Calculation of the high vibration modes of the tower

Static equilibrium is the principle of static equivalence. Atmospheric pressure decreases as altitude increases. When an air mass is in static equilibrium with the forces acting on its various surfaces in the horizontal direction canceling each other out, the net upward pressure acting on it in the vertical direction (the difference between the upward and downward pressures) must be balanced by gravity; that is, dp = –ρgdz or –dp/dz = ρg. In these equations, ρ represents the density of the air mass, and g is the acceleration due to gravity. This is the equation of static equilibrium, commonly referred to as the static equation. It represents the quantitative relationship between air pressure and altitude when the forces acting in the vertical direction are in balance. The above equation shows that the difference in air pressure at two different heights (dp) is equal to the weight of the air column per unit area between these two heights (ρgdz). The negative sign in the formula indicates that air pressure decreases as altitude increases. When dz＞0, dp＜0 because neither ρ nor g on the right side of the equation can be negative values ； Conversely, when dz < 0, then dp > 0. Since g can be approximated as a constant, the rate at which air pressure decreases with height depends mainly on air density. In dense air layers, atmospheric pressure decreases rapidly with height ； In gas layers with low density, the air pressure decreases slowly. The law of pressure variation with height reflected in the hydrostatic equation is applicable to almost all atmospheric motions, with only significant errors occurring during periods of strong vertical motion. Its conclusions have been widely applied in meteorology.