An almost exact solution is derived for the forced vibration of a composite beam with periodically varying non-smooth interface through a moderate weak-form formulation. The material property of a non-uniform beam is characterized by its flexural rigidity function R(x). In the novel method, R(x) is relaxed to be an integrable function rather than a \({\mathcal{C}}^2\) smooth function in the usual approach. The R(x)-orthogonal bases in the linear span of all boundary functions are derived such that the second-order derivatives of the bases elements are orthogonal with respect to the weight function R(x). When the deflection of the beam is expressed in terms of the bases, the expansion coefficients can be determined exactly in closed form owing to the R(x)-orthogonality of the bases. The solution obtained is almost exact, since its accuracy can be up to the order \(10^{-15}\). This powerful method is used to analyze the forced vibration behavior of composite beams with three different periodic interfaces.

通过适度的弱形式公式，对于具有周期性变化的非光滑界面的复合梁的强迫振动，得出了几乎精确的解决方案。非均匀梁的材料特性以其弯曲刚度函数R（x）为特征。在新颖的方法中，R（x）被放宽为可积函数，而不是通常方法中的\（{\ mathcal {C}} ^ 2 \）光滑函数。得出所有边界函数的线性跨度中的R（x）正交基，使得基元素的二阶导数相对于权重函数R（x）。当梁的挠度用基数表示时，由于基数的R（x）正交性，可以精确地以闭合形式确定膨胀系数。所获得的解几乎是精确的，因为其精度可以达到\（10 ^ {-15} \）的量级。该功能强大的方法用于分析具有三个不同周期界面的复合梁的强迫振动行为。