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Books > Science & Mathematics > Mathematics > Applied mathematics
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Eigenvalues of Inhomogeneous Structures - Unusual Closed-Form Solutions (Paperback)
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Eigenvalues of Inhomogeneous Structures - Unusual Closed-Form Solutions (Paperback)
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The engineering community generally accepts that there exists only
a small set of closed-form solutions for simple cases of bars,
beams, columns, and plates. Despite the advances in powerful
computing and advanced numerical techniques, closed-form solutions
remain important for engineering; these include uses for
preliminary design, for evaluation of the accuracy of approximate
and numerical solutions, and for evaluating the role played by
various geometric and loading parameters. Eigenvalues of
Inhomogeneous Structures: Unusual Closed-Form Solutions offers the
first new treatment of closed-form solutions since the works of
Leonhard Euler over two centuries ago. It presents simple solutions
for vibrating bars, beams, and plates, as well as solutions that
can be used to verify finite element solutions. The closed
solutions in this book not only have applications that allow for
the design of tailored structures, but also transcend mechanical
engineering to generalize into other fields of engineering. Also
included are polynomial solutions, non-polynomial solutions, and
discussions on axial variability of stiffness that offer the
possibility of incorporating axial grading into functionally graded
materials. This single-package treatment of inhomogeneous
structures presents the tools for optimization in many
applications. Mechanical, aerospace, civil, and marine engineers
will find this to be the most comprehensive book on the subject. In
addition, senior undergraduate and graduate students and professors
will find this to be a good supplement to other structural design
texts, as it can be easily incorporated into the classroom.
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