5

Determine the mass-orthonormalised modeshape vectors for the following

data.
12000 00 0
[]ಎ| 180001 and 0
0 ௦ 18000
1.000 10 1.000
modal matrix, ‏س2‎ = 0.759 - 0.805 - 2.455

0.336 -1.158 2.571
(3)

a. Describe the mode superposition method for the forced vibration analySis
of a multi- degree of freedom system. (6)

3 Explain the concept of shear building model for the analysis of a multistoreyed

7. 2.

building frame. (3)

A three storeyed building frame of storey height 3.2 m and beam span 8 m is
loaded on the top beam with a IJDL of 25 kN/m and the other beams carry a
UDL of 35 பியா. If the columns have a uniform moment of inertia of 5x10
7mm ‘and if ಎ 2x10 °N/mm?, compute the frequencies and mode shapes
of the frame using Stodola's method. (9)

PART ^
(Answer any TWO questions)

Derive the solution for the differential equation of undamped free flexural

vibration of an one dimensional distributed mass system. (6)

b.

8. a.

Plot the first three possible modeshapes of a beam with distributed mass
under the following support conditions: (i). Both ends hinged (ii). Both ends
fixed (111). One end fixed and the other end free (6)

Derive the equation of motion and the solution for the axial vibration of a

prismatic member. (5)

b.

b,

. 4.

Derive the differential equation of motion for the flexural vibration of beams
including shear deformation and rotary inertia. (7)

Derive the equations of motion for a two degree of freedom system using
Lagrange's equation. (4)

Determine the amplitude of the response at quarter point from the left
support of a simply supported beam due to the first three modes, neglecting
damping, for the beam particulars given below. m = 200Nsec?/cm per cm
of span, El = 500Nmm ° , 1, = 320 cm, P(t)- 1000 Sin 500 t N applied at
midspan. (8) http://www.ktuonline.com