Papers by Keyword: Random Response

Abstract: The seismic spectral computation of structures is time-consuming under multiple-support excitations. The seismic spectral response of structures can be expressed based on several correlation coefficients and the time consumption can be greatly reduced if the coefficients are expressed in closed-form. In this paper, approximate expressions of spatial coherence functions are suggested. Then integrals for the coefficients are carried out analytically and their closed-form expressions are obtained. The closed-form expressions are developed from Clough-Penziens APSD and Hus APSD. The numerical results show that the approximate closed-form expressions of correlation coefficients are of enough engineering accuracy and high efficiency.

Abstract: This paper based on the generalized probabilistic perturbation finite element method solves the random response analysis problem of vibration transfer path systems with translational and rotational motions. The effective random response analysis approaches are achieved using Kronecker algebra, matrix calculus, generalized second moment technique of vector-valued functions and matrix-valued functions. For the vibration transfer path system with multi-dimensional paths, the random response is described correctly and expressly in time domain as uncertain factors, which include mass, damping, stiffness and position, are considered. The mathematical expressions of the first order and second order moments for the random vibration response of vibration transfer path are obtained. According to the corresponding numerical example, the results of calculation are consistent with the results of Monte-Carlo simulation, which shows the method is feasible theoretically.

Abstract: On the basis of the dynamic equations of rotor system with pedestal looseness, the random response method of rotor system with pedestal looseness is researched. The method is based on stochastic perturbation theory and the Kronecker algebra, matrix calculus and random perturbation are used. The reliability model of rotor system with pedestal looseness is proposed. The reliability of rotor system with pedestal looseness is obtained by way of statistical fourth moment method, random perturbation technique. Numerical results are also presented and discussed.

Abstract: The evolutionary power spectrum which can reflect the non-stationary characteristics of earthquake ground motion is estimated by the Hilbert-Huang Transform (HHT), and with reference to the experiential statistical method, an evolutionary spectrum prediction model for given earthquake magnitude and distance is established based on the 121 near-source acceleration records at rock surface with large magnitude from the ground motion database of western U S. The pseudo excitation method is adopted to acquire the solution for structure random response under specific non-stationary seismic excitation. The results demonstrate that the non-stationary contents included in seismic excitation will enlarge greatly the random response of structure in comparison with uniform modulation random excitation.

Abstract: An orthogonal expansion method for earthquake ground motion was introduced in the first part of the paper. In the method, seismic acceleration process is represented as a linear combination of deterministic functions modulated by 10 uncorrelated random variables. In the second part of the paper, the recently developed probability density evolution method (PDEM) is employed to study linear random response of structures subjected to the external excitations. In the PDEM, a completely uncoupled one-dimensional governing partial differential equation, the generalized density evolution equation, is derived first with regard to evolutionary probability density function of the stochastic response for nonlinear structures. The solution of this equation can put out the instantaneous probability density function. So it is natural to combine the PDEM and the orthogonal expansion of seismic ground motion to study the linear random earthquake response. Finally, combining an example of a linear frame structure subjected to non-stationary ground motions, this paper validate the proposed approach and expounds the application of this method.

Abstract: A straightforward numerical method for the computation of response of non-linear finite element system with uncertain parameters under stochastic loading is presented. This method is based on the special form of the probability destiny function of the random variables and, in particular, on the Gauss-Hermite integration rules to compute the response. In the method, a direct and simple formulation, which can just be signed as a symbol of function, is given to represent the relationships between random response and the randomness of the system parameters. In this way, it becomes much easier to obtain the response quantities by computing the double integrals, in which the stochastic parameter of the finite element system is considered as one of the integration variables in the computational procedure, as well as the external force with random characteristic. An example shows the performance of the method.

Abstract: The rubbing phenomenon occurs when a rotating element eventually hits a stationary part of the rotating machinery. Increasing the rotor speed and decreasing the radial clearance between the rotating and the non-rotating parts can enhance the performance of the rotating machinery. This leads to an increased risk of rubbing contact. Rotor rubbing is the source of numerous different phenomena, for example sub- and super-harmonic vibrations, amplitude jumps and rotor instability. So the reliability analysis and sensitivity analysis of rotor system with rubbing is important for design purposes. Reliability analysis can help the designer to establish acceptable tolerance on rotor system. Sensitivity analysis can help the designer to know which problem in rotor system with rubbing is being solved and how the solution may affect the design of rotor system for system correction and reanalysis. On the basis of the dynamic equations of the cracked rotor system model and with consideration of the random parameters including shaft stiffness and damping, disk damping, radial clearance and stator radial stiffness, the random responses of cracked rotor system are researched. The reliability and sensitivity analysis of the cracked rotor system with rubbing are studied. According to the discretization of random process and stress-strength interference theory, the transient reliability model of cracked rotor system with rubbing is proposed. The reliability for rubbing in cracked rotor system is obtained by way of statistical fourth moment method, Edgeworth series technique and first passage theory. Numerical results are also presented and discussed.