Nonlinear oscillations exact solutions and their approximations /: exact solutions and their approximations. (2020)

• Record Type: Book
• Further Information: Note: Ivana Kovacic.
• Other Names: Kovacic, Ivana, 1972-
• Contents: 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) 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 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 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 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
• Publisher Details: Cham : Springer
• Publication Date: 2020
• Extent: 1 online resource (278 p.)
• Subjects: 531/.32; Nonlinear oscillations; Nonlinear science; Mechanics of solids; Mechanical engineering; Science -- Chaotic Behavior in Systems; Technology & Engineering -- Mechanical; Nonlinear oscillations; Electronic books; Electronic books
• Languages: English
• ISBNs: 9783030531720; 3030531724
• Related ISBNs: 3030531716; 9783030531713
• Notes: Note: Includes bibliographical references.
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.