Fuzzy Fractional Structural Problems

• Published in: Fuzzy Arbitrary Order System pp. 87 - 119
• Main Authors: Tapaswini, Smita, Chakraverty, Snehashish, Behera, Diptiranjan
• Format: Book Chapter
• Language: English
• Published: United States John Wiley & Sons, Incorporated 2016; John Wiley & Sons, Inc
• Subjects: ELECTRONICS & COMMUNICATIONS ENGINEERING; fractional‐order discrete system; fuzzy fractionally damped structural systems; fuzzy‐based approach; homotopy perturbation method; Mathematical modelling; MATHEMATICS; mechanical spring‐mass system; uncertain response analysis
• ISBN: 9781119004110; 111900411X
• DOI: 10.1002/9781119004233.ch8

This chapter presents the solution of fuzzy fractionally damped structural systems. It discusses the solution of imprecisely defined fractional‐order discrete system, subject to unit step and impulse loads. The chapter explores a mechanical spring‐mass system having fractional damping of order 1/2 with fuzzy initial conditions. Fuzziness appeared in the initial conditions are modeled through different types of convex, normalized fuzzy sets, namely triangular, trapezoidal, and Gaussian fuzzy numbers. Homotopy perturbation method (HPM) is used with fuzzy‐based approach to obtain the uncertain response. Fuzzy fractionally damped continuous system, namely beam, has been studied using the double parametric form of fuzzy numbers subject to unit step and impulse loads. Depending on the values of natural frequency and damping ratio different cases have been studied. The chapter examines the fuzzy response of the dynamic system subject to unit step and impulse loading conditions. It finally considers numerical results corresponding to the discussed loads.