Question 19.P.3: Repeat Problem 19.2 using for each component one free interf...

Dynamics of Structures

Repeat Problem 19.2 using for each component one free interface normal mode and two residual flexibility attachment modes corresponding to d.o.f. 3 and 4.

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Question: 19.6

The beam in Example 19.5 is subjected to a vertical upward force P along d.o.f. 5 of component 2. What are the resulting vertical displacements at each node of the finite element mesh. ...

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Referring to the d.o.f. of component 2 the force v...

Question: 19.5

The beam referred in Section 19.4.4 is divided into 2 components, each component being subdivided into 4 finite elements of equal length as shown in Figure 19.5. Find the coupled transformed mass and stiffness matrices for the beam. Determine the first 3 frequencies for the beam and compare them ...

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Corresponding to the d.o.f. shown in Figure [latex...

Question: 19.4

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Question: 19.3

The flexural beam shown in Figure E19.3a has negligible mass, is rigidly supported against translation at its left hand end, and supported by a spring of stiffness αk at its right-hand end. The beam supports a mass 2m at mid-span and another mass m at the right-hand end. The flexural stiffness of ...

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The flexibility matrix corresponding to the two d....

Question: 19.2

For the uniform bar of Example 19.1 obtain the reduced stiffness and mass matrices of the two components using free interface normal modes. Couple the matrices by enforcing compatibility of displacement along the interface between components 1 and 2. ...

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Question: 19.1

The uniform bar of length L, mass per unit length m, and cross sectional area A shown in Figure E19.1 is clamped at its left hand end and free at the right hand end. It is allowed to vibrate in the axial direction. The bar is divided into two components and both components are further subdivided ...

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Question: 19.P.7

For CMS of the components of the uniform beam referred to in Problem 19.6 it is decided to model each component by one fixed-interface normal mode and an appropriate number of constraint modes. For component 1 the number of constraint modes is 2, related to the two d.o.f. at the interface with ...

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19.7 \omega=\left[\begin{array}{llll}3.516 ...

Question: 19.P.5

The uniform bar shown in Figure P19.5 is fixed at both ends and is undergoing vibrations in an axial direction. It is divided into three components and each component is further subdivided into 2 finite elements. Model each of components 1 and 3 by one normal mode and one residual flexibility ...

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\omega=\left[\begin{array}{lllll}3.18 &...

Question: 19.P.1

The simply supported uniform beam shown in Figure P19.1 represents one component in CMS. It is divided into two finite elements as shown. The beam has four normal modes corresponding to the two interior d.o.f. 1 and 2 and the two unconstrained interface d.o.f. 3 and 4 . Obtain the four normal modes ...

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The four normal modes are

\Phi=\left[\begin...