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| The Difference on Steady State Responses of a Strongly Nonlinear System via Harmonic Balance Method and Complexification-averaging Technique |
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Abstract Recently, many scholars introduce intentional strong nonlinearities in the studied objects to enhance vibration control or energy harvesting. The responses of strongly nonlinear systems deserve to be evaluated more accurately in order to predict nonlinear effects in theory. Besides, as is known, the nonlinear energy sink (NES) can transfer or absorb the broadband vibration energy of a structure at both high and low frequencies its cubic nonlinear stiffness. First, both the harmonic balance method and the complexification-averaging technique are adopted and compared for acquiring steady state responses of the nonlinear dynamic system. The studied strongly nonlinear system contains a two-degree-of-freedom primary structure, which is subjected to a harmonic excitation, and a NES-piezo device. The NES-piezo device is composed of the nonlinear energy sink (NES) and a piezoelectric energy harvester. The two kinds of approximate analytical results are compared with numerical results. It is found that the two methods have a little difference in steady state responses when the nonlinearity of the system is not very strong. But if the system shows strong nonlinearity, the complex-averaging technique fails to obtain the high order’s responses, while the harmonic balance method can do this. Based on the conclusion, harmonic balance method is adopted to analyze the effect of an adding NES-piezo device on broadband vibration reduction. Two vibration cases are compared. One case applies the NES-piezo device and the other case only uses the NES. Results indicate that using the NES-piezo device will not deteriorate the efficiency of broadband vibration reduction. Furthermore, the responses near the first order resonant frequency can be improved slightly. Besides, results also demonstrates the integration of broadband vibration reduction and piezoelectric energy harvesting by an appropriate NES-piezo device. This research work shows similarities and differences of two approximate methods in solving problems of strong nonlinearity. It will contribute to choosing an appropriate approach when facing different nonlinear situation. And the integration of broadband vibration reduction and piezoelectric energy harvesting provide a theory significance.
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Received: 16 July 2019
Published: 07 November 2019
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2019, Vol. 40 
