The article presents a new method called Modified Fourier Series for analyzing clamped beams and plates. The researchers from Bengal Engineering College in India aimed to improve the accuracy of predicting the behavior of these structures under different conditions. By using this method, they were able to better understand how clamped beams and plates respond to external forces. The key findings suggest that the Modified Fourier Series can provide more precise results compared to traditional methods, offering a valuable tool for engineers and scientists working on similar problems.