Solution Of Steady-state Response Research Articles

Effects of the fluid-solid interface conditions on the dynamic responses of the saturated seabed during earthquakes

In this paper, the effects of the fluid-solid interface conditions between seawater and seabed on the dynamic responses of the seabed during earthquakes are investigated. Based on Biot's porous media theory, a semi-analytical solution of the 1D transient response and an analytical solution of the 1D steady-state response of the saturated seabed under different fluid-solid interface conditions are given, respectively. Based on the transient response solution, it is found that the fluid-solid interface conditions have a significant effect on slow waves and a small effect on fast waves. Based on the steady-state response solution, it is found that the effects of the fluid-solid interface conditions on the displacement amplification factor and pore-water pressure vary under different incident wave frequencies. In the low-frequency region, the lower the interface permeability, the smaller the displacement amplification factor. In the high-frequency region, the lower the interface permeability, the larger the displacement amplification factor. Moreover, the fluid-solid interface conditions affect the dynamic response of the seabed with different permeability coefficients to different degrees. As the seabed permeability coefficient decreases, the effects of the fluid-solid interface conditions on the dynamic responses of the seabed gradually decrease.

Analytical solutions for steady state responses of an infinite Euler-Bernoulli beam on a nonlinear viscoelastic foundation subjected to a harmonic moving load

The paper deals with the steady state responses of an infinite Euler-Bernoulli beam resting on a nonlinear foundation under a harmonic moving load. Greatly different from previous works, the nonlinear partial differential governing equation of the beam motion is converted to two nonlinear Volterra integral equations by using the Fourier transform, residues Theorem and the convolution theorem. The Volterra integral equations have four different expressions depending on the damping coefficient of the foundation, the linear part of the foundation stiffness and the frequency of the moving load. The modified Adomian decomposition method in conjunction with a simple iterative formula derived from the integral equation theorems are applied to obtain analytical solutions for the steady state responses of the beam. The closed form solutions presented in this paper do not contain complicated infinite integrals, which are better to show the influence of the nonlinear part of foundation stiffness. The parametric study shows that the nonlinear part of foundation stiffness affects not only qualitative but also quantitative analysis results of the infinite Euler-Bernoulli beam under a harmonic moving load.

A nonlinear energy sink with an energy harvester: Harmonically forced responses

This study intends to achieve simultaneous vibration suppression and energy harvesting using a variant form of nonlinear energy sink (NES). The proposed apparatus is not a true NES as its spring is not essentially nonlinear. In a previous study [22] (Journal of Sound and Vibration, 333 (20) (2014)), it has been shown that the apparatus demonstrates the transient behaviors similar to those of the NES. As a sequel, the present paper focuses on harmonically forced responses of the system. First, the approximate solutions of steady state responses are derived. Using the approximate solutions, the steady state behaviors are investigated by using the numerical continuation method. This is followed by an experimental study. The study has shown that under harmonic excitation, the proposed apparatus functions similarly to the NES with the typical behaviors such as strongly modulated responses, amplitude jumping, excitation level dependence, etc. Overall, the apparatus meets the design objectives: the vibration suppression and energy harvesting in a broadband manner.

Closed-Form Steady-State Response Solution of the Twin Rotor Damper and Experimental Validation

In previous research, the twin rotor damper (TRD), an active mass damper, was presented including control algorithms for monofrequent vibrations. In a preferred mode of operation, the continuous rotation mode, two eccentric masses rotate in opposite directions about two parallel axes with a mostly constant angular velocity. The resulting control force is harmonic. Within this paper, the steady-state response of a single-degree-of-freedom (SDOF) oscillator subjected to a harmonic excitation force with and without the TRD is studied. A closed-form solution is presented and validated experimentally. It is shown that the TRD provides damping to the SDOF oscillator until a certain frequency ratio is reached. The provided damping is not only dependent on the design parameters of the TRD but also depends on the steady-state vibration amplitude. The solution serves as a powerful design tool for dimensioning the TRD. The analytical closed-form solution is applicable for other active mass dampers.

Dynamic Characteristic Research on Thin Rim Structure for Herringbone Planetary Gear Train

A torsional and translational vibration dynamics model for serial herringbone planetary gear train, which considers the effects of the time-varying errors and meshing stiffness as well as elastic coupling between two stage trains at the same time, was established by using lumped mass method. Time domain dynamic load excitation which derived from dynamics equation is taken as the input of steady-state response solution. The steady-state response of gear structure was solved with mode superposition method combined with external judgment program. The effects of rim thickness for thin wall herringbone planetary gear and single-stage internal gear were also analyzed. Through the comparison, the displacement and stress results of key locations on structure have reached the satisfying and disirable values when the rim thickness of planetary gear is greater than 4.0 mn and rim thickness of internal gear greater than 6.5 mn.

Vibration analysis of laminated FRP rectangular plates resting on some elastic point supports.

This paper presents an analytical method for determining the free vibration and the steady-state response of a laminated FRP (fiber reinforced plastic) rectangular plate resting on some elastic point supports. The bending rigidities are assumed to be complex quantities (taking into consideration material damping), and are obtained using the classical lamination theory. The Ritz approach is used to yield a governing equation of motion for the plate, and the natural frequencies, mode shapes and the steady-state response solution to a sinusoidally varying point force are derived. The method is applied to a laminated square plate elastically supported at four points symmetrically located at the corners or on the diagonal. The mechanical impedance of the plate is calculated for three types of FRP materials, and the effects of the point supports and the lamination properties upon the vibration characteristics are studied.