Dynamic Response of Linear Mechanical Systems: Modeling, by Jorge Angeles

By Jorge Angeles

Dynamic reaction of Linear Mechanical structures: Modeling, research and Simulation can be used for quite a few classes, together with junior and senior-level vibration and linear mechanical research classes. the writer connects, via a rigorous, but intuitive technique, the idea of vibration with the extra basic thought of platforms. The booklet features:

A seven-step modeling approach that is helping constitution the really unstructured technique of mechanical-system modeling

A system-theoretic method of deriving the time reaction of the linear mathematical types of mechanical systems

The modal research and the time reaction of two-degree-of-freedom systems—the first step at the good way to the extra complicated examine of multi-degree-of-freedom systems—using the Mohr circle

Simple, but strong simulation algorithms that take advantage of the linearity of the approach for either unmarried- and multi-degree-of-freedom systems

Examples and workouts that depend upon glossy computational toolboxes for either numerical and symbolic computations in addition to a strategies handbook for teachers, with whole suggestions of a pattern of end-of-chapter exercises

Chapters three and seven, on simulation, comprise in each one “Exercises” part a suite of miniprojects that require code-writing to enforce the algorithms constructed in those chapters

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Additional info for Dynamic Response of Linear Mechanical Systems: Modeling, Analysis and Simulation

Sample text

Furthermore, with regard to viscous damping, we will focus on linearly-viscous damping, which can be taken into account by linear dashpots,13 the counterparts of linear springs. Linear dashpots coupling two elements of a system at points A and B are characterized by quadratic dissipation functions. 6 Planar Motion Analysis 31 where s˙i is the relative velocity of points A and B along the direction of line AB. Note that, by virtue of the form of the dissipation function, this attains the same value whether the dashpot is stretching or contracting at the same rate.

5 A cantilever beam with a load acting at its free end Fig. 6 A shaft of circular cross section under torsion which is a translational stiffness, as it is associated with a translational spring,6 its units being N/m. Shown in Fig. 5 is a cantilever beam of length l, modulus of elasticity E, and cross-sectional area moment of inertia I, subject to a vertical load at its free end. 10) As a further example, consider a shaft of circular cross section, shear modulus G, length l, and torsion constant J, as shown in Fig.

18c. In this figure, we show in parentheses the signed magnitude of each velocity term of the righthand side of the foregoing equation. Note that, from this velocity triangle we could determine vP as such, but, as a matter of fact, we do not need it; what we need is rather the squared magnitude of this velocity vector. 6 Planar Motion Analysis 37 In fact, from the expression for Ti of Eq. 24, all that we need to find T3 is c˙ 3 2 , which can be done with much less effort than finding c˙ 3 itself.

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