Vibration analysis of a printed circuit board

The reliability of the printed circuit board assembly under dynamic environments, such as those found onboard airplanes, ships and land vehicles is receiving more attention. This research analyses the dynamic characteristics of the printed circuit board (PCB) supported by edge retainers and plug-in connectors. By modelling the wedge retainer and connector as providing simply supported boundary condition with appropriate rotational spring stiffnesses along their respective edges with the aid of finite element codes, accurate natural frequencies for the board against experimental natural frequencies are obtained. For a PCB supported by two opposite wedge retainers and a plug-in connector and with its remaining edge free of any restraint, it is found that these real supports behave somewhere between the simply supported and clamped boundary conditions and provide a percentage fixity of 39.5% more than the classical simply supported case. By using an eigensensitivity method, the rotational stiffnesses representing the boundary supports of the PCB can be updated effectively and is capable of representing the dynamics of the PCB accurately. The result shows that the percentage error in the fundamental frequency of the PCB finite element model is substantially reduced from 22.3% to 1.3%. The procedure demonstrated the effectiveness of using only the vibration test frequencies as reference data when the mode shapes of the original untuned model are almost identical to the referenced modes/experimental data. When using only modal frequencies in model improvement, the analysis is very much simplified. Furthermore, the time taken to obtain the experimental data will be substantially reduced as the experimental mode shapes are not required.In addition, this thesis advocates a relatively simple method in determining the support locations for maximising the fundamental frequency of vibrating structures. The technique is simple and does not require any optimisation or sequential search algorithm in the analysis. The key to the procedure is to position the necessary supports at positions so as to eliminate the lower modes from the original configuration. This is accomplished by introducing point supports along the nodal lines of the highest possible mode from the original configuration, so that all the other lower modes are eliminated by the introduction of the new or extra supports to the structure. It also proposes inspecting the average driving point residues along the nodal lines of vibrating plates to find the optimal locations of the supports. Numerical examples are provided to demonstrate its validity. By applying to the PCB supported on its three sides by two wedge retainers and a connector, it is found that a single point constraint that would yield maximum fundamental frequency is located at the mid-point of the nodal line, namely, node 39. This point support has the effect of increasing the structure's fundamental frequency from 68.4 Hz to 146.9 Hz, or 115% higher.

Pathways to leadership:board independence, diversity, and the emerging pipeline in the US for women directors

In the wake of this decade's corporate scandals, crimes and excesses, improving the effectiveness of corporate governance in the United States has become a priority. An important influence on a board's effectiveness at monitoring is its members’ degree of independence from senior management. While the current definition of independence revolves around the absence of familial and economic connections between a firm and its directors, research suggests that this standard may be inadequate in ensuring independent oversight. Rather, diversity along racial, gender and other dimensions has been proposed as a potentially more effective standard for board independence. This is especially welcome news for women, who currently comprise 51 per cent of the US managerial workforce but only 14.8 per cent of the directors on boards of large, publicly traded US corporations. Some explain the current dearth of women board members by claiming that there are no qualified women available for board service and/or that women are not interested in board service. However, there is more anecdotal rather than empirical evidence on the issue. Surveying women at a women's leadership conference in Boston, this research investigates the extent to which women are currently involved in some type of board service and the extent to which women aspire to future board service. We find that women are currently more active in governance activities than prior research on corporate boards suggests and that they aspire to play a continued and expanded role in governance activities.