A Dynamic Modeling Method for the Bi-Directional Pneumatic Actuator Using Dynamic Equilibrium Equation

Dynamic modeling of soft pneumatic actuators are a challenging research field. In this paper, a dynamic modeling method used for a bi-directionaly soft pneumatic actuator with symmetrical chambers is proposed. In this dynamic model, the effect of uninflated rubber block on bending deformation is considered. The errors resulting from the proposed dynamic equilibrium equation are analyzed, and a compensation method for the dynamic equilibrium equation is proposed. The equation can be solved quickly after simplification. The results show that the proposed dynamic model can describe the motion process of the bi-directional pneumatic actuator effectively.

Theory of Nonlinear Vibrations for Antisymmetric Cross-Ply Bistable Laminated Shells

In this paper, on the basis of taking the von Karman nonlinear factors into consideration, the constitutive equation of the antisymmetric cross-ply laminated composite was used to calculate the internal force and internal moment of the bistable structure, and the dynamic equilibrium equation and the compatible equation were constructed, respectively. The two equations were combined to establish a nonlinear dynamic model for the antisymmetric cross-ply laminated glass fiber resin bistable shell. Then, the finite element numerical simulation software ABAQUS was adopted to perform simulation modeling and numerical analysis on a series of bistable specimens, so as to study the impact of different geometric parameters on the frequencies, mode shapes, and other vibration characteristics of the antisymmetric laminated fiber resin bistable shell. Galerkin discretization was conducted on the vibration partial differential equation. Since there are only even-order partial differential terms of deflection w with respect to x and y in the vibration partial differential equation at this time, the form of series obtained by each term is the same, which simplifies the discretization of the dynamic equilibrium equation and the compatible equation. Finally, the two equations after discretization were merged to obtain the three-degree-of-freedom nonlinear ordinary differential equation of the antisymmetric cross-ply laminated glass fiber resin bistable shell. The system averaged equation was acquired by perturbation analysis through a multiscale method, and the periodic solution of the antisymmetric laminated bistable system was studied. Moreover, the system’s nonlinear dynamic behavior characteristics such as bifurcation and chaos were explored when the main resonance Ω is close to ω 1 and ω 2 , respectively, and the internal resonance is 1 : 2 : 3.

Static response analysis of a dual crane system using fuzzy parameters

Static response analysis of a dual crane system (DCS) is conducted using fuzzy parameters. The fuzzy static equilibrium equation is established and two fuzzy perturbation methods, including the compound function/fuzzy perturbation method (CFFPM) and modified compound function/fuzzy perturbation method (MCFFPM), are presented. The CFFPM employs the level-cut technique to transform the fuzzy static equilibrium equation into several interval equations with different cut levels. The interval Jacobian matrix, the first and second interval virtual work vectors, and the inverse of interval Jacobian matrix are approximated by the first-order Taylor series and Neumann series. The fuzzy static response field for every cut level is obtained by a synthesis of the compound function technique, the interval perturbation method, and the fuzzy algorithm. In the MCFFPM, the fuzzy static response field for every cut level is derived based on the surface rail generation method, the modified Sherman–Morrison–Woodbury formula, and the fuzzy theory. Compared with the Monte Carlo method (MCM), numerical examples demonstrate that the MCFFPM has a better accuracy than the CFFPM and both of them bring a higher efficiency than the MCM, especially when it comes to uncertainty quantification of fuzzy parameters on the static response of the DCS.

Dynamic Equilibrium Equations in Unified Mechanics Theory

Traditionally dynamic analysis is done using Newton’s universal laws of the equation of motion. According to the laws of Newtonian mechanics, the x, y, z, space-time coordinate system does not include a term for energy loss, an empirical damping term “C” is used in the dynamic equilibrium equation. Energy loss in any system is governed by the laws of thermodynamics. Unified Mechanics Theory (UMT) unifies the universal laws of motion of Newton and the laws of thermodynamics at ab-initio level. As a result, the energy loss [entropy generation] is automatically included in the laws of the Unified Mechanics Theory (UMT). Using unified mechanics theory, the dynamic equilibrium equation is derived and presented. One-dimensional free vibration analysis with frictional dissipation is used to compare the results of the proposed model with that of a Newtonian mechanics equation. For the proposed entropy generation equation in the system, the trend of predictions is comparable with the reported experimental results and Newtonian mechanics-based predictions.

Evaluating the Effect of Asymmetric Cross-section in Free Vibration and Bending Analysis Results of FG Sandwich Beam by Proposing Simple Efficient Element

In this paper, the asymmetric effect of the cross-section on the free vibration and bending analysis of FG sandwich beams are evaluated. For this purpose, a simple, efficient element is formulated. The new element is created based on the Timoshenko beam theory. The third- and second-order polynomials will be used for vertical displacement and rotation fields, respectively. The proposed formulation will be written based on satisfying the equilibrium equation. Satisfying the equilibrium equation of the Timoshenko beam, in addition to increasing element efficiency, will reduce the number of nodal unknowns. Several benchmark tests with different boundary conditions are used for thin and thick beams to prove the efficiency of the proposed element. The responses of the good elements of other researchers have been used for comparison. Numerical tests prove the rapid convergence rate and high accuracy of the proposed element in free vibration and bending analysis of the beams with various cross-section types and different boundary conditions. The pinned-sliding support conditions for the beam are used to evaluate the asymmetric effect of the cross-section. The use of asymmetric cross-sections creates additional axial displacements and intensifies the deflection of the beam under the lateral load. By increasing the asymmetry, the additional axial displacement and vertical displacement increase. These additional deflections for thin beams are more than thick ones. Also, asymmetry results in increasing the natural frequencies of beams. In the free vibration analysis, the effect of asymmetry on thick beams is more than thin ones.

Non-equilibrium Equation of State in the Approximation of the Local Density Functional and Its Application to the Emission of High-Energy Particles in Collisions of Heavy Ions

The non-equilibrium equation of state is found in the approximation of the functional on the local density, and its application to the description of the emission of protons and pions in heavy ion collisions is considered. The non-equilibrium equation of state is studied in the context of the hydrodynamic approach. The compression stage, the expansion stage, and the freeze-out stage of the hot spot formed during the collisions of heavy ions are considered. The energy spectra of protons and subthreshold pions produced in collisions of heavy ions are calculated with inclusion of the nuclear viscosity effects and compared with experimental data for various combinations of colliding nuclei with energies of several tens of MeV per nucleon.

Numerical Assessment of Lateral Deflection Equation of Single-Storey Light-Frame Wood Shearwalls

Based on the decomposition of the deflection into bending, panel shear, nail slip, and base rotation terms, the nonlinear four-term equation specified by the Canadian wood design code provides an estimate of the total lateral deflection of light-frame wood shear walls. This paper reports the creation of a numerical procedure for separating the responses for each term using a detailed nonlinear finite element modeling (FEM) that simulates individual components of shear walls. Since sheathing panel stiffness is not considered in computations of the bending term, the study reveals that bending deformation results calculated using the equation are more conservative than the FEM results. The nail slip term does not reflect the real nail base connection properties. A new equilibrium equation for determining the lateral deflection due to base rotation is presented. The equation is generally conservative because of the omission of some practical considerations.

Calculation accuracy of mathematical homogenization method for thermo-mechanical coupling problems

The paper analyzes the thermo-mechanical couplinag phenomenon under the condition of sliding contact, establishes the finite element analysis continuous model of thermo-mechanical coupling, and proposes the system dynamic equilibrium equation and thermodynamic equilibrium equation. The article analyzes the contact conditions between the objects in the system and obtains the objects? contact conditions? mathematical expression. On this basis, the constraint function is used to express the mathematical homogenization. We apply the variation principle to the constraint function and form a non-linear equation group with the system balance equation solve the thermal-mechanical coupling problem. The example shows that we use the constraint function method to solve the thermo-mechanical coupling problem, which has good convergence, stable algorithm, and the calculation result can reflect the actual situation.