Nonlinear oscillations : exact solutions and their approximations / Ivana Kovacic.
This book presents exact, closed-form solutions for the response of a variety of nonlinear oscillators (free, damped, forced). The solutions presented are expressed in terms of special functions. To help the reader understand these `non-standard' functions, detailed explanations and rich illust...
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| Format: | Ebook |
| Language: | English |
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2020.
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| Online Access: | Springer eBooks |
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| 100 | 1 | |a Kovacic, Ivana, |d 1972- |e author. |9 415559 | |
| 245 | 1 | 0 | |a Nonlinear oscillations : |b exact solutions and their approximations / |c Ivana Kovacic. |
| 264 | 1 | |a Cham : |b Springer, |c 2020. | |
| 300 | |a 1 online resource (278 pages) | ||
| 336 | |a text |b txt |2 rdacontent | ||
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| 500 | |a Description based upon print version of record. | ||
| 500 | |a 4.3.2 Tuning the Excitation in Oscillators with Higher Order Odd-Power form Nonlinearity of the Restoring Force. | ||
| 504 | |a Includes bibliographical references. | ||
| 505 | 0 | |a Intro -- Preface -- Contents -- 1 Oscillators and Oscillatory Responses in Practical and Theoretical Systems -- 1.1 Oscillators and Oscillatory Responses in Practical Systems -- 1.2 Oscillators in Theory: From Mechanical to Mathematical Models -- 1.2.1 Linear (Simple Harmonic) Oscillators -- 1.2.2 Duffing-Type Oscillators -- 1.2.3 Purely Nonlinear Oscillators -- 1.2.4 Oscillators with a Constant Restoring Force -- References -- 2 Free Conservative Oscillators: From Linear to Nonlinear Systems -- 2.1 Introduction -- 2.2 Linear (Simple Harmonic) Oscillators (SHOs) | |
| 505 | 8 | |a 2.3 Duffing-Type Oscillators -- 2.3.1 Briefly About Jacobi Elliptic Functions -- 2.3.2 Hardening Duffing Oscillators (HDOs) -- 2.3.3 Pure Cubic Oscillators (PCOs) -- 2.3.4 Softening Duffing Oscillator (SDO) -- 2.3.5 Bistable Duffing Oscillators (BDOs) -- 2.4 Quadratic Oscillators (QOs) -- 2.5 Purely Nonlinear Oscillators (PNOs) -- 2.5.1 On the Period of Oscillations -- 2.5.2 On the Motion of Conservative Oscillators -- 2.6 Oscillators with Constant Restoring Force (CRFO) -- References -- 3 Free Damped Oscillators -- 3.1 Introduction | |
| 505 | 8 | |a 3.2 Oscillators with Linear Viscous Damping: Lagrangians and Conservation Laws -- 3.2.1 Linear Oscillators -- 3.2.2 Duffing Oscillators -- 3.3 Purely Nonlinear Oscillators with Quadratic Viscous Damping: Exact Solution Based on Energy Considerations and Approximations via Trigonometric Functions -- 3.3.1 Energy-Displacement Function -- 3.3.2 Phase Trajectories and Some Characteristics of Motion -- 3.3.3 Maximal Velocities -- 3.3.4 Approximate Solutions for Motion -- 3.4 Purely Nonlinear Oscillators with Fractional Damping: Approximate Solutions via Trigonometric Functions | |
| 505 | 8 | |a 3.4.1 Approximate Solutions via Trigonometric Functions -- 3.5 Non-conservative Purely Nonlinear Oscillators: Approximate Solutions via Elliptic Functions -- 3.5.1 Conservative Oscillator: Generative Solution -- 3.5.2 Non-conservative Oscillator: Approximate Solutions via Elliptic functions -- 3.6 Non-conservative Oscillators with Constant Restoring Force: Approximate Solutions via Wave Functions -- 3.6.1 Conservative Oscillator: Generative Solution -- 3.6.2 Non-conservative Oscillator: Approximate Solutions via Wave functions | |
| 505 | 8 | |a 3.6.3 Example 3.9 Antisymmetric Oscillator with Linear Viscous Damping -- 3.6.4 Example 3.10 Antisymmetric Oscillator with Quadratic Damping -- References -- 4 Forced Oscillators -- 4.1 Introduction -- 4.2 Forced Response of Duffing-Type Oscillators: Exact Solutions -- 4.2.1 Motivation for the Methodology -- 4.2.2 Duffing Oscillators -- 4.2.3 Simplification to the Case of Harmonic Excitation: Related Approximations -- 4.3 Tuning the Excitation in Odd-Parity Oscillator to Make It Respond ... -- 4.3.1 Tuning the Excitation in a Hardening Duffing Oscillator | |
| 520 | |a This book presents exact, closed-form solutions for the response of a variety of nonlinear oscillators (free, damped, forced). The solutions presented are expressed in terms of special functions. To help the reader understand these `non-standard' functions, detailed explanations and rich illustrations of their meanings and contents are provided. In addition, it is shown that these exact solutions in certain cases comprise the well-known approximate solutions for some nonlinear oscillations. | ||
| 588 | |a Machine converted from AACR2 source record. | ||
| 650 | 0 | |a Nonlinear oscillations. |9 329925 | |
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