Planetary Gear Modal Vibration Experiments and Correlation against Lumped-Parameter and Finite Element Models

Experimental modal analysis techniques are applied to characterize the planar dynamic behavior of two spur planetary gears. Rotational and translational vibrations of the sun gear, carrier, and planet gears are measured. Experimentally obtained natural frequencies, mode shapes, and dynamic response are compared to the results from lumped-parameter and finite element models. Two qualitatively different classes of mode shapes in distinct frequency ranges are observed in the experiments and confirmed by the lumped-parameter model, which considers the accessory shafts and fixtures in the system to capture all of the natural frequencies and modes. The finite element model estimates the high-frequency modes that have significant tooth mesh deflection without considering the shafts and fixtures. The lumped-parameter and finite element models accurately predict the natural frequencies and modal properties established by experimentation. Rotational, translational, and planet mode types presented in published mathematical studies are confirmed experimentally. The number and types of modes in the low-frequency and high-frequency bands depend on the degrees of freedom in the central members and planet gears, respectively. The accuracy of natural frequency prediction is improved when the planet bearings have differing stiffnesses in the tangential and radial directions, consistent with the bearing load direction. (C) 2012 Elsevier Ltd. All rights reserved.

Investigating the Effects of Various Crowd Characteristics on the Dynamic Properties of an Occupied Structure

One of the challenges for structural engineers during design is considering how the structure will respond to crowd-induced dynamic loading. It has been shown that human occupants of a structure do not simply add mass to the system when considering the overall dynamic response of the system, but interact with it and may induce changes of the dynamic properties from those of the empty structure. This study presents an investigation into the human-structure interaction based on several crowd characteristics and their effect on the dynamic properties of an empty structure. The dynamic properties including frequency, damping, and mode shapes were estimated for a single test structure by means of experimental modal analysis techniques. The same techniques were utilized to estimate the dynamic properties when the test structure was occupied by a crowd with different combinations of size, posture, and distribution. The goal of this study is to isolate the occupant characteristics in order to determine the significance of each to be considered when designing new structures to avoid crowd serviceability issues. The results are presented and summarized based on the level of influence of each characteristic. The posture that produces the most significant effects based on the scope of this research is standing with bent knees with a maximum decrease in frequency of the first mode of the empty structure by 32 percent atthe highest mass ratio. The associated damping also increased 36 times the damping of the empty structure. In addition to the analysis of the experimental data, finite element models and a two degree-of-freedom model were created. These models were used to gain an understanding of the test structure, model a crowd as an equivalent mass, and also to develop a single degree-of-freedom (SDOF) model to best represent a crowd of occupants based on the experimental results. The SDOF models created had an averagefrequency of 5.0 Hz, within the range presented in existing biomechanics research, and combined SDOF systems of the test structure and crowd were able to reproduce the frequency and damping ratios associated with experimental tests. Results of this study confirmed the existence of human-structure interaction andthe inability to simply model a crowd as only additional mass. The two degree-offreedom model determined was able to predict the change in natural frequency and damping ratio for a structure occupied by multiple group sizes in a single posture. These results and model are the preliminary steps in the development of an appropriate methodfor modeling a crowd in combination with a more complex FE model of the empty structure.

Investigation of Human-Structure Interaction Through Experimental and Analytical Studies

Vibration serviceability is a widely recognized design criterion for assembly-type structures, such as stadiums, that are likely subjected to rhythmic human-induced excitation. Human-induced excitation of a structure occurs from the movement of the occupants such as walking, running, jumping, or dancing. Vibration serviceability is based on the level of comfort that people have with the vibrations of a structure. Current design guidance uses the natural frequency of the structure to assess vibration serviceability. However, a phenomenon known as human-structure interaction suggests that there is a dynamic interaction between the structure and passive occupants, altering the natural frequency of the system. Human-structure interaction is dependent on many factors, including the dynamic properties of the structure, posture of the occupants, and relative size of the crowd. It is unknown if the shift in natural frequency due to humanstructure interaction is significant enough to warrant consideration in the design process. This study explores the interface of both structural and crowd characteristics through experimental testing to determine if human-structure interaction should be considered because of its potential impact on serviceability assessment. An experimental test structure that represents the dynamic properties of a cantilevered stadium structure was designed and constructed. Experimental modal analysis was implemented to determine the dynamic properties of the empty test structure and when occupied with up to seven people arranged in different locations and postures. Comparisons of the dynamic properties were made between the empty and occupied testing configurations and analytical results from the use of a dynamic crowd model recommended from the Joint Working Group of Europe. Data trends lead to the development of a refined dynamic crowd model. This dynamic model can be used in conjunction with a finite element model of the test structure to estimate the dynamic influence due to human-structure interaction due to occupants standing with straight knees. In the future, the crowd model will be refined and can aid in assessing the dynamic properties of in-service stadium structures.

Experimental Evaluation of the Influence of Human-Structure Interaction for Vibration Serviceability

The effects of human-structure interaction on the dynamic performance of occupied structures have long been observed. The inclusion of the effects of human-structure interaction is important to ensure that the dynamic response of a structure is not overestimated. Previous observations, both in service and in the laboratory, have yielded results indicating that the effects are dependent on the natural frequency of the structure, the posture of the occupants, and the mass ratio of the occupants to the structure. These results are noteworthy, but are limited in their application,because the data are sparse and are only pertinent to a specific set of characteristics identified in a given study. To examine these characteristics simultaneously and consistently, an experimental test structure was designed with variable properties to replicate a variety of configurations within a controlled setting focusing on the effects of passive occupants. Experimental modal analysis techniques were employed to both the empty and occupied conditions of the structure and the dynamic properties associated with each condition were compared. Results similar to previous investigations were observed, including both an increase and a decrease in natural frequency of the occupied structure with respect to the empty structure, as well as the identification of a second mode of vibration. The damping of the combined system was higher for all configurations. Overall, this study provides a broad data set representing a wide array of configurations. The experimental results of this study were used to assess current recommendations for the dynamic properties of a crowd to analytically predict the effects of human-structure interaction. The experimental results were used to select a set of properties for passive, standing occupants and develop a new model that can more accurately represent the behavior of the human-structure system as experimentally measured in this study.