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A novel symplectic superposition method has been proposed and developed for plate and shell problems in recent years. The method has yielded many new analytic solutions due to its rigorousness. In this study, the first endeavor is made to further developed the symplectic superposition method for the free vibration of rectangular thin plates with mixed boundary constraints on an edge. The Hamiltonian system-based governing equation is first introduced such that the mathematical techniques in the symplectic space are applied. The solution procedure incorporates separation of variables, symplectic eigen solution and superposition. The analytic solution of an original problem is finally obtained by a set of equations via the equivalence to the superposition of some elaborated subproblems. The natural frequency and mode shape results for representative plates with both clamped and simply supported boundary constraints imposed on the same edge are reported for benchmark use. The present method can be extended to more challenging problems that cannot be solved by conventional analytic methods.

We consider different models of thermoelastic plates in a bounded reference configuration: with Fourier heat conduction or with the Cattaneo model, and with or without inertial term. Some models exhibit exponential stability, others are not exponential stable. In the cases of exponential stability, we give an explicit estimate for the rate of decay in terms of the essential parameters appearing (delay τ ≥ 0 , inertial constant μ ≥ 0 ). This is first done using multiplier methods directly in L 2 -spaces, then, second, with eigenfunction expansions imitating Fourier transform techniques used for related Cauchy problems; also here essentially energy estimates are used, a spectral analysis is avoided. The explicit estimates allow for a comparison. The singular limits τ → 0 , and μ → 0 are also investigated in order to understand the mutual relevance for the (non-) exponential stability of the models. Numerical simulations underline the results obtained analytically, and exhibit interesting coincidences of analytical and numerical estimates, respectively. [ABSTRACT FROM AUTHOR]

Purpose: To systematically review the outcomes of surgical treatments of chronic acromioclavicular joint dislocation.Methods: Studies were identified by electronic databases (Ovid, PubMed). All studies reporting functional and radiological outcomes of surgical treatments of chronic acromioclavicular joint dislocations were included. Following data were extracted: authors and year, study design, level of evidence, number of patients, age, classification of acromioclavicular joint dislocation, time to surgery, surgical technique, follow-up, clinical and imaging outcomes, complications and failures. Descriptive statistics was used, when a data pooling was not possible. Comparable outcomes were pooled to generate summary outcomes reported as frequency-weighted values. Quality appraisal was assessed through the MINORS checklist.Results: Fourty-four studies were included for a total of 1020 shoulders. Mean age of participants was 38 years. Mean follow-up was 32.9 months. Arthroscopic techniques showed better results than open approach (p < 0.0001). Synthetic reconstructions demonstrated better functional outcomes compared to internal fixation and biologic techniques (p < 0.0001). Among biologic techniques, combined coracoclavicular and acromioclavicular ligaments reconstruction showed better Constant (p = 0.0270) and ASES (p = 0.0113) scores compared to isolated coracoclavicular ligaments reconstruction; anatomic biologic non-augmented graft reconstruction showed better Constant (p < 0.0001), VAS (p < 0.0001) and SSV (p = 0.0177) results compared to augmented techniques. No differences in functional outcomes could be found between anatomic biologic non-augmented graft versus synthetic reconstructions. Overall, methodological quality of the included studies was low.Conclusion: Anatomic reconstructions, both synthetic and biologic, showed the best functional results.Level Of Evidence: IV. [ABSTRACT FROM AUTHOR]