Narrow bandwidth is the major challenge to today’s vibration-based energy harvesters. Compared with other broadband approaches that involve moving parts and control electronics, a double-mass piezoelectric cantilever beam provides a simple and reliable solution to widen the effective bandwidth as a vibration energy harvester. In this article, a continuum model of a double-mass lead zirconate titanate cantilever subject to sinusoidal base excitation is presented. First, the undamped equation of motion along with boundary and transition conditions is derived from Hamilton’s principle, followed by modal analysis that determines the eigenfunctions and natural frequencies. Next, the coupled electromechanical equations for sinusoidal base excitation are obtained. The output voltage and relative displacement are solved analytically. The frequency response function and mode shapes predicted by the model are validated against experiments.

No abstract

No abstract

BackgroundTo investigate the association between coping styles, gender, their interactions and non-suicidal self-injurious (NSSI) behaviors among middle school students in rural western China under COVID-19.MethodsA multicentre cross-sectional study method was used to conduct an online survey of 8,361 students from 23 middle schools in the northern Sichuan region by clustering sampling, using the General Information Questionnaire, the Ottawa Self-Injury Inventory, and the Coping Style Scale for Middle School Students.ResultsThe past year prevalence of NSSI among middle school students in rural west China was 5.7%. The differences in scores between those with and without NSSI on all dimensions of coping styles were statistically significant (p < 0.001). Multivariate logistic regression analysis revealed that vocational high school (OR = 1.67), girls (OR = 2.5), single parent with divorced parents (OR = 1.89), remarriage with divorced parents (OR = 1.81), and tolerance (OR = 1.17), venting emotions (OR = 1.15) and fantasy/denial (OR = 1.07) in coping styles may increase the risk of NSSI among middle school students, while problem solving (OR = 0.9) and seeking social support (OR = 0.9) among coping styles may reduce the risk of NSSI among middle school students. The interaction results show that gender has a moderating role in the process of endurance, avoidance, venting of emotions, and fantasy/denial influencing non-suicidal self-injury in middle school students.ConclusionThere is an association between coping styles and self-injury among middle school students in rural areas in western China, with gender playing a moderating role. Active attention should be paid to students' coping styles and encouraging them to adopt positive coping styles as well as avoid negative coping styles, especially in the case of girls, which can help prevent self-injury.

While vibration energy harvesting has become a viable means to power wireless sensors, narrow bandwidth is still a hurdle to the practical use of the technology. For conventional piezoelectric or electromagnetic harvesters, having multiple proof masses mounted on a beam is one way to widen the effective bandwidth. This is because the addition of proof masses increases the number of resonant modes within the same frequency range. Based on the assumptions of the Euler-Bernoulli beam theory, this paper presents a continuum-based model for a two-mass cantilever beam. First, the equation of motion is derived from Hamilton's principle. Next, the modal analysis is presented and a steady state solution for harmonic base excitation is derived. The two-mass beam is considered as two serially connected beam segments. In the derivation, emphasis is given to the transition conditions, which would otherwise not appear in the traditional single mass beam model. Experimental validation on a stainless steel beam confirms that the model can accurately predict both natural frequencies and the frequency response of an arbitrary point along the beam. The derivation procedure presented in this paper is applicable to a beam with any number of proof masses. Lastly, it is demonstrated how the model can be applied to a piezoelectric energy harvester.Qing Ou, XiaoQi Chen (senior member of IEEE) and Stefanie Gutschmidt are with the Mechanical Engineering Department,