振动与冲击
振動與遲擊
진동여충격
JOURNAL OF VIBRATION AND SHOCK
2014年
19期
8-16
,共9页
压电发电悬臂梁%材料非线性%多尺度法%主共振
壓電髮電懸臂樑%材料非線性%多呎度法%主共振
압전발전현비량%재료비선성%다척도법%주공진
piezoelectric cantilevered energy harvesters%material nonlinearity%multi-scale method%primary resonance
针对单晶压电悬臂梁发电系统进行了动力学建模及主共振响应分析。首先在考虑压电材料非线性的情况下，利用广义Hamilton原理、Rayleigh-Ritz法、Euler-Bernoulli 梁理论等建立了单晶压电悬臂梁发电结构的机电耦合模型；其次利用多尺度法对系统进行了主共振二次近似响应分析，得到了谐振频率附近解的特性与系统参数的关系，揭示了压电材料非线性、外激励参数及负载电阻对系统响应的影响规律；最后通过数值计算验证了解析解的正确性。结论表明，压电材料的非线性特性会导致近似解的共振峰向左偏移，呈现软特性的非线性特征；当激励频率变化时，系统响应存在多解、跳跃等现象，多解区有2个稳定焦点和1个不稳定鞍点；主共振解的真正实现取决于系统的稳定性条件及初始条件的选取；系统存在最佳匹配负载电阻范围，对应系统的发电功率较大。
針對單晶壓電懸臂樑髮電繫統進行瞭動力學建模及主共振響應分析。首先在攷慮壓電材料非線性的情況下，利用廣義Hamilton原理、Rayleigh-Ritz法、Euler-Bernoulli 樑理論等建立瞭單晶壓電懸臂樑髮電結構的機電耦閤模型；其次利用多呎度法對繫統進行瞭主共振二次近似響應分析，得到瞭諧振頻率附近解的特性與繫統參數的關繫，揭示瞭壓電材料非線性、外激勵參數及負載電阻對繫統響應的影響規律；最後通過數值計算驗證瞭解析解的正確性。結論錶明，壓電材料的非線性特性會導緻近似解的共振峰嚮左偏移，呈現軟特性的非線性特徵；噹激勵頻率變化時，繫統響應存在多解、跳躍等現象，多解區有2箇穩定焦點和1箇不穩定鞍點；主共振解的真正實現取決于繫統的穩定性條件及初始條件的選取；繫統存在最佳匹配負載電阻範圍，對應繫統的髮電功率較大。
침대단정압전현비량발전계통진행료동역학건모급주공진향응분석。수선재고필압전재료비선성적정황하，이용엄의Hamilton원리、Rayleigh-Ritz법、Euler-Bernoulli 량이론등건립료단정압전현비량발전결구적궤전우합모형；기차이용다척도법대계통진행료주공진이차근사향응분석，득도료해진빈솔부근해적특성여계통삼수적관계，게시료압전재료비선성、외격려삼수급부재전조대계통향응적영향규률；최후통과수치계산험증료해석해적정학성。결론표명，압전재료적비선성특성회도치근사해적공진봉향좌편이，정현연특성적비선성특정；당격려빈솔변화시，계통향응존재다해、도약등현상，다해구유2개은정초점화1개불은정안점；주공진해적진정실현취결우계통적은정성조건급초시조건적선취；계통존재최가필배부재전조범위，대응계통적발전공솔교대。
Dynamic modeling and primary resonance response analysis of cantilevered piezoelectric energy harvesters were presented.Firstly,the electromechanical coupling model of a cantilevered piezoelectric harvester was established considering nonlinearities of piezoelectric material using Hamilton principle,Rayleigh-Ritz method,Euler-Bernoulli beam theory and constant electrical field across the piezoelectric element.Then,the second order approximate solution to the primary resonance response of the system was investigated by using the multi-scale method.The influences of piezoelectric material nonlinearity and external excitation on the system response,and those of load resistance on the output power of the system were analyzed.By exploring the nonlinear characteristics of the response of the system near the resonant frequencies,the nature of the multi-solution and jump phenomena in the resonance region were revealed.It was shown that the realization of primary resonance depends on the stability conditions and initial conditions of the system;in addition,the generation power of the system reaches the maximum by properly selecting resistance.Finally,numerical integral results verified the correctness of the analysis.
