Discretized perturbation analysis based upon a structure's single (finite) mode Galerkin-truncated model may lead to erroneous results in comparison with full-basis discretization (or, equivalently, direct perturbation method). This error is due to the two involved analytical steps, i.e., multi-scale expansion and mode truncation, being non-commutative with each other. However, the key underlying physical origin for this error (or non-commutativity) is still unclear. The novelty of the current work is to propose a new physics-based error source interpretation, and accordingly, a general perturbation correction procedure. Explicitly, a general physics-based interpretation for the error source is referred to the incomplete characterization of low-order non-secular effects due to both spectrum mixture and single (finite) mode truncation. Three typical dynamical scenarios, i.e., hard external excitation, quadratic nonlinearity, and hard boundary motion, are addressed in the same unified framework. By introducing a full spectrum decomposition and a complete elimination of the non-secular term in a physically equivalent manner, a general correction procedure of the finite mode truncation often used in perturbation analysis is proposed and then validated through numerical examples.

与全基离散化（或等效地，直接微扰法）相比，基于结构的单（有限）模伽辽金截断模型的离散化扰动分析可能会导致错误的结果。该错误是由于涉及的两个分析步骤，即多尺度扩展和模式截断，彼此不可交换。然而，这个错误（或非交换性）的关键潜在物理起源仍不清楚。当前工作的新颖之处在于提出了一种新的基于物理学的误差源解释，并因此提出了一般的扰动校正程序。明确地，对误差源的基于物理学的一般解释是指由于光谱混合和单（有限）模式截断导致的低阶非长期效应的不完整表征。三个典型的动力学场景，即硬外部激励、二次非线性和硬边界运动，在同一个统一框架中得到解决。通过引入全谱分解并以物理等效的方式完全消除非世俗项，提出了微扰分析中经常使用的有限模式截断的一般校正程序，然后通过数值例子进行了验证。