In this study, a new closed-form solution for transverse free vibration analysis of laminated composite beams (LCBs) with arbitrary number of concentrated masses is developed. The LCB is modeled based on the Euler–Bernoulli beam theory and concentrated masses are simulated considering Dirac delta function. Obtained governing equations are, then, solved semianalytically, while the frequency equation and mode shapes are extracted for two different boundary conditions, i.e., clamped-free and simply supported. In order to verify the closed-form solution, the represented model is simplified for a beam without concentrated mass and outcomes are compared with available results in the literature. Finally, the effects of mass as well as location and number of concentrated masses on the free vibration response of the beam are investigated in detail. The results highlight that with increase in the value of point masses, the natural frequencies decrease. Also, it was revealed that the number of point masses influences on the vibration of cantilever beam more than the simply supported one. These outcomes would practically be used to minimize detrimental effects of vibrational noises, leading to increase in the structural components’ lifetime.

在这项研究中，开发了一种新的封闭形式的解决方案，该解决方案用于任意数量的集中质量的叠层复合梁（LCB）的横向自由振动分析。LCB是基于Euler-Bernoulli束理论建模的，并考虑了Diracδ函数来模拟集中质量。然后，对获得的控制方程进行半解析求解，同时针对两个不同的边界条件（即，无钳位和简单支持）提取频率方程和模式形状。为了验证封闭形式的解决方案，简化了表示模型​​的梁不集中质量的情况，并将结果与​​文献中的可用结果进行了比较。最后，详细研究了质量以及质量的位置和数量对梁自由振动响应的影响。结果表明，随着点质量值的增加，固有频率降低。而且，揭示了点质量的数量比悬臂梁的受支撑的数量更多地影响悬臂梁的振动。这些结果实际上将用于最小化振动噪声的有害影响，从而延长结构部件的使用寿命。