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A classic-type SPAR has a natural heave period in the range of 25–30 seconds, making it vulnerable to resonance when wave periods approach this range. To reduce resonance effects, this study investigates the influence of a spring-mass type Tuned Mass Damper (TMD) on the SPAR’s heave motion response. Simulations were performed using a frequency-domain numerical method with Nemoh software to obtain the heave Response Amplitude Operator (RAO). Key parameters evaluated include the TMD mass ratio to SPAR displacement, spring stiffness coefficient, and damping coefficient. Results indicate that TMD parameter variations significantly affect the RAO curve, altering the height of resonance peaks, generating new peaks, and shifting the resonance frequency. The most effective configuration reduced the maximum RAO from 2.216 m/m without TMD to 1.536 m/m. However, in spectral response analyses under 1-year and 100-year wave conditions at the West Seno site, the TMD showed limited effectiveness due to a mismatch between the structure’s critical RAO frequency and the dominant energy regions of the wave spectrum. This highlights the importance of aligning TMD design with site-specific wave characteristics for optimal performance.

In this study,a new approach of optimization algorithm is developed. The optimum distribution of elastic springs on which a cantilever Timoshenko beam is seated and minimization of the shear force on the support of the beam is investigated.The Fourier transform is applied to the beam vibration equation in the time domain and transfer function, independent from the external influence, is used to define the structural response. For all translational modes of the beam, the optimum locations and amounts of the springs are investigated so that the transfer function amplitude of the support shear force is minimized. The stiffness coefficients of the springs placed on the nodes of the beam divided into finite elements are considered as design variables. There is an active constraint on the sum of the spring coefficients taken as design variables and passive constraints on each of them as the upper and lower bounds. Optimality criteria are derived using the Lagrange Multipliers method. The gradient information required for solving the optimization problem is analytically derived. Verification of the new approach optimization algorithm was carried out by comparing the results presented in this paper with those ones from analysis of the model of the beam without springs, with springs with uniform stiffness and with optimal distribution of springs which support a cantilever beam to minimize the tip deflection of the beam found in the literature. The numerical results show that the presented method is effective in finding the optimum spring stiffness coefficients and location of springs for all translational modes.The proposed method can give designers an idea of how to support the cantilever beams under different harmonic vibrations.

This study presents a spectro-geometric vibration model for analyzing free as well as forced vibration properties for FGM cylindrical double-walled shells with internal structures. The boundary conditions and coupling effects are modeled using an artificial virtual spring approach, which allows for the simulation of arbitrary boundary and coupling conditions by varying the elastic spring stiffness coefficients. The spectral geometry method is employed to represent the displacement variables of the FGM substructure, overcoming the discontinuity phenomenon commonly observed when traditional Fourier series are used. The dynamic equations of the FGM cylindrical double-walled shell with an internal structure are derived using the first-order shear deformation assumption and the Rayleigh–Ritz method, and the corresponding vibration solutions are computed. The model’s reliability and prediction accuracy are confirmed through convergence checks and numerical comparisons. Additionally, parametric studies are conducted to examine the influence of material constants, position parameters, and geometric parameters on the shell’s inherent characteristics and steady-state response.

AbstractThe Discrete Element Method (DEM) is a numerical technique proposed for solving mechanics problems of non-continuous media. However, applications of DEM in continuous media structures are relatively limited. In this manuscript, a modification of the torsional spring stiffness coefficient of the simply supported boundary contact element is proposed based on our previous work. Then, the plate DEM based on modifying the torsional spring stiffness coefficient is adopted to solve the load-bearing problems of cylindrical shells. This study aims to investigate the validity of using the plate DEM based on modification of the torsional spring stiffness coefficient for nonlinear large deformation analysis of shell-type structures. Compared to traditional methods, continuity of displacement and deformation coordination are not required for the plate DEM, and there is no need to assemble a stiffness matrix, so matrix non-convergence problems are evitable. To evaluate accuracy of the developed plate DEM, several popular benchmark problems of geometric nonlinearity for shells are solved by adopting the plate DEM. The results demonstrate that the proposed numerical method can obtain highly accurate solutions in the nonlinear large deformation numerical calculations of shells, which further confirms the feasibility of the plate discrete element method in solving the geometric nonlinear problems of plate and shell structures.

The microphonic noise induced by the vibration from cryocoolers has been found to cause energy resolution degradation in vibration-sensitive instruments. In this paper, theoretical and experimental research on the vibration generation mechanism of an aerospace-grade coaxial pulse-tube cryocooler (CPTC) is presented. Accordingly, suggestions for suppressing the vibration of the pulse-tube cryocooler are provided. A vibration model for the Oxford-type dual-opposed linear compressor is established, and the mechanism of vibration induced by the compressor is theoretically analyzed. A numerical simulation indicates that deviations in the compressor’s inductance coefficient, electromagnetic force coefficient, and flexure spring stiffness coefficient significantly affect the axial vibration of the compressor. The theoretical and experimental studies show that the high-order harmonic vibrations of the compressor are determined by both the resonance of the flexure springs and the high-order harmonics of the driving power supply. Through experiments and simulations, it is revealed that the dynamic gas pressure only induces vibration axially at the cold tip, while the radial vibration at the cold tip is determined by the heat head ‘s vibration and the structural response characteristics of the cold finger.

In view of the bending failure problem of segmented buried pipelines under the condition of foundation soil settlement, this paper establishes a structural state identification method suitable for segmented buried pipelines based on distributed optical fiber sensing technology to study the structural response of segmented buried pipelines under the condition of foundation soil settlement. Based on the Ω-type bell-and-spigot joint monitoring unit, this study realizes the nondestructive monitoring of segmented pipeline structure response using distributed optical fiber sensing technology. The distributed optical fiber sensing system is used to monitor the bending strain curve of the pipe body under the action of foundation settlement based on Brillouin optical time-domain analysis (BOTDA) principle, the bending strain of the segmented buried pipeline body was determined. Through the parameter sensitivity analysis of the segmented buried pipeline-soil finite element model, it is determined that the vertical spring stiffness coefficient of the foundation soil is the main factor affecting the vertical displacement and bending strain of the segmented buried pipeline. Then, the vertical spring stiffness coefficient of the foundation soil is used as the correction term, and the bending strain monitoring value of the pipe body is used as the objective function to correct the finite element model of the segmented buried pipeline. Based on the revised pipeline finite element model, we obtain the real stiffness of the foundation soil, and invert the vertical displacement of the pipeline and the bending angle of the socket and socket of buried pipelines to realize structural status recognition for segmented buried pipelines. The effectiveness of the method is verified by full-scale experiments.

To realize the adaptive grasping of objects with diverse shapes and to capture the joint angles of the finger, a multi degree of freedom (DOF) adaptive finger for prosthetic hand is proposed in this paper. The fingers are designed with three joints. The maximum rotation angle of the finger joints is 90°. The angle at which the finger joints bend can be captured. Firstly, the prototype design, forward kinematics and force analysis of phalanges are described in detail. In order to achieve an adaptive motion pattern similar to that of the human hand, this paper investigates the optimization of the torsion spring stiffness coefficient so that the metacarpophalangeal (MCP) joints, proximal interphalangeal (PIP) joints, and distal interphalangeal (DIP) joints of the bionic finger meet a motion ratio of approximately 3:3:1. Then, in order to realize the joint angle measurement in the process of grasping an object, the mechanical-sensor integrated finger joint is designed, and the composition, angle measurement principle and measurement circuit are introduced in detail. Finally, joint angle measurement, movement law evaluation and object grasping experiments are performed to verify the validity of the designed finger. The experimental results show that the root-mean-square (RMS) of the DIP, PIP and MCP angle measurement errors are 0.36°, 0.59° and 0.32°, respectively. The designed finger is able to grasp objects with different shapes stably.

The spring-loaded inverted pendulum (SLIP) model is often used to describe the interaction between hindlimbs and the ground during the locomotion of animals or humans. This model is frequently adopted to qualitatively explain the flexible deformation of legs and feet and the trajectory change of center of mass (COM), caused by the impact between hindlimbs and the ground. However, such research cannot provide precise reference on the structural parameters, spring and damper selections and their collocations for the design of robotic legs and feet. In this study, an SLIP model was established on the multi-rigid-body dynamics software Adams. The main influence factors on the SLIP model were determined by targeting at the touchdown-phase duration of animal or human locomotion. Then the main factors were quantitatively studied by combining a multivariate orthogonal polynomial regression design. Simulation showed that spring stiffness coefficient (Z1), damping coefficient (Z2), swing angular velocity (Z3) and initial swing position (Z4) were the main factors affecting the trajectory of COM. Multivariate orthogonal polynomial regression analyses showed the relationship between the COM fluctuation (y) and the main factors satisfied the following equation: y = 217.33 - 16.25 Z1 + 0.3975 Z12 - 194.6 Z2 - 0.953 Z3 + 0.755 Z4 + 8.1 Z1 Z2 + 0.043 Z1 Z3 + 0.6 Z2 Z3 - 0.0055 Z3 Z4.

The comfort of a bus running on different road conditions is a matter of public concern. In this paper, the differential equations of motion are established for a bus running on different road conditions and the whole driving process is mechanically analyzed. Firstly, the bump degree at different positions is quantitatively analyzed and it is found that the rear row is bumpier on different roads. Then, the relationship between the speed of the bus and the vertical displacement and acceleration is quantitatively described. Regardless of the speed, a similar displacement and acceleration will be eventually achieved, but the speed is higher, and the duration of maximum displacement and acceleration is longer. When the speed is 8 m/s, resonance occurs on the bus during road condition II. Finally, the change in vertical displacement and acceleration under the action of different spring stiffness coefficient ratios of the front and rear wheels is quantitatively analyzed. High stiffness ratios mean less displacement and acceleration. By establishing an actual excitation road surface, the differential equations and analytical solutions in this paper can be used to roughly analyze the mechanical response of a traveling bus. These results can provide some guidance for the design and driving of buses.

Taking the rigid NACA0012 airfoil as the object, the key structural parameters of the spring–mass system that govern the dynamics of the double-elastic-constrained flapping hydrofoil are numerically studied in this paper. A two-dimensional numerical model, based on the CFD software FINE/Marine, is established to investigate the influence of the spring stiffness coefficient, frequency ratio, and damping coefficient on the motion and performance of the flapping hydrofoil. This study demonstrates that when the structural parameters are adequately adjusted, the power factor exceeding 1.0 has been achieved, and the corresponding efficiency is up to 37.8%. Moreover, this system can start and work within a wide range of damping coefficients. However, the hydraulic efficiency and power coefficient are sensitive to the change in damping coefficient, so it is very necessary to design an appropriate power output. Lastly, the most obvious parameter affecting the energy acquisition performance is the spring stiffness coefficients. Frequency ratios in the two directions have little influence on the peak value of the power coefficient, but they will cause the change of damping coefficients of the peak point. The key structural parameters studied in this paper provide a useful guideline for an optimized design of this interesting system through searching for the best performance.