Modeling Dynamic Behavior of Stacked Sliding-Rocking Rigid Blocks Subjected to Base Excitation

A system of stacked rigid blocks can be found in many applications of non-structural components: a statue resting on the top of a table is such an example. Previous studies usually assume that the friction at contact interface is so large that only rocking motion can be activated. However, this assumption may not be realistic when assessing the seismic response of unanchored non-structural components. Motivated from this constraint, this paper contributes to the state-of-the-art research of the classical rocking problem by presenting a numerical model within which sliding, rocking and sliding-rocking response of stacked rigid blocks can be computed by the time-history analysis. The exact fully nonlinear equations of motion, transition criteria for different response modes and treatment to handle the impact are presented in detail. The accuracy of the developed model is validated. A case study is also provided to investigate the overall failure probability of the stacked rigid blocks with realistic friction coefficient. In this particular case study, it is also shown that increasing the friction coefficient makes the stacked rigid blocks more susceptible to failure.

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A Reliable Pre-Processing for the Simulation of Friction Joints in Turbomachineries and its Validation: A Case Study With Policontact

Volume 7B: Structures and Dynamics ◽

10.1115/gt2019-91764 ◽

2019 ◽

Author(s):

Christian M. Firrone ◽

Giuseppe Battiato

Keyword(s):

Equations Of Motion ◽

Good Practice ◽

Forced Response ◽

Mathematical Basis ◽

Reduction Techniques ◽

Safety Margins ◽

Pass Through ◽

Nonlinear Equations Of Motion ◽

Physical Phenomena

Abstract Industry and University collaborates to develop methods to simulate the nonlinear dynamics of components in rotating assemblies like turbine or compressor modules in the presence of friction joints. This collaboration produced fruitful results providing a family of numerical solvers with the goal of foreseeing the safety margins against High Cycle Fatigue failure. Softwares are therefore intended as design tools to exploit the damping effect of joints by controlling geometrical features, materials and contact loads. Contact models, reduction techniques to handle complex blade geometries modeled by Finite Element softwares, and numerical techniques to solve the nonlinear equations of motion are refined to provide the level of vibration amplitude as fast as possible by keeping the representativeness of the physical phenomena that are involved. A reliable compromise between speed and accuracy must be confirmed by several ‘gates’ to pass through during all the simulation process, in particular during pre-processing phase. The objective of this paper is to propose a good practice made of a list of actions to check the goodness of the mathematical basis to obtain reliable results from simulation. Experience gained thanks to the long-lasting collaboration between Politecnico di Torino and GE Avio for the development of the software Policontact provides a case study of an effective synthesis between two requirements that are often opposed to each other: complex mathematical models to simulate the nonlinear forced response of rotating components on one side and a robust, confident implementation of an easy-to-use tool intended for industrial staff with complementary background on the other side.

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Differential Formulation for the Coefficient of Restitution of a Rigid Link

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.762.175 ◽

2015 ◽

Vol 762 ◽

pp. 175-182 ◽

Cited By ~ 1

Author(s):

Dorian Cojocaru ◽

Dan B. Marghitu

Keyword(s):

Mobile Robots ◽

Initial Conditions ◽

Equations Of Motion ◽

Coefficient Of Restitution ◽

Numerical Techniques ◽

Differential Impact ◽

Differential Formulation ◽

Nonlinear Contact ◽

Nonlinear Equations Of Motion ◽

The Impact

The differential impact equations of motion are developed using an nonlinear contact force. The nonlinear equations of motion are written using symbolical MATLAB and are solved using numerical techniques. The impact equations are based on the Kogut-Etsion model. The numerical results are obtained for different geometries of the link, different coefficients of friction, and different initial conditions. The coefficient of restitution (COR) is discussed for specific cases. The results can be used for the impact of mobile robots with different type of surfaces.

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