... Direct Method,” J. Franklin Inst. , 281 , pp. 51 – 72 . 10.1016/0016-0032(66)90067-6 03 08 2009 13 04 2011 02 05 2011 28 11 2011 28 11 2011 boundary layers compressible flow dams flow control Lyapunov methods nonlinear differential equations partial...

... 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...

... response nonlinear differential equations plates (structures) structural acoustics vibrations rectangular thin plate nonlinear vibration frequency-response function Thin plates have been widely used in many engineering structures, such as shuttles and large space stations...

... equations are derived: conservative, nonconservative, and diagonal. The CESE method is used to numerically solve the conservative form. 04 03 2009 14 01 2010 19 08 2010 19 08 2010 diffusion elastic waves hyperbolic equations nonlinear differential equations oscillations...

... differential equations partial differential equations springs (mechanical) vibrations nonhomogeneous nonlinear spring-mass system rotating beam multiple time scale The overall performance of various engineering systems, such as turbomachinery, wind turbines, robotic manipulators...

... the nonlinear differential equation with odd nonlinearity. Based on the nonlinear differential equation with odd and even nonlinearities, two new nonlinear differential equations with odd nonlinearity are introduced for constructing the analytical approximations to the nonlinear differential equation...

... compressible flow compressors nonlinear differential equations partial differential equations pipe flow pipes pulsatile flow pressure pulsation piping system reciprocating compressor finite disturbance theory acoustic theory Pressure pulsation with large amplitude affects valve...

...M. Kamel; H. S. Bauomy The rotor-active magnetic bearing system subjected to a periodically time-varying stiffness having quadratic and cubic nonlinearities is studied and solved. The multiple time scale technique is applied to solve the nonlinear differential equations governing the system up...

... via the linear and the nonlinear creep models are studied and compared. When α i = 1 , the heuristic nonlinear creep model [Eq. 7 ] is reduced to the linear creep model, and the nonlinear differential equations [Eqs. 23 , 24 ] can be reduced to the governing differential equations...

... and γ 1 , 2 ′ = 0 , and substituting relation 22 into Eqs. 18 , 19 , 20 , 21 gives two nonlinear differential equations 23 − μ + ( s 1 + s 2 + s 3 ) a 2 = − F sin ϕ 24 σ + 2 ( r 1 + r 2 + r 3 ) a 2 = − 2 F cos ϕ...

... 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...

... of which is rather involved. On the other hand, if the two variables appearing in the formulation are coupled using a coupling equation, the final equation is an ordinary nonlinear differential equation, the solution of which becomes much simpler and can be solved by using any standard method to obtain...

... of motion are the coupled nonlinear differential equations. It is difficult to figure out the qualitative relations of physical parameters. However, since the roll motion will result in lateral forces, Eq. 24 , this may explain the fact that in most cases, the critical hunting speeds evaluated by the 6-DOF...

... Kirk. 01 June 2003 08 10 2003 machine bearings nonlinear differential equations limit cycles shear modulus rotors vibrations structural engineering computing continuum mechanics Lund set out to define the circumstances under which stable limit-cycle orbits could...

... in the Jørgen Lund Special Issue of the JOURNAL OF VIBRATION AND ACOUSTICS . Manuscript received June 2003. Guest Associate Editor: R. Gordon Kirk. 01 June 2003 08 10 2003 machine bearings vibrations continuum mechanics elasticity nonlinear differential equations rotors Jørgen...

... brakes vibration control acoustic noise numerical stability elasticity mechanical contact finite element analysis nonlinear differential equations eigenvalues and eigenfunctions structural acoustics There are many engineering systems involving moving loads, such as vehicle brakes...

... between the drillstring and the well bore-hole. In addition, stabilizers are used to guide the drill-collars in the same way as the bearings in rotor machinery. machining rotation sliding friction bending nonlinear differential equations oil technology natural gas technology abrasion...

... for publication in the JOURNAL OF VIBRATION AND ACOUSTICS . Manuscript received July 2001; revised March 2002. Associate Editor: L. A. Bergman. 01 July 2001 01 March 2002 20 09 2002 damping stress-strain relations nonlinear differential equations viscoelasticity oscillations...

... of Section II is used together with relation ( 23 ) for estimating the stiffness parameters z t . The resulting nonlinear differential equation is solved using Monte Carlo simulation for three different values of the relaxation slope parameter λ=0.05, 0.1, and 0.15 and the corresponding results...

... AND ACOUSTICS . Manuscript received March 1999; revised May 2000. Associate Technical Editor: C. Pierre. 01 March 1999 01 May 2000 vibrations nonlinear differential equations resonance oscillations nonlinear dynamical systems In this paper we analyze the modal equations obtained...