Fundamentals of Multibody Dynamics: Theory And Applications by Farid M. L. Amirouche | 9780817642365 | 0817642366 | Holooly

Mechanical Engineering

Fundamentals of Multibody Dynamics: Theory And Applications

84 SOLVED PROBLEMS

Question: 7.8.2

Consider Example 7.7.2 and let m0 = m = 1 kg, L = 1m, S = R = 1 Nm, x2 = 30°, x3 = 60°, and x2 = 1 rad/s. Find the acceleration of the slide using the embedding method. ...

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From equation (7.99) the constraint equations are ...

Question: 10.3.1

Consider the bar shown in Figure 10.9 undergoing a large rotation and assumed to be elastic. Assume that E, the modulus of elasticity, me, the mass density, and A, the cross-sectional area, are all known constants relating the properties of the bar. Let us assume that the damping coefficient of the ...

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As shown in Figure 10.10, the shape function matri...

Question: 10.2.1

Consider the planar two-bar system shown in Figure 10.3. Find the explicit form of the velocity and acceleration of an arbitrary point p on the flexible link with the boundary conditions given by equations (10.3). ...

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Let us write the transformation matrices between b...

Question: 9.8.2

Use the subspace iteration method to solve for the eigenvalue problem given by Example 9.8.1. ...

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The following stiffness and mass are given: [latex...

Question: 9.8.1

Supposing that the mass matrix M = I , and the stiffness matrix is given by K = [3 -1 -1 -1 3 -1 -1 -1 3] Use the Jacobi method to find the eigenvalues and eigenvectors for such a system. ...

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For i = 1, j = 2, from equation (9.248) we get [la...

Question: 9.5.2

Suppose that K and M are given by K = [3 -1 -1 -1 3 -1 -1 -1 3], M = [ 1 0 0 0 1 0 0 0 1] Use the Rayleigh–Ritz method to solve for the eigenvalues and eigenvectors of the system. ...

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Let

W=\alpha_1 \begin{array}{r c} \begin{bm...

Question: 9.2.4

Consider Example 6.12.3, dealing with the pantograph. Obtain the linearized equations of motion of the mechanical system (follow procedures outlined in the above example). ...

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The systems has two degrees of freedom, selected t...

Question: 9.2.3

Consider the planar pendulum shown in Figure 9.3, which consists of three slender rods. Find the linearized equations of motion of the system. ...

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Let us formulate the kinematics of the system. Not...

Question: 7.13.1

Let D denote the coin that is a sharp-edged circular disk that rolls on a plane support S fixed in a reference frame R (Figure 7.19). Line n1 is the tangent to the periphery of D at the point of contact C between D and S. Let n1^1, n2^1 and n3^1 be three mutually perpendicular unit vectors, as ...

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Let the rolling coin be body

B_1

an...

Question: 9.5.1

Consider the system shown in Figure 9.8, where the clamped–free slender bar of a parabolic side is assumed to oscillate longitudinally. Our task is to extract the eigenvalues and the corresponding mode shapes using the Rayleigh–Ritz method discussed above. ...

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The mass per unit length and the stiffness along x...

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