Effect of sensor placement on measuring higher modes of vibration for a thin flexible cantilever beam in free vibration

The controllability of flexible structures is directly dependent on the accuracy of the sensor outputs, and sensor location is a crucial design criterion for active control. Various sensor placement strategies aim to maximize the measurement of the pertinent modes of vibration to completely identify how a system responds to an input; however, most methodologies are highly computational by design and usually rely on complex optimization algorithms to obtain a solution. To investigate the effect of sensor location on identifying the modes of vibration of flexible structures, a MATLAB computer program was developed to numerically model the free vibratory response of a simple flexible cantilever beam due to static tip displacement and impulse stimulus. The program was designed to take a user defined uniform cantilever beam and calculate the natural frequencies of eight modes of vibration as well as model the dynamic response of the beam at given sensor locations. Sensor locations were chosen based on the results of an existing observeability/controllability based methodology for optimal sensor placement in addition to being placed at locations deliberately chosen to highlight the shortcomings of placing a sensor near a modal.;An experimental set-up was designed for the purpose of validating the numerical results in terms of accurate identification of (1) the modal frequencies of vibration and (2) the magnitude of the displacement at a given sensor position for a predominately first mode vibratory response. A one metre long, aluminum, lightly damped experimental beam was equipped with both piezoelectric film sensors and strain gauges, placed in the same locations used in the numerical model. The beam was excited with an impulse by means of an impact hammer and the sensor outputs were compared. Frequency analysis of the experimental sensor outputs yielded the damped natural frequencies of vibration which were compared to the undamped frequencies obtained numerically.;Both test objectives were successful and the modelling program was validated as a reliable tool for exploring the variation in the modal composition of the sensor output as the sensor location is varied. Computer simulations at various sensor locations confirmed that placing a sensor near or at a mode shape node will jeopardize the detectability of the corresponding vibration mode(s) to the sensor output and that the contribution of a given mode to the sensor output is at a maximum at those sensor locations corresponding to the mode shape maxima for the same mode of vibration, independent of the initial conditions. In conclusion, a guideline for sensor placement was established in that a sensor placed at or in the vicinity of the first occurring mode shape maxima for the Nth mode of vibration will maximize the collective contribution of all N modes of vibration in the sensor output as well as minimize the proximity to modal nodes.