Nonlinear Vibration Caused by Beam of Cable Structures
The nonlinear vibrations of cables excited by thevibration of beam were investigated. At first, a simpleconnection condition and boundary condition of thecable-stayed beam structure were applied. Thenonlinear equations of motion of the cable-stayedbeam structure were derived, and the static sag of thecable as well as the geometric nonlinearity wasconsidered, moreover, Appling the multi-scaleperturbation method, the nonlinear vibrations ofcables were studied, the nonlinear vibration responseof cables was analyzed by the Runge-Kutta numericalmethod to obtain the frequency-response curves. Theresults indicate that the beam small scale vibration canstimulate the cable the large scale movement whenlocal oscillation frequency of beams is in the certainregion, it affects the cable-stayed beam structure thestability and the security in the Engineering. For thesystem in which the damping and the frequency ratiowas given, the enough low excitation amplitudes canavoid the system resonances.
On the symmetric modal interaction of the suspended cable: Three-to-one internal resonance
Abstract The two-mode nonlinear response of a suspended cable subjected to the primary resonance is investigated, and the three-to-one internal resonance is analyzed. Because the treatment of Galerkin discrete models of spatially continuous systems with initial curvature may lead to erroneous quantitative or even qualitative results, the method of multiple scales is applied to directly attack the nonlinear partial differential equation and the boundary conditions, which leads to the modulation equations for the primary resonance of either the first or third symmetric mode. The Newton–Raphson method and the pseudo-arclength scheme are used to obtain the frequency-response curves and force-response curves, and the dynamic solutions of the modulation equations are also investigated.
Computational spectroscopy of carbon monoxide isotopomers in helium clusters.
The rotational excitation spectrum, including the vibrational shift of the rotational band, of several CO isotopomers solvated in He clusters has been calculated. Reptation quantum Monte Carlo simulations are used in conjunction with an accurate He-CO potential energy surface, which quantitatively describes the rovibrational spectrum of the binary complex. Our simulations, when compared with number-selective infrared spectra taken for different isotopomers, help discriminate among the alternative assignments proposed for cluster sizes around 15 He atoms. The origin of the vibrational band has a red shift that is nearly linear with the cluster size within the first solvation shell and is almost constant up to the largest cluster studied, well beyond completion of the second solvation shell. A blue upturn at even larger sizes would be needed to attain the nanodroplet limit, as recently estimated from the isotopic dependence of the measured R(0) transitions.