Dynamic Analysis of Nonlinear Multi-degree-of-Freedom System Subjected to Combined Gaussian and Poisson White Noises

Inclusion of ground motion–induced uncertainty in structural response evaluation is an essential component for performance-based earthquake engineering. In current practice, ground motion uncertainty is often represented in performance-based earthquake engineering analysis empirically through the use of one or more ground motion suites. How to quantitatively characterize ground motion–induced structural response uncertainty propagation at different seismic hazard levels has not been thoroughly studied to date. In this study, a procedure to quantify the influence of ground motion uncertainty on elastoplastic single-degree-of-freedom acceleration responses in an incremental dynamic analysis is proposed. By modeling the shape of the incremental dynamic analysis curves, the formula to calculate uncertainty in maximum acceleration responses of linear systems and elastoplastic single-degree-of-freedom systems is constructed. This closed-form calculation provided a quantitative way to establish statistical equivalency for different ground motion suites with regard to acceleration response in these simple systems. This equivalence was validated through a numerical experiment, in which an equivalent ground motion suite for an existing ground motion suite was constructed and shown to yield statistically similar acceleration responses to that of the existing ground motion suite at all intensity levels.

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Accelerometer correction for the dynamic analysis of damped multi-degree of freedom systems

Bulletin of the Seismological Society of America ◽

10.1785/bssa0590041591 ◽

1969 ◽

Vol 59 (4) ◽

pp. 1591-1598

Author(s):

G. A. McLennan

Keyword(s):

Dynamic Response ◽

Dynamic Analysis ◽

Degrees Of Freedom ◽

Degree Of Freedom ◽

Exact Method ◽

Three Degrees Of Freedom

Abstract An exact method is developed to eliminate the accelerometer error in dynamic response calculations for damped multi-degree of freedom systems. It is shown that the exact responses of a system can be obtained from the approximate responses which are conventionally calculated from an accelerogram. Response calculations were performed for two typical systems with three degrees of freedom for an assumed pseudo-earthquake. The results showed that the approximate responses may contain large errors, and that the correction developed effectively eliminates these errors.

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Dynamic Modeling of a Multi-Legged Robotic Vehicle: Part 2 — Dynamic Analysis

13th Design Automation Conference: Volume 2 — Robotics, Mechanisms, and Machine Systems ◽

10.1115/detc1987-0109 ◽

1987 ◽

Author(s):

R. A. Hart ◽

N. D. Ebrahimi

Keyword(s):

Dynamic Analysis ◽

Dynamic Model ◽

Dynamic Modeling ◽

Kinetic Equations ◽

Euler Method ◽

Degree Of Freedom ◽

Time Response ◽

Robotic Vehicle

Abstract In Part 1 of this report, we described the overall objective of the investigation; that is, the formulation of a dynamic model for determining the time response of a multi-legged robotic vehicle traveling on a variable-topographic terrain. Specifically, we developed expressions for the joint variables, and their rates, which are essential for describing the system’s links orientations, velocities, and accelerations. This procedure enabled us to determine the kinematic quantities associated with the entire vehicular system in accordance with the Newton-Euler method. In the present paper, we formulate the kinetic equations for the multi-degree-of-freedom leg assemblies, the rigid wheels, and the platform of the vehicle to achieve the prescribed motion and corresponding configuration of the system.

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