... structures. National Natural Science Foundation of China 10.13039/501100001809 11972125 nonlinear vibration axially loaded beam nonlinear foundation Galerkin method elastic boundary restraint dynamics nonlinear vibration structural dynamics and control vibration control...

..., 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...

... 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 ...

... 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...

... Excitations ,” J. Sound Vib. 0022-460X , 329 , pp. 3621 – 3631 . 10.1016/j.jsv.2010.04.002 29 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...

... 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...

... 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...

... 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...

... 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...

... (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...

... 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...

.... 169 – 186 . 03 08 2004 27 05 2005 chaos laminates Galerkin method boundary-value problems vibrations structural acoustics transient response oscillations modal analysis Nonlinear dynamic response of a thin laminate can be induced by mechanical and thermal loads...

... 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...

... 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) In the next section, we present a description...

... for publication in the JOURNAL OF VIBRATION AND ACOUSTICS . Manuscript received June 2001; Revised Dec. 2003. Associate Editor: J. P. Cusumano. 01 June 2001 01 Dec 2003 30 07 2004 surface acoustic waves vibrations acoustic resonance Galerkin method 7 (a) Time history...

... 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...

.... Associate Editor: R. P. S. Han. 01 August 2001 01 December 2002 26 02 2004 nonlinear dynamical systems bifurcation Fourier analysis Galerkin method minimisation vibrations flexible structures Nonlinear systems are quite commonplace in the study of aerospace...

... 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...

.... 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...

... 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...