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The tension string system with concentrated viscous damping belongs to a hybrid dynamic system in mechanical models. Approximate methods are typically used to solve its inherent problems for engineering applications. In order to further clarify the vibration characteristics of the system, two centrally damped symmetrical damping string systems were taken as the basic research object, and their complex eigenvalues were solved analytically. The complex frequency equation and the eigenvalue expression of the system were derived, and the transformation of the complex frequency equation beyond the function form was treated as algebraic form, and the explicit solution of the complex eigenvalue of the system was given by the algebraic equation. The structure and properties of the complex eigenvalues of the system were analyzed, and the variation of vibration characteristics with damping coefficient was discussed. The results show that the eigenvalue solution of the system can be divided into three branches, in which the real part of the eigenvalue(the inverse is the decay rate) does not change with the order of the system motion, but the imaginary part of the eigenvalue(the frequency) increases with the order of the motion. The decay rate curves corresponding to each solution branch increase first and then decrease with the damping coefficient, and in the damping range of the decay rate curve, the frequencies of each order of the system are equal.
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| 科 Family | 属数 Number of genus | 种数 Number of species | 占总种数比例 Percentage of total species (%) | 属 Genus | 种数 Number of species | 占总种数比例 Percentage of total species (%) |
|---|---|---|---|---|---|---|
| 鹅膏菌科Amanitaceae | 2 | 11 | 5.26 | 鹅膏菌属 Amanita | 10 | 4.78 |
| 小菇科 Mycenaceae | 2 | 12 | 5.74 | 丝盖伞属 Inocybe | 5 | 2.39 |
| 多孔菌科 Polyporaceae | 8 | 14 | 6.70 | 蜡蘑属 Laccaria | 5 | 2.39 |
| 红菇科 Russulaceae | 3 | 23 | 11.00 | 小皮伞属 Marasmius | 6 | 2.87 |
| 小菇属 Mycena | 11 | 5.26 | ||||
| 光柄菇属 Pluteus | 5 | 2.39 | ||||
| 红菇属 Russula | 17 | 8.13 | ||||
| 栓菌属 Trametes | 5 | 2.39 |
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