Calculate the damped and undamped natural vibration frequency for right angle section beams (simply supported, fixed, and cantilever beams).
For beams with axial load the axis with minimum stiffness (I1 or I2) should be used unless the beam is constrained to deflect on an alternative axis (buckling normally occurs on the minimum stiffness axis). Use the general beam calculators for cases where vibration and buckling are not parallel. The buckling load can be calculated using either the Euler equation (suitable for long beams), or the Johnson equation (suitable for short beams). The buckling load is dependent on the end type, and is used for mode 1 vibration only.
Added mass should be included for submerged or wet beams. The added mass coefficient can be calculated in accordance with DNVGL RP F105. The submerged natural frequency is calculated for still water conditions, with no vortex shedding. For beams on a soft foundation such as soil, use the effective length factor to allow for movement at the beam ends. For defined beam ends such as structures, the effective length factor should be set to one. The axial load is calculated from temperature.
For longitudinal and torsional vibration, the natural frequency is independent of the cross section, and the general beam calculators can be used.
The mode factor k is dependent on the mode number, and the beam end type. The k factors have been taken from the Shock and Vibration handbook. The damping factor should be set to zero for undamped vibration or set greater than zero and less than or equal to one for damped vibration. The right angle beams are assumed to have equal leg length and leg thickness.
Use the Result Table and Result Plot options to display tables and plots. Refer to the figures and help pages for more details about the tools.
References :
Shock And Vibration Handbook, Cyril M Harris, McGraw Hill
Roark's Formulas For Stress And Strain, Warren C Young, McGraw Hill
Change Module :