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This paper investigates the nonlinear free vibration of spinning pre-twisted functionally graded material (FGM) plates in thermal environment. Based on the Kirchhoff plate theory and von Kármán large-deformation theory, the nonlinear dynamic model is established via the Lagrange equation, where the warping effect is taken into account. The material properties are related to temperature and change according to a power-law exponent distribution. The theoretical solution of nonlinear-free vibration is obtained using the multiple scale method. The effects of power-law exponent, temperature difference, spinning speed, hub radius ratio, and twist angle on nonlinear-free vibration characteristics of the spinning pre-twisted cantilever FGM plates are discussed. The results show that the spinning pre-twisted cantilever FGM plate exhibits nonlinear hardening-spring vibration behavior, while the characteristics weaken with the increase of spinning speed. The twist angle and setting angle have coupling effects on the nonlinear vibration characteristics of spinning pre-twisted FGM plates. [ABSTRACT FROM AUTHOR]

The thickness configuration effect on natural frequency and critical speed of spinning variable-thickness cylindrical shells is investigated in this paper. Based on Love's thin shell theory, the eigenfrequency equation is derived by employing the Rayleigh–Ritz method in conjunction with Chebyshev polynomials, considering the effects of Coriolis and centrifugal forces due to rotation. Seven types of thickness configurations and various classical boundary conditions are taken into account. Backward and forward wave frequencies, the critical speed, and the mode shapes of the spinning variable-thickness cylindrical shells are solved. Results show that the thickness configuration not only changes circumferential wave number corresponding to the lowest natural frequency, but also affects the critical speed. However, the influence of thickness configuration on mode shapes of the shell is not obvious. The stronger the boundary constraints, the more obvious effect of slope of thickness variation on the critical speed of spinning cylindrical shells. [ABSTRACT FROM AUTHOR]

Acupuncture reduces pain by activating specific areas called acupoints on the patient's body. When these acupoints are fully activated, sensations of soreness, numbness, fullness, or heaviness called De qi or Te qi are felt by clinicians and patients. There are two kinds of acupuncture, manual acupuncture and electroacupuncture (EA). Compared with non-acupoints, acupoints are easily activated on the basis of their special composition of blood vessels, mast cells, and nerve fibers that mediate the acupuncture signals. In the spinal cord, EA can inhibit glial cell activation by down-regulating the chemokine CX3CL1 and increasing the anti-inflammatory cytokine interleukin-10. This inhibits P38 mitogen-activated protein kinase and extracellular signal-regulated kinase pathways, which are associated with microglial activation of the C-Jun N-terminal kinase signaling pathway and subsequent astrocyte activation. The inactivation of spinal microglia and astrocytes mediates the immediate and long-term analgesic effects of EA, respectively. A variety of pain-related substances released by glial cells such as the proinflammatory cytokines tumor necrosis factor α , interleukin-1 β , interleukin-6, and prostaglandins such as prostaglandins E2 can also be reduced. The descending pain modulation system in the brain, including the anterior cingulated cortex, the periaqueductal gray, and the rostral ventromedial medulla, plays an important role in EA analgesia. Multiple transmitters and modulators, including endogenous opioids, cholecystokinin octapeptide, 5-hydroxytryptamine, glutamate, noradrenalin, dopamine, γ -aminobutyric acid, acetylcholine, and orexin A, are involved in acupuncture analgesia. Finally, the "Acupuncture + " strategy is introduced to help clinicians achieve better analgesic effects, and a newly reported acupuncture method called acupoint catgut embedding, which injects sutures made of absorbable materials at acupoints to achieve long-term effects, is discussed. [ABSTRACT FROM AUTHOR]

The thermo-electro-mechanical nonlinear vibration of circular cylindrical nanoshells on the Winkler–Pasternak foundation is investigated. The nanoshell is made of functionally graded piezoelectric material (FGPM), which is simulated by the nonlocal elasticity theory and Donnell's nonlinear shell theory. The Hamilton's principle is employed to derive the nonlinear governing equations and corresponding boundary conditions. Then, the Galerkin's method is used to obtain the nonlinear Duffing equation, to which an approximate analytical solution is obtained by the multiple scales method. The results reveal that the system exhibits hardening-spring behavior. External applied voltage and temperature change have significant effect on the nonlinear vibration of the FGPM nanoshells. Moreover, the effect of power-law index on the nonlinear vibration of the FGPM nanoshells depends on parameters such as the external applied voltage, temperature change and properties of the Winkler–Pasternak foundation. [ABSTRACT FROM AUTHOR]

This paper examines the nonlinear dynamics of a translational functionally graded material (FGM) plate. The plate is composed of nickel and stainless steel, and its property is graded in the thickness direction that obeys a power-law distribution. By adopting the Kármán nonlinear geometrical relations, the equation of motion is derived from the D'Alembert's principle by considering the dynamic equilibrium relationships for the out-of-plane vibration of the plate. The equation of motion is discretized by using the Galerkin method and thus a series of ordinary differential equations with mode-coupling terms are obtained. These ordinary differential equations are then solved by utilizing the method of harmonic balance. The analytical results are verified by the adaptive step-size fourth-order Runge-Kutta technique. The stability analysis of analytical solutions is also carried out by introducing small perturbation for steady state solutions. Both natural frequency and nonlinear frequency-amplitude characteristics are presented. In the translational FGM plate, strong nonlinear mode interaction phenomenon has been detected. The nonlinear frequency response shows intensive hardening-spring characteristics. Moreover, various system parameters such as power-law distribution, translating speed of the plate, in-plane tension force, damping coefficient and external excitation amplitude are selected as the controlled variables to present parametric study. Their effects on the nonlinear dynamical response of the translational FGM plate are highlighted. [ABSTRACT FROM AUTHOR]

The instability of longitudinally variable speed viscoelastic plates in contact with ideal liquid is studied for the first time. The effect of free surface waves is taken into account in the present study. The viscoelasticity is considered by using the Kelvin-Voigt viscoelastic constitutive relations. The classical theory of thin plate is utilized to derive the governing equation of variable speed plates. The fluid is assumed to be incompressible, inviscid and irrotational. Additionally, the velocity potential and Bernoulli's equation are utilized to describe the fluid pressure acting on the vibrating plates. The fluid effect on the vibrational plates is described as the added mass of the plates which can be formulated by the kinematic boundary conditions at the structure-fluid interfaces. Parametric instability is analyzed by directly applying the method of multiple scales to the governing partial-differential equations and boundary conditions. The unstable boundaries are derived from the solvability conditions and the Routh-Hurwitz criterion for principal parametric, sum-type and difference-type combination resonances. Based on the numerical simulation, the effects of some key parameters on the unstable boundaries are illustrated in the excitation frequency and excitation amplitude plane in detail. [ABSTRACT FROM AUTHOR]

The vibration characteristics of an axially moving vertical plate immersed in fluid and subjected to a pretension are investigated, with a special consideration to natural frequencies, complex mode functions and critical speeds of the system. The classical thin plate theory is adopted for the formulation of the governing equation of motion of the vibrating plates. The effects of free surface waves, compressibility and viscidity of the fluid are neglected in the analysis. The velocity potential and Bernoulli's equation are used to describe the fluid pressure acting on the moving plate. The effect of fluid on the vibrations of the plate may be regarded as equivalent to an added mass on the plate. The formulation of added mass is obtained from kinematic boundary conditions of the plate-fluid interfaces. The effects of some system parameters such as the moving speed, stiffness ratios, location and aspect ratios of the plate and the fluid-plate density ratios on the above-mentioned vibration characteristics of the plate-fluid system are investigated in detail. Various different boundary conditions are considered in the study. [ABSTRACT FROM AUTHOR]

The stability and dynamics of an axially moving unidirectional plate partially immersed in a liquid and subjected to a nonlinear aerodynamic excitation are investigated. The method of singular functions is adopted to study the dynamic characteristics of the unidirectional plates with discontinuous characteristics. Nonlinearities due to large-amplitude plate motions are considered by using the classical nonlinear thin plate theory, with allowance for the effect of viscous structural damping. The velocity potential and Bernoulli's equation are used to describe the fluid pressure acting on the unidirectional plate. The effect of fluid on the vibrations of the plate may be equivalent to added mass of the plate. The formulation of added mass is obtained from kinematic boundary conditions of the plate-fluid interfaces. The system is discretized by Galerkin's method while a model involving two degrees of freedom, is adopted. Attention is focused on the behavior of the system in the region of dynamic instability, and several motions are found by numerical simulations. The effects of the moving speed and some other parameters on the dynamics of the system are also investigated. It is shown that chaotic motions can occur in this system in several certain regions of parameter space. [ABSTRACT FROM AUTHOR]