Determine an expression for the natural frequencies of a fixed-pinned bar in lateral vibration. Problem 2
Calculate the first three frequencies of axial vibration of a bar fixed at one end.
Problem 4 (20%) Figure 5 shows a uniform elastic bar fixed at one end and attached to a mass M at the other end. The cross sectional area for the bar is A, mass density per unit length p, modulus of elasticity E and second moment of area I. For the longitudinal vibration: S Set the necessary coordinate system, governing equation of motion and boundary conditions a. b. Derive the general solution. Explain how you can obtain the natural frequencies...
Determine the natural frequency of vibration of the system shown in Fig. 1-1. Assume the bar AB to be rigid and weightless with c as the mid-point. k3 Fig. 1-1.
Determine the natural frequencies and vibration modes of the two degree of freedom rectilinear system shown in the following figure. please detail all the steps ans: k m, ww m2 DCL LEE LFF Оn1 — 0 k(m1+m2) Wn2 7ш.Тш X1 X2 -т, — Х, ( X2 X1 т2
ww Ww Assignment Problem 1 Determine the natural frequencies and relative amplitudes of the following spring-mass systems with two degrees of freedom. (To be submited in the next class session) Show all the work- should include the following: ki FBD's of the two masses Equation of motion of each mass using equation of dynamic equilibrium Derivation of amplitude ratios (Modes of vibration) Derivation of frequency equation ili. iv. ki XPII ww Ww Assignment Problem 1 Determine the natural frequencies and...
Problem#2 A W12 x58, A992 column is pinned at the top and fixed at the bottom as shown. Lateral bracing is provided to assist with weak-axis buckling strength 12.5 ft from the ground level. For the condition where the column only supports axial load, determine the design strength of the column. K 1.0 7.5 ft K- 0.8 20 ft K = 0.8 | 12.5 ft
Problem 3) A uniform rod of length Lis pinned at both ends. Show that the frequencies of longitudinal vibrations are conic/L, where c= is the velocity of longitudinal waves in the rod, and n = 0,1,2,3,4....... Note: You must show all the steps. b) Plot the first three natural modes.
Problem 1. The natural frequencies wn of free vibration of a cantilever beam are determined from the roots of the equation: ET Cantilever beam Wn = (k~L)2 VPALA in which E = 2.0 x 1011 N/m is the elastic modulus, L = 0.45 m is the beam length, 1 = 4.5 x 10-11 m is the moment of inertia, A = 6.0 x 10-5 mº is the cross-sectional area, and p = 6850 kg/m' is the density per unit length....
Problem 7 - Vibration (10 pts) Determine the equation of motion and natural frequency wn of vertical oscillations of the cylinder of mass m. the mass and friction of the stepped drum are negligible. T 2r m
determine characteristic frequencies of radial vibration of an elastic cylinder with radius R