The near resonant response of suspended, elastic cables driven by planar excitation is investigated using a three degree-of-freedom model. The model captures the interaction of a symmetric in-plane mode with two out-of-plane modes. The modes are coupled through quadratic and cubic nonlinearities arising from nonlinear cable stretching. For particular magnitudes of equilibrium curvature, the natural frequency of the in-plane mode is simultaneously commensurable with the natural frequencies of the two out-of-plane modes in 1:1 and 2:1 ratios. A second nonlinear order perturbation analysis is used to determine the existence and stability of four classes of periodic solutions. The perturbation solutions are compared with results obtained by numerically integrating the equations of motion. Furthermore, numerical simulations demonstrate the existence of quasiperiodic responses.
SUMMARY
Sixty‐seven children who had been operated on for equinus deformity due to spastic cerebral palsy were studied retrospectively. The recurrence rate of equinus after 51 Baker‐Strayer gastrocnemius lengthenings was 29 per cent, and after the sliding Hoke type of tendo calcaneus lengthenings it was 9 per cent. In both groups the postoperative care was the same: no bracing, no night splints, and no stretching. The recurrence rate of equinus after tendo calcaneus lengthening is comparable with other reported series.
RÉSUMÉ
Correction chirurgicale de l'équin dans I'infirmite motrice cérébrale Soixante‐sept enfants presentant un équin liéà une forme spastique d'iMC ont été etudies retrospectivement. Le taux de recidive de I'equin apres 51 allongements des jumeaux type Baker‐Strayer a été de 29 pour cent et apres l'allongement du tendon d'Achille par glissement type Hoke de 9 pour cent. Dans les deux groupes, les soins post‐operatoires ont été identiques: pas d'attelles de jour oude nuit et pas d'etirement. Cette frequence de recidive de I'equin apres allongement du tendon d'Achille est comparable a celle qui est rapportee dans d'autres series.
ZUSAMMENFASSUNG
Chirurgische Korrektur einer Spitzfußstellung bei Cerebralparese 67 Kinder mit einer Spitzfulistellung aufgrund einer Cerebralparese wurden nachunt‐ersucht. Die Rezidivrate nach 51 Verlangerungen des Gastrocnemius nach Baker‐Strayer betrug 29 Prozent, nach der Verlangerung der Achillessehne nach Hoke 9 Prozent. Die postoperative Behandlung war bei beiden Gruppen dieselbe: keine Bandage, keine Nachtschiene und kein Streckverband. Die Rezidivhaufigkeit nach der Verlangerung der Achillessehne bei dieser Untersuchungsserie ist vergleichbar mit anderen in der Literatur beschriebenen Serien.
RESUMEN
Correction quirurgica de la deformidad en equino en la parálisis cerebral Sesenta y siete niños con deformidad en enquino debida a parálisis cerebral espastica fueron estudiados retrospectivamente. El porcentaje de recurrencia del equino despues de 51 elongaciones del gastrocnemio por la tecnica de Baker‐Strayer fue de 29 por ciento y despues de la tecnica de deslizamiento de Hoke para elongacion del tendon de aquiles fue de 9 por ciento. En ambos grupos los cuidados postoperatorios fueron los mismos: no utilization de vendajes, no ferulas nocturnas y no alargamientos. Este tanto por ciento de recurrencia despues de la elongacion del tendon de aquiles en el pie de equino es comparable con las cifras aportadas en otras series.
The near-resonant response of suspended, elastic cables driven by planar excitation is investigated using a two degree-of-freedom model. The model captures the interaction of a symmetric in-plane mode and an out-of-plane mode with near commensurable natural frequencies in a 2:1 ratio. The modes are coupled through quadratic and cubic nonlinearities arising from nonlinear cable stretching. The existence and stability of periodic solutions are investigated using a second order perturbation analysis. The first order analysis shows that suspended cables may exhibit saturation and jump phenomena. The second order analysis, however, reveals that the cubic nonlinearities and higher order corrections disrupt saturation. The stable, steady state solutions for the second order analysis compare favorably with results obtained by numerically integrating the equations of motion.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.