. The inverse problem of interest...
Journal Articles
Journal Articles
Publisher: ASME
Article Type: Technical Papers
J. Vib. Acoust. January 2003, 125(1): 73–79.
Published Online: January 6, 2003
... characteristics of the structure dealt with, the differential equations of the forced motion caused by a time dependent axial loading of the form P = P 0 + P t cos θ t are reduced to a set of Mathieu-Hill type equations. These may be thereafter tackled and the dynamic stability problem comprehensively discussed...