Prestressed piezoelectric energy harvesters (PEH) provide benefits referred to higher generation levels and scavenge energy from lower frequency sources. In the study of axially loaded beams subject to lateral base forces, it is common to assume that the axial displacement is of a lower order than the lateral one. When the beam is slender enough, it is well known from experimental and numerical results, that this hypothesis is satisfied. Although this relation arises naturally from reducing the axial equation, diverse approaches can be found by applying different boundary conditions for the axial problem. Among several combinations, two ideal extreme cases can be distinguished: assuming that the beam is fixed at one end and (a) loaded at the other one; or (b) considering the prescribed displacement produced by the same load, according to the linear static problem. Even though both approaches seem similar, the final expressions of the nonlinear geometric stiffness are drastically modified, which is reflected in the disagreement with the predicted hardening behavior as the forces increase. In order to identify the effect of these assumptions in the dynamic response, the equations of motion are derived and solved for both cases. On the other hand, as an intermediate and non-ideal case (c), an elastic restraint on the end of the beam where the load is applied is proposed. For this last one, both assumptions (a) and (b) can be recovered by choosing the appropriate combination of the elastic restraint $k$ and a proposed dimensionless parameter. The experimental findings are compared with numerical predictions on the voltage of different PEH samples that show the need for the elastic constraint to reproduce the experimental data from our proposed device.

预应力压电能量收集器 (PEH) 具有更高的发电水平和从低频源收集能量的优点。在研究承受侧向基础力的轴向载荷梁时，通常假设轴向位移比横向位移低。当梁足够细长时，从实验和数值结果中众所周知，该假设得到满足。虽然这种关系是通过减少轴向方程自然产生的，但可以通过对轴向问题应用不同的边界条件来找到不同的方法。在几种组合中，可以区分两种理想的极端情况：假设梁的一端固定，(a) 另一端加载；或 (b) 考虑由相同载荷产生的规定位移，根据线性静力问题。尽管这两种方法看起来很相似，但非线性几何刚度的最终表达式被彻底修改，这反映在随着力的增加与预测的硬化行为不一致。为了识别这些假设在动态响应中的影响，推导出和求解这两种情况的运动方程。另一方面，作为中间和非理想情况（c），建议在梁的施加载荷的端部进行弹性约束。对于最后一个，可以通过选择适当的弹性约束组合来恢复假设 (a) 和 (b) 随着力的增加，这反映在与预测的硬化行为的不一致上。为了识别这些假设在动态响应中的影响，推导出和求解这两种情况的运动方程。另一方面，作为中间和非理想情况（c），建议在梁的施加载荷的端部进行弹性约束。对于最后一个，可以通过选择适当的弹性约束组合来恢复假设 (a) 和 (b) 随着力的增加，这反映在与预测的硬化行为的不一致上。为了识别这些假设在动态响应中的影响，推导出和求解这两种情况的运动方程。另一方面，作为中间和非理想情况（c），建议在梁的施加载荷的端部进行弹性约束。对于最后一个，可以通过选择适当的弹性约束组合来恢复假设 (a) 和 (b) 建议在施加载荷的梁端采用弹性约束。对于最后一个，可以通过选择适当的弹性约束组合来恢复假设 (a) 和 (b) 建议在施加载荷的梁端采用弹性约束。对于最后一个，可以通过选择适当的弹性约束组合来恢复假设 (a) 和 (b)$克$和建议的无量纲参数。将实验结果与不同 PEH 样品电压的数值预测进行比较，这表明需要弹性约束来重现我们提出的设备的实验数据。