Transverse Vibration Characteristics of Clamped-Elastic Pinned Beam Under Compressive Axial Loads

Abstract Based on the Bernoulli–Euler theory, the vibration characteristics of a clamped-elastic pinned beam under the elastic constraint and the compressive axial loads are derived and verified by finite element method. The results of examples show that the natural frequency of the beam decreases with loads increase and the frequency increases with the increase of the elastic constraint stiffness. When the constraint stiffness increases from 10 4 to 10 8 N/m, the first-order natural frequency becomes 4.24 times, the second-order natural frequency becomes 2.19 times, and the third-order natural frequency becomes 1.57 times; when the constraint is weak, the loads change is mainly reflected in the first mode shape. When the constraint stiffness is 10 4 N/m, the first-order natural frequency decreases by 20%, the second-order modal natural frequency changes by 3%, and the third-order natural frequency changes by less than 1%. The range of the elastic constraints with significant changes in the natural frequencies of the higher-order modes is larger. When the first-order frequency is taken to 100EI/l 3 , the change tends to be flat, the second-order frequency is about five times that of the first-order, and the range of the third-order frequency is 15 times or more.