Qualitative behaviour of L1 and L2 standard deviation in insulations measurements according to standard UNE EN ISO 140-4

Knowledge of the uncertainty of measurement of testing results is important when results have to be compared with limits and specifications. In the measurement of sound insulation following standards UNE EN ISO 140-4 the uncertainty of the final magnitude is mainly associated to the average sound pressure levels L1 and L2 measured. A parameter that allows us to quantify the spatial variation of the sound pressure level is the standard deviation of the pressure levels measured at different points of the room. In this work, for a wide number of measurements following standards UNE EN ISO 140-4 we analyzed qualitatively the behaviour of the standard deviation for L1 and L2. The study of sound fields in enclosed spaces is very difficult. There are a wide variety of rooms with different sound fields depending on factors as volume, geometry and materials. In general, we observe that the L1 and L2 standard deviations contain peaks and dips independent on characteristics of the rooms at single frequencies that could correspond to critical frequencies of walls, floors and windows or even to temporal alterations of the sound field. Also, in most measurements according to UNE EN ISO 140-4 a large similitude between L1 and L2 standard deviation is found. We believe that such result points to a coupled system between source and receiving rooms, mainly at low frequencies the shape of the L1 and L2 standard deviations is comparable to the velocity level standard deviation on a wall

Efectos de la vibración de la pared sobre la desviación estándar de L2 en ensayos UNE EN ISO 140-4 y 140-5

En los ensayos de aislamiento acústico según normas UNE EN ISO 140-4 y 140-5 el valor de L2 es un promedio espacio-temporal de los niveles de presión sonora medidos en diferentes posiciones de la sala receptora. La desviación estándar de estos valores se puede considerar como una medida de la uniformidad del campo sonoro en el recinto. Se analiza este parámetro en función de la frecuencia y se propone un cálculo teórico del mismo como una incertidumbre combinada de la desviación estándar derivada de modelos teóricos centrados en la geometría del recinto y la desviación estándar asociada a la vibración de la pared separadora

Dynamic stabilization of L2 periodic orbits using attitude-orbit coupling effects

Numerical explorations show how the known periodic solutions of the Hill problem are modified in the case of the attitude-orbit coupling that may occur for large satellite structures. We focus on the case in which the elongation is the dominant satellite’s characteristic and find that a rotating structure may remain with its largest dimension in a plane parallel to the plane of the primaries. In this case, the effect produced by the non-negligible physical length is dynamically equivalent to the perturbation produced by an oblate central body on a mass-point satellite. Based on this, it is demonstrated that the attitude-orbital coupling of a long enough body may change the dynamical characteristics of a periodic orbit about the collinear Lagrangian points.

Dynamic stabilization of L2 periodic orbits using attitude-orbit coupling effects

Numerical explorations show how the known periodic solutions of the Hill problem are modified in the case of the attitude-orbit coupling that may occur for large satellite structures. We focus on the case in which the elongation is the dominant satellite?s characteristic and find that a rotating structure may remain with its largest dimension in a plane parallel to the plane of the primaries. In this case, the effect produced by the non-negligible physical dimension is dynamically equivalent to the perturbation produced by an oblate central body on a masspoint satellite. Based on this, it is demonstrated that the attitude-orbital coupling of a long enough body may change the dynamical characteristics of a periodic orbit about the collinear Lagrangian points.

Contribución de la vibración de las paredes de un recinto a la desviación estándar de l2 en medidas de aislamiento a ruido aéreo

Previamente se ha establecido que un parámetro que permite cuantificar la variación espacial de L2 es su desviación estándar. Dados los múltiples factores de los que depende la transmisión del sonido es difícil establecer un modelo teórico que permita explicar la dependencia espectral de este parámetro. En este trabajo se analiza el efecto de la desviación estándar de la vibración no solo de la pared separadora sino de todas las paredes que delimitan el volumen del recinto receptor.

Initial design with L2 Monge-Kantorovich theory for the Monge–Ampère equation method of freeform optics

The Monge–Ampère (MA) equation arising in illumination design is highly nonlinear so that the convergence of the MA method is strongly determined by the initial design. We address the initial design of the MA method in this paper with the L2 Monge-Kantorovich (LMK) theory, and introduce an efficient approach for finding the optimal mapping of the LMK problem. Three examples, including the beam shaping of collimated beam and point light source, are given to illustrate the potential benefits of the LMK theory in the initial design. The results show the MA method converges more stably and faster with the application of the LMK theory in the initial design.