In this study, broadband frequency-response of a bi-stable piezo-magneto-elastic harvester is extended by analytically characterizing many subharmonic-$n$ solutions. The energy principle-based model considers the continuous analytical mode-shapes of a compound beam, rotational inertia of the tip mass, and nonlinear geometry effect. A modified higher-order Harmonic Balance (HB) approach proposed here is effective not only in characterizing the frequency-responses of harmonic-1 and subharmonic-$n$ solutions, but also in estimating the chaotic response zones of any multi-stable harvester. Balancing between the computational cost and solution convergence, intra-well (IW) and cross-well (CW) period-$n$ solutions of general-type upto period-4 and odd-type upto period-7 are characterized. Effectiveness and convergence of the modified HB approach are demonstrated through good qualitative and quantitative agreements observed between the numerical sweep and HB results. Dynamical behaviors of several period-$n$ solutions from different branches are revealed through the self-evident plots of displacement and voltage time histories, frequency spectra, and phase-portraits. Novel observations regarding the role of various sub- and super-harmonics in producing only CW orbits and mixed-orbits; and subsequently, asymmetric solution branches appearing due to the nonlinear geometry effect are reported. Besides the customary voltage and power output analyses, the assessment of maximum and average strains induced in the piezoelectric material is presented. Such an assessment has proved quite useful in identifying the alternate low-strain inducing and next best power-producing solutions to harmonic-1 responses. The characterized subharmonic-$n$ solutions produce $20\mathrm{\mu }\text{W–}90$ mW of RMS power and span the entire range of 1–30 Hz considered in this investigation.

在这项研究中，通过分析表征许多次谐波，扩展了双稳态压电磁弹性采集器的宽带频率响应$n$解决方案。基于能量原理的模型考虑了复合梁的连续分析模态形状、尖端质量的转动惯量和非线性几何效应。这里提出的一种改进的高阶谐波平衡 (HB) 方法不仅在表征谐波 1 和次谐波 - 的频率响应方面有效$n$解决方案，而且还用于估计任何多稳态收割机的混沌响应区。计算成本与解收敛性、井内 (IW) 和井间 (CW) 周期之间的平衡-$n$表征了高达 4 周期的一般型解决方案和高达 7 周期的奇型解决方案。通过在数值扫描和 HB 结果之间观察到的良好的定性和定量一致性，证明了修改后的 HB 方法的有效性和收敛性。几个时期的动力学行为-$n$来自不同分支的解决方案通过不言而喻的位移和电压时间历史、频谱和相图来揭示。关于各种次谐波和超谐波在仅产生 CW 轨道和混合轨道中的作用的新观察；随后，报告了由于非线性几何效应而出现的不对称解分支。除了常规的电压和功率输出分析外，还介绍了对压电材料中感应的最大和平均应变的评估。事实证明，这种评估对于确定谐波 1 响应的替代低应变诱导和下一个最佳发电解决方案非常有用。表征的次谐波-$n$解决方案产生$20\mathrm{\mu }\text{W-}\mathrm{90后}$mW 的 RMS 功率并跨越本调查中考虑的 1–30 Hz 的整个范围。