Impact Load on a Visco-elastic Model | Online Calculator

Impact Loads Calculators

Visco-Elastic Model of Kelvin-Voigt on Impact

In this calculation, a viscoelastic model is considered, which is the most common combination of two system characteristics, namely, stiffness K and damping b. At that, the movable element of mass m1 falls on the structure of reduced mass m2 with initial speed W0. The differential equation of motion for this model shall be represented as follows:

mY'' = - (K*Y + b*Y')

As a result of solving this equation, the maximum impact load P and maximum system deformation Y are determined.

Calculation of visco-elastic model on impact
Visco-elastic model under impact load

INITIAL DATA

m1 - Mass of moving element;

k - Structure stiffness;

b - Structure damping factor;

m2 - Reduced mass of structure;

W0 - Initial speed of the moving element.

RESULTS DATA

P - Maximum impact force;

Y - Maximum deformation on impact.
In general, force at maximum deformation is not equal to maximum impact force.

Mass of moving element (m1)

Initial speed (W0)

Structure stiffness (К)

Damping factor (b)

Reduced mass (m2)

Maximum impact force (Р)

Maximum deformation (Y)

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BASIC FORMULAS

Maximum deformation:

Y = ((m1 + m2)*(W12) / (b2/(m1 + m2)) + K)1/2;

Force at maximum deformation:

P = [W1 - ((Y2*(b2 / (m1 + m2) + K)) / (m1 + m2))1/2]*b + K*Y.

W1 - the total speed of the moving element m1 and mass m2 at the moment of impact.

INITIAL DATA

m1 - Mass of the moving element;

k - Structure stiffness;

b - Structure damping factor;

m2 - Reduced mass of structure;

W0 - Initial speed of the moving element.

RESULTS DATA

P - Maximum impact force;

Y - Maximum deformation on impact.
In general, force at maximum deformation is not equal to maximum impact force.

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