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Keywords: Galerkin method
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Journal Articles
Article Type: Research Papers
J. Vib. Acoust. December 2022, 144(6): 061003.
Paper No: VIB-22-1133
Published Online: September 13, 2022
... by the Technical Committee on Vibration and Sound of ASME for publication in the J ournal of V ibration and A coustics . 18 04 2022 09 08 2022 10 08 2022 13 09 2022 nonlinear vibration axially loaded beam nonlinear foundation Galerkin method elastic boundary restraint dynamics...
Journal Articles
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
Article Type: Research Papers
J. Vib. Acoust. June 2011, 133(3): 031006.
Published Online: March 25, 2011
... equation Galerkin boundary element method boundary-elements methods eigenvalues and eigenfunctions Galerkin method nondestructive testing 18 06 2009 04 08 2010 25 03 2011 25 03 2011 2011 American Society of Mechanical Engineers ...
Journal Articles
Article Type: Research Papers
J. Vib. Acoust. June 2011, 133(3): 031001.
Published Online: March 24, 2011
... for determining the natural frequencies and the modal shapes of an inclined taut cable. The accuracy of the proposed formulae is validated by numerical results obtained by the Galerkin method. The influences of two characteristic parameters λ and ε on the natural frequencies and modal shapes of an inclined taut...
Journal Articles
Article Type: Research Papers
J. Vib. Acoust. February 2011, 133(1): 011007.
Published Online: December 17, 2010
... 01 2010 30 05 2010 17 12 2010 17 12 2010 energy harvesting Galerkin method vibrations Building scalable, low cost, and long lasting power sources for low-power consumption electronics has been the focus of many research efforts in recent years. Today, many critical...
Journal Articles
Article Type: Research Papers
J. Vib. Acoust. October 2010, 132(5): 051012.
Published Online: September 1, 2010
... to the stress function and transverse displacement are found. These eigenfunctions produce an equation that can be used in Galerkin’s method. The initial nonflatness is assumed to be a linear combination of the eigenfunctions of the transverse displacement of the stationary disk problem. Since the initial...
Journal Articles
Article Type: Research Papers
J. Vib. Acoust. October 2010, 132(5): 051001.
Published Online: August 18, 2010
... boundary conditions, is applied to obtain the vibration modes of the plate. The nonlinear vibrations are expanded using these vibrations modes. The dynamical system with three degrees of freedom is derived by Galerkin method. The influence of cut-outs size on linear and nonlinear vibrations of the plate...
Journal Articles
Article Type: Research Papers
J. Vib. Acoust. June 2009, 131(3): 031001.
Published Online: April 7, 2009
... discretizations may be chosen to obtain high eigenfrequencies. We discuss the stability and convergence of the proposed method. Finally we show some examples. 04 05 2005 19 01 2009 07 04 2009 architectural acoustics boundary-elements methods eigenvalues and eigenfunctions Galerkin method...
Journal Articles
Article Type: Research Papers
J. Vib. Acoust. April 2009, 131(2): 021011.
Published Online: February 19, 2009
... nondimensional temporal form by using the generalized Galerkin method. The temporal equation of motion of the system contains nonlinearities of geometric and inertial types along with parametric excitation and nonlinear damping terms. Method of multiple scales is used to determine the instability region...
Journal Articles
Article Type: Technical Papers
J. Vib. Acoust. August 2007, 129(4): 425–433.
Published Online: February 7, 2007
... (with prevalent longitudinal motion). Moreover, an extension of Irvine’s model to moderately nonshallow cables is proposed to determine the frequencies and mode shapes in closed form. 10 12 2005 07 02 2007 elastodynamics wires kinematics elasticity vibrations Galerkin method...
Topics: Cables
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 Papers
J. Vib. Acoust. August 2006, 128(4): 429–438.
Published Online: May 27, 2005
... is a generalized Galerkin’s method ( 14 ), or the method of weighted residuals, rather than the standard Galerkin’s method itself ( 14 15 ). This choice is necessary for the modal decoupling, from which a Duffing equation with constant coefficients is directly obtained due to the orthogonal set of functions...
Journal Articles
Article Type: Technical Papers
J. Vib. Acoust. December 2005, 127(6): 575–587.
Published Online: September 8, 2004
... shapes are calculated using Galerkin’s method. Stiffness for the cracked beam (backbone) has been calculated using an energy procedure. Experimental values have been compared with the results of theoretical predictions and the agreement between the two found to be good. The frequency contour method has...
Journal Articles
Article Type: Technical Papers
J. Vib. Acoust. July 2004, 126(3): 332–342.
Published Online: July 30, 2004
... September 2003. Associate Editor: K. Grosh. 01 February 2003 01 September 2003 30 07 2004 damping nonlinear dynamical systems vibrations Galerkin method elasticity electrostatic actuators beams (structures) Pull-in instability of electrostatically driven MEMS...
Journal Articles
Article Type: Technical Papers
J. Vib. Acoust. July 2004, 126(3): 422–429.
Published Online: July 30, 2004
... at the outer radius r = b . In this paper we investigate the possibility of secondary resonance of a spinning disk under space-fixed excitations. The equations of motion are formulated by using von Karman’s plate model. Galerkin’s method is then employed to discretize the equations of motion...
Journal Articles
Article Type: Technical Papers
J. Vib. Acoust. April 2004, 126(2): 173–183.
Published Online: May 4, 2004
... of the expansion chamber. By this means, the characteristic functions can be analytically determined despite the non-uniform geometry of the expansion chamber. Using the Galerkin method, a variational principle is transformed into linear algebraic equations that are solved to determine the transmission coefficient...
Journal Articles
Article Type: Technical Papers
J. Vib. Acoust. January 2004, 126(1): 92–100.
Published Online: February 26, 2004
... 02 2004 nonlinear dynamical systems bifurcation Fourier analysis Galerkin method minimisation vibrations flexible structures Nonlinear systems are quite commonplace in the study of aerospace and mechanical systems such as gear-trains, linkages, deployable space structures...
Journal Articles
Article Type: Technical Papers
J. Vib. Acoust. July 2002, 124(3): 387–396.
Published Online: June 12, 2002
... into symmetric and antisymmetric groups, each given by a Fourier series in the meridional coordinate. The solutions (natural frequencies and mode shapes) are obtained using Galerkin’s method and verified with published results. The natural frequencies are also obtained for a circular cylinder with shear...
Journal Articles
Article Type: Technical Papers
J. Vib. Acoust. April 2002, 124(2): 310–320.
Published Online: March 26, 2002
.... For the shear stress/strain fields, a quadratic distribution over the beam depth is assumed, which is a refinement of the typical constant shear stress distribution implicit in the Timoshenko model for uncracked beams. The resulting equations of motion are solved by a Galerkin method using local B-splines...
Journal Articles
Article Type: Technical Papers
J. Vib. Acoust. October 2001, 123(4): 510–523.
Published Online: April 1, 2001
... regardless of the probability distribution of the random parameters or the coupling strengths between the substructures. This approximation is derived using Galerkin’s method, in which each modal response is expanded in locally linear interpolation functions in the random system parameters. The proposed...