Presently, ship-mounted cranes are playing more and more important roles in modern ocean transportation and logistics. Different from traditional land-fixed crane systems, ship-mounted cranes present much more complicated nonlinear dynamical characteristics and they are persistently influenced by different mismatched disturbances due to harsh sea environments, e.g., sea waves, ocean currents, sea winds, and so forth; these unfavorable factors bring about many challenges for the development of effective control schemes. This paper presents a novel nonlinear stabilizing control strategy for underactuated ship-mounted crane systems. Specifically, some novel coordinate change procedures are first introduced to tackle the disturbing terms by transforming the original dynamics into a new form, which facilitates both controller design and stability analysis. After that, a nonlinear control law is constructed to regulate the cargo position to the desired location asymptotically, in the presence of ship roll and heave movements. The boundedness and convergence of the closed-loop signals are proven with Lyapunov-based analysis. To the best of our knowledge, this is the first closed-loop scheme that can achieve asymptotic control results, without linearizing/approximating the original nonlinear dynamics when performing controller design and stability analysis, for underactuated ship-mounted cranes with ship roll and heave movements. Hardware experimental results are included to show that the proposed control method can achieve satisfactory control performance and it admits strong robustness against external perturbations.

In the paper, basing on a refined beam model and considering the effects of thermal and elastic foundation, the nonlinear dynamic responses of functionally graded tubes applied to a moving load which keeps at a constant velocity are studied. This refined beam model is expanded by Laurent series expansion which can fulfill the shear stress on the inner and outer surfaces. The whole governing equations are obtained by Hamilton’s principle, and solved by Galerkin method and Newmark method. In the numerical examples, the effects of transverse shear deformation, geometric nonlinearity, functionally graded index, inner radius, temperature, elastic foundation stiffness, and velocity of moving load on the dynamic responses of FGM tubes are discussed. For present beam model, it is more suitable and convenient to analyze the nonlinear dynamic responses of FGM tubes with circular cross section subjected to a moving load, especially for exact stress analysis.

The nonlinear dynamic responses of the fiber-metal laminated beam resting on a tensionless elastic foundation and subjected to a moving harmonic load and thermal load are investigated in the paper. The beam-foundation interaction force that only reacts in compression is established by introducing the hyperbolic tangent function, and the steady temperature field is deduced by solving the one-dimensional steady-state heat transfer equation. The nonlinear governing equations are derived by application of Hamilton principle and solved by finite difference method, Newmark method and Newton-Raphson method. In numerical results, FML beams constrained by different boundary conditions are selected to reveal the dynamic properties of FML beams. The effects of some parameters are discussed in detail, and some meaningful conclusions are concluded.

Based on a new modified couple stress theory for composite laminates, considering geometric nonlinear theory and Timoshenko beam hypothesis, the governing equations for size-dependent composite laminated microbeams in thermal environment are derived using Hamilton's principle. Analytical and numerical solutions are employed in solving the present problem, respectively. An auxiliary function is introduced to reduce the governing equations to a single fourth-order integral-differential equation, and the exact solutions for the thermal buckling and postbuckling of microbeams with combination of in-plane immovable simply supported boundary conditions are obtained. By introducing the differential quadrature method, the governing equations are transferred into a system of nonlinear algebraic eigenvalue equations. In numerical examples, comparison between the present results and those obtained in the literature verifies the validity and efficiency of the present analytical and numerical methods. The effects of thermal expansion coefficients and material length scale parameter are discussed. Numerical results indicate that the above-mentioned effects play very important roles for the thermal buckling and postbuckling of the composite laminated microbeams.

The present study considered the free and forced vibration of cracked fiber metal laminated (FML) beams with a damper subjected to a moving load, and the detection of the cracks by using continuous wavelet transform (CWT). The beam is regarded as multi segments which are assumed to obey the Euler-Bernoulli beam hypothesis and the crack is modeled as rotational spring with sectional flexibility. The modal expansion theory and Newmark method are employed to solve the dynamic responses of FML beam numerically. Two classes of boundary conditions are considered and the dynamic responses at the tip of a FML cantilever beam with a single crack are obtained for various load velocity, and the outcome results have been compared to the results obtained by literature. The influences of crack depth, crack location, ply angle of the fiber layer, stiffness coefficient of the damper and velocity of the moving load on free vibration and forced vibration of FML cantilever beams are investigated. Numerical results indicate that the above-mentioned effects play a very important role on both free vibration and dynamic responses of the beam. In the end of the numerical examples, continuous wavelet transform is used to detect the location of the cracks of a clamped-clamped FML beam.

This paper investigates the nonlinear transient thermal responses of functionally graded beams resting on tensionless foundation under unsteady heat conduction. The interaction between functionally graded beams and tensionless foundation is only compressive without tensile reaction. The whole model is established based on Euler beam theory and solved by the combination of differential quadrature method (DQM), Newmark method and Newton–Raphson method. Some detailed numerical results are carried out to reveal the transient heat conduction procedure and the mechanical behaviors of functionally graded beam resting on tensionless foundation.

In this paper, considering the small scale effect, the linear free vibration in pre/post-buckled states and nonlinear dynamic stability of lipid tubules with in-plane movable ends are studied. The small scale effect is characterized by nonlocal elasticity theory. The vibration in pre/post-buckled regions is solved by the differential quadrature method (DQM), and the nonlinear dynamic stability is solved by incremental harmonic balance method (IHBM). In numerical results, the effects of small scale parameter, types of lipid tubule on vibration in pre/post-buckled states and nonlinear dynamic stability are discussed.

The present study is concerned with the nonlinear dynamic behaviors of fiber metal laminated (FML) beams subjected to moving loads in thermal environments. Based on von Kármán geometric nonlinear theory and Euler–Bernoulli beam hypothesis, the nonlinear equations of motion for the fiber-metal laminated beams under moving loads are derived by using Hamilton’s principle. Galerkin method and Newmark method are employed to solve the dynamic responses of FML beam numerically. The dynamic responses at the midspan of the FML beam are obtained for various load velocity and temperature rise and the outcome results have been compared to the results with those obtained from linear solution. The influences of temperature, geometric nonlinearity, material parameters and velocity of the moving load on the dynamic responses of fiber-metal laminated beams are investigated. Numerical results indicate that the above-mentioned effects play a very important role on the dynamic responses of the beam.

This article studies nonlinear dynamic stability of carbon nanotube-reinforced composite (CNTRC) plates resting on an elastic foundation. The single-walled carbon nanotubes (SWCNTs) are aligned and distributed in the form of uniformly distributed (UD) and functionally graded (FG) reinforcements. The governing equations are established based on classic plate theory, which is converted to a Mathieu-type equation by using a two-step perturbation technique, and then solved by adopting an incremental harmonic balanced (IHB) method. In numerical results, the effects of nonlinear geometric factor, distribution and fraction volume of CNTs, and foundation stiffness on principle dynamic unstable regions are discussed.

This article presents the nonlinear dynamic response of functionally graded (FG) shallow spherical shells in thermal environments subjected to low-velocity impact by an elastic ball. The material properties of a FG shallow spherical shell vary continuously through the thickness according to a power law distribution of the volume fraction of the constituents. The temperature field is considered to vary along the thickness direction due to the steady state heat transfer. Based on the higher order shear deformation theory, the governing equations of motion for the shell, which account for geometric nonlinearity is obtained using Hamilton's principle. The contact force between the shell and the impactor is relative to local deformation and calculated using a numerical method. Then, the governing equations of motion are solved numerically by the Chebyshev collocation method and Newmark scheme. This is a complete model that can not only fully model the dynamic behavior of the shell but also fully model the impactor's dynamic behavior. In the numerical example, the effects of material properties, temperature, initial impact velocity and mass of the impactor on the dynamic behavior of the shells, and contact force are discussed in detail.

This paper studies the nonlinear bending and vibration problems of functionally graded tubes with temperature-dependent material properties based on a refined beam model. The tubes are exposed to a uniform distributed temperature field and are placed on elastic foundation. The refined beam model for tubes can satisfy the stress boundary conditions on inner and outer surfaces. The governing equations of nonlinear bending and vibration for the functionally graded tubes are derived by using Hamilton's principle and are solved by introducing a two-step perturbation technique. Some comparisons for bending and vibration are presented to valid the correctness of present beam model and solution method. In numerical results, the effects of transverse shear deformation, the volume fraction, inner radius and elastic foundation stiffness as well as the temperature on the natural frequency, amplitude-frequency responses and nonlinear bending responses are discussed. (C) 2016 Elsevier Inc. All rights reserved.

The present study is concerned with the nonlinear dynamic responses for the viscoelastic fiber–metal-laminated beams subjected to thermal shock. First, the one-dimensional heat conduction equation with variable coefficients in the direction of thickness is established, and this equation is solved by differential quadrature method (DQM) and the fourth-order Runge–Kutta method. An effective numerical approach is presented to solve this kind of problem. The fiber layer is considered to be the standard linear material. Based on von Kármán geometric nonlinear theory and Timoshenko beam hypothesis, using Hamilton’s principle, the governing equations of dynamic for the fiber–metal-laminated beam under thermal shock are derived. The dynamic equations in terms of the displacements are discretized in spatial domain by adopting DQM and discretized in time domain by Newmark method synthetically. Then the Newton iteration method is used to solve the nonlinear algebraic equations at every grid of the time domain. Eventually, the temperature field in the beam and the dynamic displacement fields, and the stress responses of the beam are obtained. In numerical examples, the influences of temperature, geometric nonlinearity, and material parameters on the dynamic responses of the beam are discussed.

As a powerful large-scale construction tool, a tower crane is a strongly nonlinear underactuated system presenting complicated dynamical characteristics. Existing control methods for tower cranes are developed on the basis of simplified (i.e., linearized/approximated) crane dynamics, and most of them require exact model knowledge. However, practical tower cranes usually suffer from uncertainties (e.g., unknown rope length and payload mass); moreover, when the state variables are not close enough to the equilibrium point due to unexpected disturbances, simplified models might not reflect the actual dynamics any longer, which usually badly degrades the control performance. To tackle these problems, this paper proposes an adaptive control scheme for underactuated tower cranes to achieve simultaneous slew/translation positioning and swing suppression, which can reduce unexpected overshoots for the jib/trolley movements. The closed-loop stability is backed up with the rigorous mathematical analysis. To the best of our knowledge, the proposed controller is the first method for tower cranes with parametric uncertainties, which is developed without linearizing/approximating their nonlinear dynamics. Finally, we introduce our self-built multifunctional hardware crane experiment testbed and present experimental studies for the proposed method. Experimental results show that the new control approach is effective and admits satisfactory robustness.

A facile co-calcination strategy with simultaneous N-doping, carbon graphitization, and palladium ion (Pd2+) reduction under high temperature was used to derive Pd nanoparticles budded on N-doped ordered mesoporous graphitic carbon nanospheres (Pd/N-MCN). Pd/N-MCN was exploited as a cathode catalyst for the oxygen reduction reaction (ORR). It demonstrated strong stability with a relative current of 95% still persisting after 40 000 s. Most importantly, hybrids exhibited superior methanol tolerance, remaining stable after the addition of 2M methanol in electrolyte. The outstanding performance of Pd/N-MCN in ORR could be attributed to its ordered mesopores, large surface area, homogeneous budding of abundant Pd active sites, graphitization generated by Pd catalysis, and the synergistic effects of Pd nanoparticles strongly coupled to N-MCN. (C) 2015 Published by Elsevier Ltd.

The thermoelastoplastic behavior of a high strength low alloy (HSLA) steel plate subjected to low-velocity impact is investigated in this paper. A yield criterion related to the spherical tensor of stress is proposed to describe the mixed hardening of the orthotropic material. Based on the classical nonlinear thin plate theory, the incremental nonlinear motion equations are obtained, and are solved by the combination of finite difference method and Newmark method with iterations. To explain the contact process, a thermoelastoplastic contact criterion is developed, of which the validity has been proved. Numerical results show that the radius of the impactor, initial impact velocity, environment temperature, and the thickness of the HSLA steel plate all have great influences on the thermoelastoplastic behavior of the HSLA steel plate subjected to low-velocity impact.

This paper studies the thermal buckling and postbuckling of functionally graded tubes whose material properties are temperature-dependent based on a refined beam model. Firstly, the displacement field of the tubes is expanded in a Laurent series expansion form so that the shear stress on the inner and outer surfaces is vanished. Then, the nonlinear governing equations of the tubes are obtained by the generalized variational principle. Finally, the problem is solved by adopting a two-step perturbation technique. In order to valid the correctness of a present high-order beam model and calculation method, the analytical solution of Timoshenko beam model and Euler beam model for thermal postbuckling are presented. In numerical results, effects of transverse shear deformation, the volume fraction and inner radius on critical thermal buckling and postbukling are investigated.

Based on the higher order shear deformation theory and the geometric nonlinear theory, the nonlinear motion equations, to which the effects of the positive and negative piezoelectric and the thermal are introduced by piezoelectric fiber metal laminated (FML) plates in an unsteady temperature, are established by Hamilton's variational principle. Then, the control algorithm of negative-velocity feedback is applied to realize the vibration control of the piezoelectric FML plates. During the solving process, firstly, the formal functions of the displacements that fulfilled the boundary conditions are proposed. Then, heat conduction equations and nonlinear differential equations are dealt with using the differential quadrature (DQ) and Galerkin methods, respectively. On the basis of the previous processing, the time domain is dispersed by the Newmark-beta method. Finally, the whole problem can be investigated by the iterative method. In the numerical examples, the influence of the applied voltage, the temperature loading and geometric parameters on the nonlinear dynamic response of the piezoelectric FML plates is analyzed. Meanwhile, the effect of feedback control gain and the position of the piezoelectric layer, the initial deflection and the external temperature on the active control effect of the piezoelectric layers has been studied. The model development and the research results can serve as a basis for nonlinear vibration analysis of the FML structures.

The elasto-plastic postbuckling of fiber metal laminated beams with delamination and the energy release rate along the delamination front are discussed in this paper. Considering geometrical nonlinearity, thermal environment and geometrical initial imperfection, the incremental nonlinear equilibrium equations of delaminated fiber metal laminated beams are established, which are solved using the differential quadrature method and iterative method. Based on these, according to the J-integral theory, the elasto-plastic energy release rate is studied. The effects of some important parameters on the elasto-plastic postbuckling behavior and energy release rate of the aramid reinforced aluminum laminated beams are discussed in details.

In the present paper, we suggest a novel robust control strategy for the control problem of double pendulum crane systems. More precisely, we first derive a reduced crane model that can well depict the original double pendulum dynamics. After that, a super-twisting-based nonlinear control law is presented, which can make the crane follow preset trajectories and eliminate the double pendulum swing angles. We include some numerical simulation results to examine the performance and robustness of the proposed method.

During the past decades, increasing requirement in aircraft for high-performance, lightweight structures have caused strong interests on the development of fiber-metal laminates (FMLs), which are manufractured from thin layers of glass fibre reinforced composite and alluminium alloy. In this paper, the nonlinear dynamic response problem of the FML plate subjected to unstable temperature with interfacial damage is analyzed. Based on the weak bonded theory, the interfacial constitutive relations of the FML are constructed. According to the Hamiltons variance principle, the nonlinear motion equations of the FML with interfacial damages subjected to the unstable thermal field are obtained. And then, the finite difference, Newmark-and the iteration method are applied to solve the nonlinear motion equations. In the numerical examples, the effects of the interface damage, the amplitude and frequency of imposed loads and the temperature fields on the nonlinear dynamic response of the FML plates are investigated. And in conclusion, the effects of various type of temperature on the nonlinear dynamic response of FML plate are different obviously.