A Model For General Periodic Excitation With Random Disturbance and its Application

Many vibration problems involve a general periodic excitation such as those of a triangular or rectangular waveform. In practice, the periodic excitation may become disordered due to uncertainties. This paper presents a stochastic model for general periodic excitations with random disturbances which is constructed by introducing random amplitude and phase disturbances to individual terms in the Fourier series of the corresponding deterministic periodic function. Mean square convergence of the random Fourier series are discussed. Monte Carlo simulation of disordered sawtooth, triangular, and quadratic wave forms are illustrated. An application of the excitation is demonstrated by vibration analysis of a single-degree-of-freedom (SDOF) hydraulic valve system subjected to a disordered periodic fluid pressure. In the present study only the phase disturbance is considered. Effects of the intensity of phase modulation on up to fourth order moment response and the convergence rate of the random Fourier series are studied by numerical results. It is found that a small random disturbance in a general periodic excitation may significantly change the response moment

Relativistic Chasles' theorem and the conjugacy classes of the inhomogeneous Lorentz group

This work is devoted to the relativistic generalization of Chasles' theorem, namely to the proof that every proper orthochronous isometry of Minkowski spacetime, which sends some point to its chronological future, is generated through the frame displacement of an observer which moves with constant acceleration and constant angular velocity. The acceleration and angular velocity can be chosen either aligned or perpendicular, and in the latter case the angular velocity can be chosen equal or smaller than than the acceleration. We start reviewing the classical Euler's and Chasles' theorems both in the Lie algebra and group versions. We recall the relativistic generalization of Euler's theorem and observe that every (infinitesimal) transformation can be recovered from information of algebraic and geometric type, the former being identified with the conjugacy class and the latter with some additional geometric ingredients (the screw axis in the usual non-relativistic version). Then the proper orthochronous inhomogeneous Lorentz Lie group is studied in detail. We prove its exponentiality and identify a causal semigroup and the corresponding Lie cone. Through the identification of new Ad-invariants we classify the conjugacy classes, and show that those which admit a causal representative have special physical significance. These results imply a classification of the inequivalent Killing vector fields of Minkowski spacetime which we express through simple representatives. Finally, we arrive at the mentioned generalization of Chasles' theorem.Comment: Latex2e, 49 pages. v2: few typos correcte

A geometrical introduction to screw theory

This work introduces screw theory, a venerable but yet little known theory aimed at describing rigid body dynamics. This formulation of mechanics unifies in the concept of screw the translational and rotational degrees of freedom of the body. It captures a remarkable mathematical analogy between mechanical momenta and linear velocities, and between forces and angular velocities. For instance, it clarifies that angular velocities should be treated as applied vectors and that, under the composition of motions, they sum with the same rules of applied forces. This work provides a short and rigorous introduction to screw theory intended to an undergraduate and general readership.Comment: Latex2e, 24 pages. v2: expanded introduction, added 2 figure

Short-Term Impact of Bracing in Multi-Level Posterior Lumbar Spinal Fusion

Background: Clinical practice in postoperative bracing after posterior lumbar spine fusion (PLF) is inconsistent between providers. This paper attempts to assess the effect of bracing on short-term outcomes related to safety, quality of care, and direct costs. Methods: Retrospective cohort analysis of consecutive patients undergoing multilevel PLF with or without bracing (2013-2017) was undertaken (n = 980). Patient demographics and comorbidities were analyzed. Outcomes assessed included length of stay (LOS), discharge disposition, quality-adjusted life years (QALY), surgical-site infection (SSI), total cost, readmission within 30 days, and emergency department (ED) evaluation within 30 days. Results: Amongst the study population, 936 were braced and 44 were not braced. There was no difference between the braced and unbraced cohorts regarding LOS (P = .106), discharge disposition (P = .898), 30-day readmission (P = .434), and 30-day ED evaluation (P = 1.000). There was also no difference in total cost (P = .230) or QALY gain (P = .740). The results indicate a significantly lower likelihood of SSI in the braced population (1.50% versus 6.82%, odds ratio = 0.208, 95% confidence interval = 0.057-0.751, P = .037). There was no difference in relevant comorbidities (P = .259-1.000), although the braced cohort was older than the unbraced cohort (63 versus 56 y, P = .003). Conclusion: Bracing following multilevel posterior lumbar fixation does not alter short-term postoperative course or reduce the risk for early adverse events. Cost analysis show no difference in direct costs between the 2 treatment approaches. Short-term data suggest that removal of bracing from the postoperative regimen for PLF will not result in increased adverse outcomes