Group 1
Name
ID
 UBAID BILAL------------------MCEN51F20R001
 MUHAMMAD HASSAN------MCEN51F20R002
 MUHAMMAD HAZIQ---------MCEN51F20R006
 HAMZA GHAFFAR------------MCEN51F20R010
 MUHAMMAD AHMED-------MCEN51F20R027
 KASHIF RIAZ-------------------MCEN51F19R034
HOLZER’S METHOD
• It is named after Austrian engineer Franz Holzer, who developed
the method in the early 20th century.
• Holzer's method can be used to determine the natural frequency and
mode shapes of a linear dynamical system.
• The method involves assuming a trial solution for the mode shape
and then using the characteristic equation to solve for the natural
frequency and the coefficients of the mode shape.
• It is a tabular method which is used for the analysis of MULTDEGREE of FREEDOM SYSTEM in vibration
Cont…
• It is useful for the analysis of free and forced vibrations and
also for the system with or without damping.
• Holzer's method can be used for fixing both linear and
tortional natural frequencies.
Method for Analysis
• Holzer’s method is essentially a trial-and-error scheme to find
the natural frequencies of undamped, damped, semi definite,
fixed, or branched vibrating systems.
• It is a trail and error method and can be used to find the higher
modes independent of fundamental mode.
• A trial frequency of the system is first assumed, and a solution
is found when the assumed frequency satisfies the constraints
of the system.
• This generally requires several trials.
Cont…
• Depending on the trial frequency used, the fundamental as
well as the higher frequencies of the system can be
determined.
• The method also gives the mode shapes.
Steps
1.Write the equation of motion for the system in terms of displacement,
velocity, and acceleration.
2.Assume a trial solution for the mode shape of the system. The trial solution
should satisfy the boundary conditions and have a general form of sin or
cosine functions.
3.Substitute the trial solution into the equation of motion and simplify the
resulting equation.
4.Use the characteristic equation to solve for the natural frequency of the
system. The characteristic equation is obtained by assuming a solution of the
form X = e^(st) and substituting it into the equation of motion.
Cont..
5.Once the natural frequency is determined, substitute it back
into the equation of motion to solve for the coefficients of the
mode shape.
6.Normalize the mode shape by dividing each coefficient by the
maximum value of the mode shape.
7.Repeat steps 2-6 for each mode shape of the system to
determine all the natural frequencies and mode shapes.
For Torsional System
• In Holzer s method, a trial frequency is assumed, and Next, 1
is arbitrarily chosen as unity.
For Mass spring system
Example (Torsional Prob.)
1. Calculate the first non zero natural frequency of the shaft-rotor
system shown in fig using Holzer’s method.
Take: J₁=J₂=J₃= 1kg. ㎡
Kt₁=Kt₂= 1Nm/rad
Solution
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