Optimal Damper Slip Force for Vibration Control Structures Incorporating Friction Device with Sway-Rocking Motion Obtained Using Shaking Table Tests

In this study, a series of shaking table tests were conducted using a specimen that consisted of a superstructure, incorporating a friction device and a sway-rocking mechanism under the superstructure to determine the optimal damper slip force of a passive vibration control system considering the effects of sway-rocking motion. The adopted simple friction device, composed of rubber bands and stainless steel plates, allowed the magnitude of the slip force to be easily set. The optimal slip force of the friction device, which minimizes the peak and root-mean-square response of the superstructure subjected to earthquakes, was determined from the shaking table tests. Based on the results, the optimal slip force of the friction device was found to vary according to the input level of the ground motions and the sway-rocking conditions. The obtained results suggest that the effect of sway-rocking motion should be considered in the design of passive control structures and the determination of their optimal damper slip force.

Transient Response of MDOF Systems With Inerters to Nonstationary Stochastic Excitation

Explicit, closed-form, exact analytical expressions are derived for the covariance kernels of a multi degrees-of-freedom (MDOF) system with arbitrary amounts of viscous damping (not necessarily proportional-type), that is equipped with one or more auxiliary mass damper-inerters placed at arbitrary location(s) within the system. The “inerter” is a device that imparts additional inertia to the vibration damper, hence magnifying its effectiveness without a significant damper mass addition. The MDOF system is subjected to nonstationary stochastic excitation consisting of modulated white noise. Results of the analysis are used to determine the dependence of the time-varying mean-square response of the primary MDOF system on the key system parameters such as primary system damping, auxiliary damper mass ratio, location of the damper-inerter, inerter mass ratio, inerter node choices, tuning of the coupling between the damper-inerter and the primary system, and the excitation envelope function. Results of the analysis are used to determine the dependence of the peak transient mean-square response of the system on the damper/inerter tuning parameters, and the shape of the deterministic intensity function. It is shown that, under favorable dynamic environments, a properly designed auxiliary damper, encompassing an inerter with a sizable mass ratio, can significantly attenuate the response of the primary system to broad band excitations; however, the dimensionless “rise-time” of the nonstationary excitation substantially reduces the effectiveness of such a class of devices (even when optimally tuned) in attenuating the peak dynamic response of the primary system.

Approximate Analytical Mean-Square Response of an Impacting Stochastic System Oscillator With Fractional Damping

The paper deals with the stochastic dynamics of a vibroimpact single-degree-of-freedom system under a Gaussian white noise. The system is assumed to have a hard type impact against a one-sided motionless barrier, located at the system's equilibrium. The system is endowed with a fractional derivative element. An analytical expression for the system's mean squared response amplitude is presented and compared with the results of numerical simulations.

Transient Response of a SDOF System With an Inerter to Nonstationary Stochastic Excitation

An analytical study is presented of the covariance kernels of a damped, linear, two-degrees-of-freedom (2DOF) system which resembles a primary system that is provided with an auxiliary mass damper (AMD), in addition to an “inerter” (a device that imparts additional inertia to the vibration damper, hence magnifying its effectiveness without a significant damper mass addition). The coupled 2DOF system is subjected to nonstationary stochastic excitation consisting of a modulated white noise. An exponential function, resembling the envelope of a typical earthquake, is considered. Results of the analysis are used to determine the dependence of the peak transient mean-square response of the system on the damper/inerter tuning parameters, and the shape of the deterministic intensity function. It is shown that, under favorable dynamic environments, a properly designed auxiliary damper, encompassing an inerter with a sizable mass ratio, can significantly attenuate the response of the primary system to broad band excitations; however, the dimensionless “rise-time” of the nonstationary excitation substantially reduces the effectiveness of such a class of devices (even when optimally tuned) in attenuating the peak dynamic response of the primary system.

Seismic Performance Reliability Analysis of Frame Structure with Special-Shaped Columns

The displacement response of special-shaped column frame structure on the elasto-plastic state was obtained with the Pushover method. Using Park-Ang model to calculate the damage level of each floor, and then using the improved mean response spectrum analysis method to compute the mean square response of the maximum elasto-plastic structure interlayer displacement and the probability of different damage levels. The result shows that the seismic performance of special-shaped column structure will be better reflected when the structure is analyzed with the methods mentioned above and these methods have some theoretical significance.

Response of a Rotating Shaft to Uniaxial Random Excitation

Random vibrations are considered for a Jeffcott rotor subject to uniaxial broadband random excitation by a lateral force along one of its transverse axes. Exact analytical solution for mean square responses is obtained which provide quantitative description of two effects: the magnification of mean square whirl radius due to rotation; and the increasing mean square response along the nonexcited direction with increasing rotation speed, that is, the spread of vibration to all directions around the shaft. The latter effect clearly corresponds to the approaching forward whirl of the shaft approaching its instability threshold; it can be used for the on-line evaluation of the rotor’s stability margin from the simple processing of its measured response signals as demonstrated by direct numerical simulation.

Stochastic Response and Stability Analysis of Two-Point Mooring System

The stochastic response and stability of a two-point mooring system are investigated for random sea state represented by the P-M sea spectrum. The two point mooring system is modeled as a SDOF system having only stiffness nonlinearity; drag nonlinearity is represented by an equivalent linear damping. Since no parametric excitation exists and only the linear damping is assumed to be present in the system, only a local stability analysis is sufficient for the system. This is performed using a perturbation technique and the Infante’s method. The analysis requires the mean square response of the system, which may be obtained in various ways. In the present study, the method using van-der-Pol transformation and F-P-K equation is used to obtain the probability density function of the response under the random wave forces. From the moment of the probability density function, the mean square response is obtained. Stability of the system is represented by an inequality condition expressed as a function of some important parameters. A two point mooring system is analysed as an illustrative example for a water depth of 141.5 m and a sea state represented by PM spectrum with 16 m significant height. It is shown that for certain combinations of parameter values, stability of two point mooring system may not be achieved.

Response Statistics and Reliability Analysis of a Mistuned and Frictionally Damped Bladed Disk Assembly Subjected to White Noise Excitation

In the design of gas turbine engines, the analysis of nonlinear vibrations of mistuned and frictionally damped blade-disk assembly subjected to random excitation is highly complex. The transitional probability density function (PDF) for the random response of nonlinear systems under white or coloured noise excitation (delta-correlated) is governed by both the forward Fokker-Planck (FP) and backward Kolmogorov equations. This paper presents important improvement and extensions to a computationally efficient higher order, finite difference (FD) technique for the solution of higher dimensional FP equation corresponding to a two degree of freedom nonlinear system representative of vibration of tip shrouded frictionally damped bladed disk assembly subjected to Gaussian white noise excitation. Effects of friction damping on the mean square response of a blade are investigated. The friction coefficient of the damper is assumed to be a function of the sliding velocity of the contact surface. The effects of stiffness and damping mistuning on the forced response of frictionally damped bladed disk are investigated. Numerical studies are presented for a pair of mistuned blades of cyclic assemblies. The response and reliability of a blade subjected to random excitation is also obtained. With time averaged probability density as an invariant measure, the probability of large excursion in case of damping mistuning is also presented. The results of the FD method are validated by comparing with Monte Carlo Simulation (MCS) results.