Description
Book SynopsisThe 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 fi
Table of ContentsForeword. Prologue. Introduction: Review of Direct, Semi-Inverse and Inverse Eigenvalue Problems. Unusual Closed-Form Solutions in Column Buckling. Unusual Closed-Form Solutions for Rod Vibrations. Unusual Closed-Form Solutions for Beam Vibrations. Beams and Columns with Higher-Order Polynomial Eigenfunctions. Influence of Boundary Conditions on Eigenvalues. Boundary Conditions Involving Guided Ends. Vibration of Beams in the Presence of an Axial Load. Unexpected Results for a Beam on an Elastic Foundation or with Elastic Support. Non-Polynomial Expressions for the Beam's Flexural Rigidity for Buckling or Vibration. Circular Plates. Epilogue. Appendices. References. Author Index. Subject Index.
