The natural frequencies and corresponding vibration modes of a cantilever sandwich beam with a soft polymer foam core are predicted using the higher-order theory for sandwich panels (HSAPT), a two-dimensional finite element analysis, and classical sandwich theory. The predictions of the higher-order theory are shown to be in good agreement with experimental measurements made with a simple experimental setup, as well as with finite element analysis. Experimental observations and analytical predictions show that the classical sandwich theory is not capable of accurately predicting the free vibration response of soft-core sandwich beams. It is shown that the vibration response of the cantilever soft-core sandwich beam consists of a group of five lower frequency shear (antisymmetric) modes that are followed by a group of four thickness-stretch (symmetric) modes. For the higher frequency range, the vibration modes alternate between groups of one-two antisymmetric and symmetric modes. For very high frequencies, interactive vibration response is observed. Experiments show that the damping properties of the foam core are manifest most noticeably in the case of thickness-stretch vibration modes, whereas the influence of damping on the anti-symmetric modes is insignificant.
SUMMARYTime delays are ubiquitous in control systems. They usually enter because of the sensors and actuators used in them. Traditionally, time delays have been thought to have a deleterious e ect on both the stability and the performance of controlled systems, and much research has been done in attempting to eliminate them, compensate for them, or nullify their presence. In this paper we take a di erent view. We investigate whether purposefully injected time delays can be used to improve both the system's stability and performance. Our analytical, numerical, and experimental investigation shows that this can indeed be done. Analytical results of the e ects of time delays on collocated and non-collocated control of classically damped and non-classically damped systems are given. Experimental and numerical results conÿrm the theoretical expectations. Issues of system uncertainties and robustness of time delayed control are addressed. The results are of practical value in improving the performance and stability of controllers because these characteristics (performance and stability) improve dramatically with the intentional injection of small time delays in the control system. The introduction of such time delays constitutes a 'minimal change' to a controller already installed in a structural system for active control. Hence, from a practical standpoint, time delays can be implemented in a nearly costless and highly reliable manner to improve control performance and stability, an aspect that cannot be ignored when dealing with the economics and safety of large structural systems subjected to strong earthquake ground shaking.
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