... determinants partial differential equations shafts silicon compounds structural acoustics variational techniques Young's modulus Model 3 deflection is shown in Fig. 5 . It is depicted as a function of ξ for various times and for the following conditions: ν = 0 . 1 , γ 1...

... oscillators was proposed in 2007 ( 2 ). nonlinear acoustics oscillators perturbation theory variational techniques 2011 American Society of Mechanical Engineers ...

.... 05 11 2003 14 07 2005 vibrations structural acoustics rotors turbomachinery bifurcation variational techniques chaos Poincare mapping boundary layers aeroacoustics Fluid-film bearings play a key role in the design of turbomachinery systems. They are important components...

... to be independent. 11 08 2003 16 11 2004 29 11 2004 turbines fault diagnosis vibrational modes aerospace industry modelling variational techniques crack detection geometry Vehicle health monitoring systems are becoming a critical safety boosting component in a significant...

... results in Ref. 4 (Fig. 13 (b)). Acceptable agreement can be confirmed. acoustic wave absorption architectural acoustics Galerkin method variational techniques linear algebra In terms of the cylindrical coordinates, the wave equation ( 3 ) and the boundary condition (6) are expressed...

... sensitivity analysis rotation variational techniques elastic constants vibrations This paper presents the case of undamped rotors, therefore the receptances [ α ii ] and [ β ii ] are of real values. For damped supports, [ β ii ] becomes...

... on Vibration and Sound for publication in the JOURNAL OF VIBRATION AND ACOUSTICS . Manuscript received June 1999; revised Aug. 2000. Associate Editor: Kon-Well Wang. 01 June 1999 01 Aug 2000 damping vibrations variational techniques frequency-domain analysis Many investigators...

...–273. oscillations variational techniques determinants limit cycles nonlinear dynamical systems Limit cycle behavior, i.e., self-sustained oscillations of an autonomous, nonlinear, non-conservative system, is observed in a wide variety of mechanical, electrical, and biological...

... time-varying systems linear systems optimisation variational techniques state-space methods Agrawal and Veeraklaew 3 describe the application of this theory for linear time-invariant systems where the states and the controls are related by an integer. Agrawal and Xu 4 extend...