10 Spring With Mass

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VERTICAL SPRING WITH MASSCONSIDER

Mass at end of mass-less spring

Spring with homogenous mass distribution

Spring with mass and point mass

At end of springAt arbitrary location

Spring with several point masses.

No damping

Transient response (breakage)

Harmonic loading

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Point mass at end. Static deflection

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mL << M

 Natural freq.

Transient resp.

Time dep. load 

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Homogenous mass distribution (wire only)

• Equilibrium of element

• Separation of variables

• Eigenvalues (fixed at x=0, no forceat x=L)

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Example. Transient response.(wire only)

Eigenmodes and modal participation

• L= 1000m

• E=2.1E11 N/m2

• R=0.03m

• Rho = 0.6*7800kg/m3

• U(L,0) = 0.44m (F(L,0)=264kN)

• Ut(L,0) = 0

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Transient response cont’d(wire only)

Response at x=L

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Transient response cont’d. (wire only)

Shock behaviour 

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Transient response cont’d (wire only)

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Transient response. Point mass at x=L.

(M=2mL)

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Transient response cont’d Point mass at x=L.

(M=2mL) Response at x=L

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Transient response cont’d Point mass at x=L.

(M=2mL)

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M=0

M=0.1mL

M=2mL