Superharmonic and Subharmonic Resonances of Spiral Stiffened Functionally Graded Cylindrical Shells under Harmonic Excitation

This paper presents the superharmonic and subharmonic resonances of spiral stiffened functionally graded (SSFG) cylindrical shells under harmonic excitation. The stiffeners are considered to be externally or internally added to the shell. Also, it is assumed that the material properties of the stiffeners are continuously graded in the thickness direction. In order to model the stiffeners, the smeared stiffener technique is used. Within the context of the classical plate theory of shells, the von Kármán nonlinear equations are derived for the shell and stiffeners based on Hooke’s law and the relations of stress-strain. Using Galerkin’s method, the equation of motion is discretized. The superharmonic and subharmonic resonances are analyzed by the method of multiple scales. The influence of the material parameters and various geometrical properties on the superharmonic and subharmonic resonances of SSFG cylindrical shells is investigated. Considering these results, the hardening nonlinearity behavior and jump value of cylindrical shell is less and more than others, when the angle of stiffeners is [Formula: see text] and [Formula: see text], respectively.

Nonparametric Identification of Nonlinear Piezoelectric Mechanical Systems

Two novel nonparametric identification approaches are proposed for piezoelectric mechanical systems. The novelty of the approaches is using not only mechanical signals but also electric signals. The expressions for unknown mechanical and electric terms are given based on the Hilbert transform. The signals are decomposed and re-assembled to obtain smooth stiffness and damping curves. The current mapping approach is developed to identify accurately a piezoelectric mechanical system with strongly nonlinear electric terms. The developed identification approaches are successfully implemented to simulate signals obtained from different nonlinear piezoelectric mechanical systems, including Duffing nonlinearity, softening and hardening nonlinearity, and Duffing nonlinearity with strong nonlinear electric terms. The proposed approaches are successfully applied to experimental signals of a circular laminated plate device in order to identify the nonlinear stiffness functions, damping functions, electromechanical coupling functions, and equivalent capacitance functions. The results show both softening and hardening nonlinearity in the stiffness characteristic and weak nonlinearity in electric characteristics. The results of the Hilbert transform based approach and the current mapping approach are compared, and the outcomes show good agreements.

Exploiting nonlinearity in a flapping wing mechanism of a bio inspired micro air vehicle to enhance energy efficiency

In recent years, there was a great interest in developing flying drones with similar capabilities as flying insects. It is suggested that the flapping frequency of insects coincides with the resonance frequency of their flight mechanism to enhance the power consumptions. In this paper, the effect of nonlinearity in the flight mechanism on the power consumption is investigated. A simple nonlinear model of the insect flight mechanism is developed and normalised to study the effect of different parameters on its performance. Both bistable and hardening nonlinearity are considered. It is shown that for a harmonic loading, the bistable systems reach their peak power at lower frequencies when compared to the corresponding linear system. The maximum power factor of nonlinear oscillator would be lower than the liner one. It is also shown that the peak active power of the bistable system has a higher value than the linear system if the loading function is a pulse square signal.

Impulsive Steering Between Coexisting Stable Periodic Solutions With an Application to Vibrating Plates

Single-degree-of-freedom (single-DOF) nonlinear mechanical systems under periodic excitation may possess multiple coexisting stable periodic solutions. Depending on the application, one of these stable periodic solutions is desired. In energy-harvesting applications, the large-amplitude periodic solutions are preferred, and in vibration reduction problems, the small-amplitude periodic solutions are desired. We propose a method to design an impulsive force that will bring the system from an undesired to a desired stable periodic solution, which requires only limited information about the applied force. We illustrate our method for a single-degree-of-freedom model of a rectangular plate with geometric nonlinearity, which takes the form of a monostable forced Duffing equation with hardening nonlinearity.