Study on resonance of multi-degree-of-freedom structure based on modal orthogonal basis

Resonance of multi-degree-of-freedom system or structure is a basic and important concept in structural vibration theory, but it lacks a complete and rigorous definition. In order to establish an accurate concept of structural resonance, based on the concept of single-degree-of-freedom system resonance and modal orthogonality, this paper discusses the necessary conditions of system resonance by analyzing the displacement response of multi-degree-of-freedom vibration system, that is, while ensuring that the vibration frequency of the system (a certain natural frequency) is equal to the excitation frequency, its displacement response should also present the corresponding modal shape. An example of simply supported beam is used to illustrate its rationality. At the same time, the theoretical method of pure modal resonance of multi-degree-of-freedom system is given by rational allocation of excitation force. The pure modal resonance of multi-degree-of-freedom system or structure can be realized, which can be used to accurately identify the modal parameters of the structure. It is of great theoretical significance and engineering application value to discriminate the concept of multi-degree-of-freedom system or structure resonance.