The Melnikov method is extended to a class of hybrid piecewise-smooth systems with impulsive effect and noise excitation when an unperturbed system is a piecewise Hamiltonian system with a homoclinic orbit. The homoclinic orbit continuously crosses the first switching manifold and transversally jumps across the second switching manifold by the impulsive effect. The trajectory of the corresponding perturbed system crosses the first switching manifold by applying the reset map describing the impact rule instantaneously. Then, the random Melnikov process of such systems is derived and the criteria for the onset of chaos with or without noise excitation are established. In addition, the complicated dynamics of concrete piecewise-smooth systems with or without noise excitation under the reset maps, impulsive effect, and non-autonomous periodic and damping perturbations are investigated by this extended method and numerical simulations.

This paper investigates the aeroelastic flutter and vibration reduction of functionally graded (FG) multilayer graphene nanoplatelets (GPLs) reinforced composite plates with piezoelectric patch subjected to supersonic flow. Activated by the control voltage, the piezoelectric patch can generate the active mass and active stiffness that can accordingly increase the base plate’s stiffness and mass. As a result, it changes the GPLs reinforced plate’s dynamic characteristics. The motion equation of the plate-piezoelectric system is derived through the Hamilton principle. Based on the modified Halpin–Tsai model, the effects of graphene nanoplatelets weight fraction and distribution pattern on the dynamic behaviors of the plate are numerically studied in detail. The result illustrates that adding a few amounts of grapheme nanoplatelets can effectually enhance the aeroelastic properties of the plates. Two kinds of control strategies, including the displacement and acceleration feedback control, are applied to suppress the occurrence of the flutter of the plate. It shows that the displacement and acceleration feedback control can improve the critical flutter Mach number of the plate by attaching active stiffness and active mass, respectively. Furthermore, the combined displacement and acceleration feedback control has a better control effect than that of considering only one of them.

This paper mainly studies the vibration isolation of negative Poisson’s ratio structure in the honeycomb base of ships. Based on the structure of the negative Poisson’s ratio structure, different laying methods and different cell structure are used to construct the honeycomb base with the re-entrant hexagonal cell, the mathematical expression of Poisson’s ratio of a single re-entrant hexagonal cell structure is obtained through theoretical analysis. The negative Poisson ratio and relative density could be got by changing the angle and side thickness of the cell structure. Based on the different energy band of the re-entrant hexagonal cell structure, the different negative Poisson’s ratio re-entrant hexagonal honeycomb base was got, the energy band and the frequency response curve of the ship base are analyzed by COMSOL software. The energy band diagram and the frequency response of the structure are obtained to analyze the vibration isolation performance of the honeycomb base. By comparing the experimental results, the following conclusions can be gotten: (1) Compared with the traditional base, the negative Poisson’s ratio base has better vibration isolation effect on external excitation; (2) Different laying method and Poisson ratios can get different isolation effect. The combined base structure can provide better isolation effect to the external excitation in a larger frequency band; (3) By adding different mass blocks to the inner or peripheral angles of the basic re-entrant hexagonal cell, the vibration isolation performance of the structure can be changed to better.

Negative Poisson’s ratio materials are increasingly used in the design of vibration isolation bases due to their unique tensile properties. In this paper, based on the expansion feature of the negative Poisson’s ratio re-entrant structure, the influence of the size of the re-entrant structure within a single structure was analyzed, and a honeycomb base was designed with a negative Poisson’s ratio re-entrant structure. A new modeling method for the honeycomb base is proposed. In the modeling process, the honeycomb base was analyzed according to its symmetry using the Lagrange equation for base modeling and the finite element consistent mass matrix was introduced to simplify the calculation. The vibration isolation performance of the honeycomb base was evaluated by vibration level difference. COMSOL software was used to simulate and analyze the cellular base in order to verify the correctness of the results obtained from numerical modeling. In conclusion, the honeycomb base had a vibration isolation effect on external excitation in the vertical direction of the base. Furthermore, the vibration isolation performance of the base was greatly related to the wall thickness and Poisson’s ratio of the re-entrant structure.

No abstract