Analysis on the Vibration Performance of Spruce Structure with Variable Cross-Section Under Snow Load by Semi-Analytical Method

Trees have various forms and structures, most of which have excellent mechanical properties. Spruce has a stable structure and excellent resistance to wind and snow loads. In this paper, the vibration performance of spruce is studied by the semi-analytical method. Based on the vibration theory of Euler-Bernoulli beam, the vibration mechanical model of the spruce trunk with variable cross-section is established by using the segmental equivalence method. Then, the natural frequency and modal function of the trunk are analyzed and the displacements are solved under snow load within one hour. The results show that the first four natural frequencies are 120.417rad/s, 188.414rad/s, 237.699rad/s and 288.964rad/s, respectively. During the continuous loading stage, the displacements increase over time. During the static load stage, the displacements change in a harmonic form. The above results are verified by an experimental measurement. This paper provides a reference for the study of the vibration performance of similar structures.