Abstract
Vibration response and amplitude frequency characteristics of a controlled nonlinear meso-scale beam under periodic loading are studied. A method including a general analytical expression for harmonic balance solution to periodic vibration and an updated cycle iteration algorithm for amplitude frequency relation of periodic response is developed. A vibration equation with the general expression of nonlinear terms for periodic response is derived and a general analytical expression for harmonic balance solution is obtained. An updated cycle iteration procedure is proposed to obtain amplitude frequency relation. Periodic vibration response with various frequencies can be calculated uniformly using the method. The method can take into account the effect of higher harmonic components on vibration response, and it is applicable to various periodic vibration analyses including principal resonance, super-harmonic resonance, and multiple stationary responses. Numerical results demonstrate that the developed method has good convergence and accuracy. The response amplitude should be determined by the periodic solution with multiple harmonic terms instead of only the first harmonic term. The damping effect on response illustrates that vibration responses of the nonlinear meso beam can be reduced by feedback control with certain damping gain. The amplitude frequency characteristics including anti-resonance and resonant response variation have potential application to the vibration control design of nonlinear meso-scale structure systems.
Highlights
The meso-scale beam is an important component of many precise instruments such as micro-sensors or micro-actuators [1]
Its nonlinear vibration equation in dimensionless form is as Equations (1) and (9), in which αi (i = 1, 2, 3, 4) are constants for the uniform beam
Numerical results on the non-dimensional vibration response and amplitude frequency relation are shown in Figures 2–14, which have been verified through direct numerical simulation
Summary
The meso-scale beam is an important component of many precise instruments such as micro-sensors or micro-actuators [1]. The large amplitude motion of the beam subjected to strong loading, e.g., a cantilever beam under strong support motion loading, leads to complicated nonlinear vibration [2], which will degrade the mechanical performance of the instruments. Vibration control of the beam is highly desirable, and in this connection, the vibration response and amplitude frequency characteristics of the controlled nonlinear beam need to be studied. Feedback control of MDOF systems has been studied [5,6,7,8,9,10,11,12,13,14]. The control effectiveness of a large damping gain on vibration mitigation of the nonlinear meso beam needs to be studied further
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