Lues maligna is a rare severe cutaneous manifestation of secondary syphilis. It is also known as malignant syphilis and ulceronodular syphilis. We report a case of a 58-year-old HIV-infected male who presented with diffuse, pruritic, non-tender, maculo-papular skin lesions, ulcerated nodules and plaques surrounded by an erythematous base. The disseminated skin lesions were at various stages and were located on his back, chest, arms and testicles. Patient had been receiving antiretroviral therapy. Laboratory studies had demonstrated CD4 lymphocyte count of 463 cells/mm3 and an undetectable HIV viral load. Workup revealed a rapid plasma reagin of 1:256 dilutions and the skin biopsy findings were compatible with syphilis. The skin lesions resolved with intramuscular penicillin. We herein describe a rare case of lues maligna in an HIV-infected patient with a preserved immune function and viral suppression. Such skin lesions can mimic fungal or mycobacterial infections and can pose a diagnostic challenge. Even in the modern era, syphilis remains the great impostor. Clinicians must be able to recognize this condition based on clinical characteristics and risk factors to diagnose and treat this condition promptly.

In this work, the dynamic response of Euler–Bernoulli beams of four different boundary conditions with fractional order internal damping under a traversing moving load is investigated. The load is assumed to be moving with different values of constant velocity. A proposed approach to obtain the closed-form solution of the problem based on Green’s functions combined with a decomposition technique in the Laplace transform domain is introduced. Several cases are studied and compared to the literature; for instance, if simply supported beam is considered, the following three cases are to be explored: the case of elastic (or undamped) beam, the damped (or viscously damped) beam, and finally the fractionally damped beam modeled by the fractional Kelvin–Voigt model. The effects to the beam dynamic response induced by magnitude of moving load velocity, damping ratio, and fractional damping order are explored. The results expressed sufficient agreement with similar problems found in literature and evidenced that the dynamic response of beams is significantly affected by varying the fractional order of beam damping as well as the moving load velocity. Accordingly, using fractionally damped materials exhibits better realistic behavior of beams and intermediate between elastic and viscous beam behaviors.

Single-degree-of-freedom (SDOF) nonlinear oscillators are widely used for modelling systems with just one degree-of-freedom in addition to single mode approximations to structural elements such as beams and cables, as well as other multi-degree-of-freedom (MDOF) applications. In this work, an investigation of the behavior of SDOF nonlinear oscillators is carried out using the method of direct normal forms. So far, this method has only been considered as a theoretical technique used for solving limited nonlinear dynamical systems in which low orders of nonlinearities appear, involving quadratic and cubic nonlinearities. In this work, thanks to the implementation of symbolic computations, the method of direct normal forms is generalized for solving nonlinear SDOF systems with any order of polynomial (or geometric) weak nonlinearities. Using this new approach, the effect of any higher order nonlinear term, or any combination of nonlinear terms can be investigated. Backbone curve relations are obtained for a selection of example systems representing both hardening and softening systems, and the results are verified by comparing the approximate analytical solutions to numerical solutions generated using COCO numerical continuation toolbox in Matlab.

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