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CALCULATOR MODULE : Beam Natural Vibration Frequency ±
Calculate the damped and undamped beam natural vibration frequency for general beams (simply supported, fixed, and cantilever beams). For other beam types (eg circular beams) refer to the module links below. The lateral natural vibration frequency beam end conditions are: pinned ends (simply supported beams), fixed ends, free fixed ends (cantilever beams), pinned fixed ends, and for beams with no load, pinned free ends, and free ends (unsupported beams). 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 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. Buckling normally occurs on the axis with lowest stiffness (I1 or I2). The bending stiffness for vibration and buckling can be defined separately for cases where vibration and buckling are not parallel. `fn = ca.cd k / (2 π) √((EI) / (m . Le^4)) `
`ca =1 / (1 + F / (Fb))) `
`cd = √(1 - fd^2) ` where : fn = lateral natural frequency [Hz]
ca = axial load coefficient
cd = damping coefficient
fd = damping factor (0 = undamped 1 = critical damping)
k = mode factor
L = effective beam length
EI = beam E I (bending modulus)
m = beam unit mass or mass per length
F = axial load (+ve in tension and -ve in compression)
Fb = buckling load The longitudinal natural vibration frequency end conditions are: free fixed ends (cantilever), fixed ends, and free ends (unsupported). The fixed ends and free ends modes have the same natural frequencies, but different mode shapes. The longitudinal natural frequency is independent of cross section, and depends on the beam elastic modulus and density. `fn = cd k / (2 π L) √(E / ρ) ` where : fn = natural frequency [Hz]
cd = damping coefficient
k = mode factor
L = beam length
E = beam elastic modulus
ρ = beam density The torsional natural vibration frequency end conditions are: free fixed ends (cantilever), fixed ends, and free ends (unsupported). The fixed ends and free ends modes have the same natural frequencies, but different mode shapes. The torsional natural frequency is independent of cross section, and depends on the beam shear modulus and density. `fn = cd k / (2 π L) √(G / ρ) ` where : fn = natural frequency [Hz]
cd = damping coefficient
k = mode factor
L = beam length
G = beam shear modulus
ρ = beam density 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. 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. Refer to the links below for other beam options. References : Shock And Vibration Handbook, Cyril M Harris, McGraw Hill
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CALCULATOR MODULE : Beam Lateral Vibration Frequency ±
Calculate the damped and undamped beam natural vibration frequency for lateral vibration (simply supported, fixed, and cantilever beams). 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 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. For multi layer pipes the bending stiffness can be calculated with the concrete stiffness factor (CSF). The CSF accounts for the additional stiffness provided by the external concrete coating. The concrete stiffness factor is calculated in accordance with DNVGL RP F105. Enter the wall thickness for all layers. Only enter the elastic modulus for layers which affect the pipe stiffness. 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
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CALCULATOR MODULE : Beam Lateral Vibration Frequency With Axial Load ±
Calculate the damped and undamped beam natural vibration frequency for lateral vibration with axial load (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. For pipes the axial load is calculated from temperature and pressure. For general beams the axial load is user defined. 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. For multi layer pipes the bending stiffness can be calculated with the concrete stiffness factor (CSF). The CSF accounts for the additional stiffness provided by the external concrete coating. The concrete stiffness factor is calculated in accordance with DNVGL RP F105. Enter the wall thickness for all layers. Only enter the elastic modulus for layers which affect the pipe stiffness. 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 : |
CALCULATOR MODULE : Circular And Semi Circular Beam Natural Vibration Frequency ±
Calculate the damped and undamped natural vibration frequency for solid and hollow circular 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 (not neccessary for round beams). 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. For hollow beams the wall thickness is assumed constant. 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
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CALCULATOR MODULE : Elliptical And Semi Elliptical Beam Natural Vibration Frequency ±
Calculate the damped and undamped natural vibration frequency for solid and hollow elliptical 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. For hollow beams the wall thickness is assumed constant. 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
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CALCULATOR MODULE : Square Beam Natural Vibration Frequency ±
Calculate the damped and undamped natural vibration frequency for solid and hollow square beams (simply supported, fixed, and cantilever beams). 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. For hollow beams the wall thickness is assumed constant. 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 : |
CALCULATOR MODULE : Rectangular Beam Natural Vibration Frequency ±
Calculate the damped and undamped natural vibration frequency for solid and hollow rectangular 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. For hollow beams the wall thickness on opposite sides is assumed to be equal. 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 : |
CALCULATOR MODULE : Parallelogram Beam Natural Vibration Frequency ±
Calculate the damped and undamped natural vibration frequency for solid and hollow parallelogram 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 (not required for square beams). 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. For hollow beams the wall thickness on opposite sides is assumed to be equal. Axis L is parallel to the base. Axis M is perpendicular to the base. Axis 1 and 2 are the principal axes. The geometry should be arranged so that the offset is positive. 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 : |
CALCULATOR MODULE : Trapezoid Beam Natural Vibration Frequency ±
Calculate the damped and undamped natural vibration frequency for trapezoid 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. 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. Axis L is parallel to the base. Axis M is perpendicular to the base. Axis 1 and 2 are the principal axes. The geometry should be arranged so that the offset is positive. 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 : |
CALCULATOR MODULE : Diamond Beam Natural Vibration Frequency ±
Calculate the damped and undamped natural vibration frequency for solid and hollow diamond 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 (not required for square diamonds). 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. For hollow sections the wall thickness is assumed constant for all four sides. 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 : |
CALCULATOR MODULE : Rectangular Channel Beam Natural Vibration Frequency ±
Calculate the damped and undamped natural vibration frequency for rectangular channel 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 wall thickness on the two sides are assumed equal. 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 : |
CALCULATOR MODULE : Triangular Beam Natural Vibration Frequency ±
Calculate the damped and undamped natural vibration frequency for solid and hollow triangle 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 (not required for equilateral triangles). 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. Equilateral triangles have three equal sides, and three equal angles. Isoceles triangles have two equal sides, and two equal angles. Scalene triangles have three unequal sides and three unequal angles. For hollow sections the wall thickness is assumed constant for all three sides. 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 : |
CALCULATOR MODULE : Right Angle Beam Natural Vibration Frequency ±
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 : |
CALCULATOR MODULE : T Section Beam Natural Vibration Frequency ±
Calculate the damped and undamped natural vibration frequency for T 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 Tee section is assumed to be symmetrical along axis 2, with flanges of equal length and 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 : |
CALCULATOR MODULE : I Section Beam Natural Vibration Frequency ±
Calculate the damped and undamped natural vibration frequency for I 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 I section is assumed to be symmetrical along axis 1 and 2, with flanges of equal length and 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 : |
CALCULATOR MODULE : Polygon Beam Natural Vibration Frequency ±
Calculate the damped and undamped natural vibration frequency for solid and hollow regular polygon beams (simply supported, fixed, and cantilever beams). For lateral vibration with axial load 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 polygon section is assumed to be symmetric along axis 1 and 2, and all sides and wall thickness are assumed to be equal. The minimum number of sides is 3. A regular polygon with 3 sides is equivalent to an equilateral triangle. A regular polygon with 4 sides is equivalent to a square. For beams with axial load the axis with minimum stiffness (I1 or I2) should be used unless the beam is constrained to deflect on the chosen axis (buckling normally occurs on the minimum stiffness axis). 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 : |
CALCULATOR MODULE : Rotated Beam Natural Vibration Frequency ±
Calculate the damped and undamped beam lateral natural vibration frequency for rotated general beams (simply supported, fixed, and cantilever beams). Enter the moment of inertia for two perpendicular axes (Il and Im), and the product of inertia about the centroid (Hlm). For the principal axes the product of inertia is zero. The rotated moment of inertia and bending modulus (EI) can be calculated for: - user defined rotation
- perpendicular to user defined rotation
- principal axis 1 (I1)
- principal axis 2 (I2)
- axis l (Il)
- axis m (Im)
- Minimum I
- Maximum I
The lateral natural vibration frequency beam end conditions are: pinned ends (simply supported beams), fixed ends, free fixed ends (cantilever beams), pinned fixed ends, and for beams with no load, pinned free ends, and free ends (unsupported beams). 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 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. Buckling normally occurs on the axis with lowest stiffness (I1 or I2). The bending axis for buckling can be defined separately for cases where vibration and buckling are not parallel: - parallel to vibration
- perpendicular to vibration
- principal axis I1
- principal axis I2
- axis l
- axis m
- minimum I
- maximum I
- user defined angle
- perpendicular to user defined angle
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. 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 : |