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Keywords: partial differential equations
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Journal Articles
Article Type: Research Papers
J. Vib. Acoust. December 2011, 133(6): 061009.
Published Online: November 28, 2011
... the perturbations grow or decay? For a deformable system such as a parachute dam, the state of membrane structure is often modeled using a partial differential equation (PDE) with a set of boundary conditions. Since there has been little stabilization and control synthesis work for PDE-based systems as compared...
Journal Articles
Article Type: Research Papers
J. Vib. Acoust. December 2011, 133(6): 061005.
Published Online: October 12, 2011
... and material density. The spatial dependence in the partial differential equation of motion is suppressed by utilizing Galerkin’s method with homogeneous beam mode shapes. To check the accuracy of this approximation, numerical solutions for the boundary value problem represented by the original partial...
Journal Articles
Article Type: Research Papers
J. Vib. Acoust. April 2011, 133(2): 021001.
Published Online: February 17, 2011
... equation of elasticity. With velocity and stress components as the unknowns, the governing equations are a set of 9, first-order, hyperbolic partial differential equations. To assess numerical accuracy of the results, the characteristic form of the equations is derived. Moreover, without using the assumed...
Journal Articles
Article Type: Research Papers
J. Vib. Acoust. December 2010, 132(6): 061009.
Published Online: October 8, 2010
... without resorting to truncation of the model and without the use of in-domain measuring and actuating devices. 29 06 2008 10 12 2009 08 10 2010 08 10 2010 laminates nonlinear differential equations partial differential equations plates (structures) vibration control...
Journal Articles
Article Type: Technical Briefs
J. Vib. Acoust. October 2010, 132(5): 054502.
Published Online: August 18, 2010
..., but the nonlinear spring-mass effect appears in the boundary conditions only. The solution is obtained by applying the method of multiple time scales directly to the nonlinear partial differential equations and the boundary conditions. The results of the linear frequencies match well with those obtained in open...
Journal Articles
Article Type: Research Papers
J. Vib. Acoust. August 2009, 131(4): 041010.
Published Online: June 8, 2009
... length varies dynamically. We first obtain the governing equations and boundary conditions, including a transversality condition involving an end moment, using Hamilton’s principle. Rescaling the variable length to a constant value, we obtain partial differential equations with time varying coefficients...
Journal Articles
Article Type: Research Papers
J. Vib. Acoust. June 2009, 131(3): 031007.
Published Online: April 22, 2009
.... In this paper, the finite disturbance theory is used to solve the nonlinear partial differential equations that describe the unsteady one-dimensional compressible flow in the complex piping system. The solution is then compared with experimental results. The comparison shows that the finite theory fits...
Journal Articles
Article Type: Research Papers
J. Vib. Acoust. April 2009, 131(2): 021012.
Published Online: February 19, 2009
... good results, and the solutions converge as the size of the time step is reduced. The formulation presented is simple and can be extended to FOC of other continuum systems. 10 11 2007 27 08 2008 19 02 2009 algebra optimal control partial differential equations time-domain...
Journal Articles
Article Type: Research Papers
J. Vib. Acoust. February 2009, 131(1): 011007.
Published Online: January 6, 2009
... function of the variable between simply supported edges, the fourth order partial differential equation governing the motion of such plates of exponentially varying thickness in another direction gets reduced to an ordinary differential equation with variable coefficients. The resulting equation...
Journal Articles
Article Type: Research Papers
J. Vib. Acoust. December 2008, 130(6): 061002.
Published Online: October 14, 2008
... is investigated analytically. For this problem, a boundary value partial differential equation is formulated via contact mechanics. In particular, the effect of interfacial pressure distribution variation at the interface of the layered structures on the energy dissipation and logarithmic damping decrement...
Journal Articles
Article Type: Research Papers
J. Vib. Acoust. April 2008, 130(2): 021013.
Published Online: March 21, 2008
... to the equations of motion. Forcing and damping effects are included in the problem. The general arbitrary number of support case is considered at first, and then 3-, 4-, and 5-support cases are investigated. The method of multiple scales is directly applied to the partial differential equations. Natural...
Journal Articles
Article Type: Technical Papers
J. Vib. Acoust. October 2006, 128(5): 611–615.
Published Online: January 14, 2006
... is used in deriving the partial differential equation of the microbeam response under the mentioned conditions. Then, implementing the Galerkin’s method the partial differential equation is converted to an ordinary nonlinear differential equation. Finally, the method of multiple scales is used...
Journal Articles
Article Type: Technical Briefs
J. Vib. Acoust. April 2003, 125(2): 244–245.
Published Online: April 1, 2003
... 2002 01 04 2003 elastic deformation partial differential equations stress analysis boundary-value problems Although the problem related to discussion on the compatibility equations possesses rather an academic value, it still attracts many researchers and many papers are devoted...
Journal Articles
Article Type: Technical Papers
J. Vib. Acoust. January 2002, 124(1): 19–25.
Published Online: July 1, 2001
...G. C. Gaunaurd, Fellow ASME; G. C. Everstine The propagation of an impulsive excitation applied at the origin of a lossy viscous medium is studied by operational techniques as the excitation advances through the medium. The solution of the governing partial differential equation (PDE...
Journal Articles
Article Type: Technical Papers
J. Vib. Acoust. April 2001, 123(2): 175–180.
Published Online: September 1, 2000
..., longitudinal tension. In this work, we study the effects of the stresses and non-flat equilibrium produced by twist on the free response. To accomplish this, the equations of motion are linearized about the equilibrium configuration, yielding a set of three, coupled, linear partial differential equations...
Journal Articles
Article Type: Technical Papers
J. Vib. Acoust. January 2001, 123(1): 45–52.
Published Online: August 1, 2000
... partial differential equation that will include the influence of the boundary conditions uncertainty. Two models of the joint stiffness uncertainty are considered. The first represents the uncertainty by a random variable, while the second considers the relaxation process of the joint under dynamic...
Journal Articles
Article Type: Technical Papers
J. Vib. Acoust. January 2001, 123(1): 53–60.
Published Online: August 1, 2000
... natural frequency, and a solution for this case is developed by applying a second order multiple scales method directly to the partial differential equations. The material nonlinearities are found to influence both the degree of nonlinearity in the response and its softening or hardening nature...