A recent theoretical breakthrough has brought a new tool, called the localization landscape, for predicting the localization regions of vibration modes in complex or disordered systems. Here, we report on the first experiment which measures the localization landscape and demonstrates its predictive power. Holographic measurement of the static deformation under uniform load of a thin plate with complex geometry provides direct access to the landscape function. When put in vibration, this system shows modes precisely confined within the subregions delineated by the landscape function. Also the maxima of this function match the measured eigenfrequencies, while the minima of the valley network gives the frequencies at which modes become extended. This approach fully characterizes the low frequency spectrum of a complex structure from a single static measurement. It paves the way for controlling and engineering eigenmodes in any vibratory system, especially where a structural or microscopic description is not accessible.
Bibliographical noteFunding Information:
The authors thank Dominique Clament for the plate design and realization. P.S. is thankful for the Agence Nationale de la Recherche support under ANR PLATON (Grant No.12-BS09-003-01), the LABEX WIFI (the Laboratory of Excellence within the French Program Investments for the Future) under Grant No.ANR-10-IDEX-0001-02 PSL? and the PICS-ALAMO. This research was supported in part by The Israel Science Foundation (Grants No.1781/15 and No.2074/15). S.M. is partially supported by the Alfred P. Sloan Fellowship, the NSF CAREER Grant No.DMS-1056004, the NSF MRSEC Seed Grant DMR 0212302, and the NSF INSPIRE Grant DMS 1344235. M.F. is partially supported by a PEPS-PTI Grant from CNRS.