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Large deployable mesh reflectors play a critical role in satellite communications, Earth observation, and deep-space exploration, offering high-gain antenna performance through precisely shaped reflective surfaces. Traditional dynamic modeling approaches—such as wave-based and finite element methods—often struggle to accurately capture the complex behavior of three-dimensional reflectors due to oversimplifications of cable members. To address these challenges, this paper proposes a novel spatial discretization framework that systematically decomposes cable member displacements into boundary-induced and internal components in a global Cartesian coordinate system. The framework derives a system of ordinary differential equations for each cable member by enforcing the Lagrange’s equations, capturing both longitudinal and transverse internal displacement of the cable member. Numerical simulations of a two-dimensional cable-network structure and a center-feed parabolic deployable mesh reflector with 101 nodes illustrate the improved accuracy of the proposed method in predicting vibration characteristics across a broad frequency range. Compared to standard finite element analysis, the proposed method more effectively identifies both low- and high-frequency modes and offers robust convergence and accurate prediction for both frequency and transient responses of the structure. This enhanced predictive capability underscores the significance of incorporating internal cable member displacements for reliable dynamic modeling of large deployable mesh reflectors, ultimately informing better design, control, and on-orbit performance of future space-based reflector systems. 

Tip relief is a critical design feature of modern spur gears, aimed at improving dynamic performance through a typical design strategy involving peak-to-peak minimization of mesh excitations. However, due to the hyperstatic nature of simultaneous tooth engagements, the applied torque not only affects mesh deformation amplitudes as normally considered but also alters mesh excitation waveforms, leaving great challenges for the typical design to meet various operating conditions. This paper develops an analytical framework to reshape mesh excitation waveforms, aimed at flexibly reducing vibration intensities across different operating loads and speeds. The load-dependency of excitation harmonics with tip relief is efficiently characterized by an improved analytical mesh excitation model. A tip relief design method is proposed, which automatically recombines harmonic contents of mesh excitations to adapt target operating speeds. Comparisons with finite element models and experiments confirmed the accuracies of quasi-static and dynamic analyses. Parametric studies and application examples further demonstrate the acceptable feasibility and effectiveness of the present method. 

Considering the elasticity of gear solid bodies, the load applied to gear teeth will force theoretically separated gear teeth to get into engaging state in advance. This phenomenon is named as the extended tooth contact (ETC). Effects of the ETC directly influence the time-varying mesh stiffness of gear pairs and subsequently alter nonlinear dynamic characteristics of gear transmission systems. Time-vary mesh stiffness, considering effects of the ETC, is thus introduced into the dynamic model of the gear transmission system. Periodic motions of a gear transmission system are discussed in detail in this work. The analytical model of time-varying mesh stiffness with effects of the ETC is proposed, and the effectiveness of the analytical model is demonstrated in comparison with finite element (FE) results. The gear transmission system is simplified as a single degree-of-freedom (DOF) model system by employing the lumped mass method. The correctness of the dynamic model is verified in comparison with experimental results. An incremental harmonic balance (IHB) method is modified to obtain periodic responses of the gear transmission system. The improved Floquet theory is employed to determine the stability and bifurcation of the periodic responses of the gear transmission system. Some interesting phenomena exist in the periodic responses consisting of “softening-spring” behaviors, jump phenomena, primary resonances (PRs), and super-harmonic resonances (SP-HRs), and saddle-node bifurcations are observed. Especially, effects of loads on unstable regions, amplitudes, and positions of bifurcation points of frequency response curves are revealed. Analytical results obtained by the IHB method match very well with those from numerical integration. 

Abstract A modified incremental harmonic balance (IHB) method is used to determine periodic solutions of wave propagation in discrete, strongly nonlinear, periodic structures, and solutions are found to be in a two-dimensional hyperplane. A novel method based on the Hill’s method is developed to analyze stability and bifurcations of periodic solutions. A simplified model of wave propagation in a strongly nonlinear monatomic chain is examined in detail. The study reveals the amplitude-dependent property of nonlinear wave propagation in the structure and relationships among the frequency, the amplitude, the propagation constant, and the nonlinear stiffness. Numerous bifurcations are identified for the strongly nonlinear chain. Attenuation zones for wave propagation that are determined using an analysis of results from the modified IHB method and directly using the modified IHB method are in excellent agreement. Two frequency formulae for weakly and strongly nonlinear monatomic chains are obtained by a fitting method for results from the modified IHB method, and the one for a weakly nonlinear monatomic chain is consistent with the result from a perturbation method in the literature. 

Abstract Tensegrity structures become important components of various engineering structures due to their high stiffness, light weight, and deployable capability. Existing studies on their dynamic analyses mainly focus on responses of their nodal points while overlook deformations of their cable and strut members. This study proposes a non-contact approach for experimental modal analysis of a tensegrity structure to identify its three-dimensional (3D) natural frequencies and full-field mode shapes, which include modes with deformations of its cable and strut members. A 3D scanning laser Doppler vibrometer is used with a mirror for extending its field of view to measure full-field vibration of a novel three-strut metal tensegrity column with free boundaries. Tensions and axial stiffnesses of its cable members are determined using natural frequencies of their transverse and longitudinal modes, respectively, to build its theoretical model for dynamic analysis and model validation purposes. Modal assurance criterion (MAC) values between experimental and theoretical mode shapes are used to identify their paired modes. Modal parameters of the first 15 elastic modes of the tensegrity column identified from the experiment, including those of the overall structure and its cable members, can be classified into five mode groups depending on their types. Modes paired between experimental and theoretical results have MAC values larger than 78%. Differences between natural frequencies of paired modes of the tensegrity column are less than 15%. The proposed non-contact 3D vibration measurement approach allows accurate estimation of 3D full-field modal parameters of the tensegrity column. 

Pipe-type cable systems, including high-pressure fluid-filled (HPFF) and high-pressure gas-filled cables, are widely used for underground high-voltage transmission. These systems consist of insulated conductor cables within steel pipes, filled with pressurized fluids or gases for insulation and cooling. Despite their reliability, faults can occur due to insulation degradation, thermal expansion, and environmental factors. As many circuits exceed their 40-year design life, efficient fault localization becomes crucial. Fault location involves prelocation and pinpointing. Therefore, a novel pinpointing approach for pipe-type cable systems is proposed, utilizing accelerometers mounted on a steel pipe to capture fault-induced acoustic signals and employing the time difference of arrival method to accurately pinpoint the location of the fault. The experimental investigations utilized a scaled-down HPFF pipe-type cable system setup, featuring a carbon steel pipe, high-frequency accelerometers, and both mechanical and capacitive discharge methods for generating acoustic pulses. The tests evaluated the propagation velocity, attenuation, and pinpointing accuracy with the pipe in various embedment conditions. The experimental results demonstrated accurate fault pinpointing in the centimeter range, even when the pipe was fully embedded, with the acoustic pulse velocities aligning closely with the theoretical values. These experimental investigation findings highlight the potential of this novel acoustic pinpointing technique to improve fault localization in underground systems, enhance grid reliability, and reduce outage duration. Further research is recommended to validate this approach in full-scale systems. 

Abstract Tensegrity structures have emerged as important components of various engineering structures due to their high stiffness, light weight, and deployable capability. Existing studies on dynamic analyses of tensegrity structures mainly focus on responses of their nodal points while overlook deformations of their cable and strut members. This study aims to propose a non-contact approach for experimental modal analysis of a tensegrity structure to identify its three-dimensional (3D) natural frequencies and full-field mode shapes, which include modes with deformations of its cable and strut members. A 3D scanning laser Doppler vibrometer (SLDV) is used with a mirror for extending its field of view to measure full-field vibration of a three-strut tensegrity column with free boundaries. Tensions and axial stiffnesses of cable members of the tensegrity column are determined using natural frequencies of their transverse and longitudinal modes, respectively, and used to build a numerical model of the tensegrity column for dynamic analysis and model validation purposes. Modal assurance criterion (MAC) values between experimental and numerical mode shapes are used to identify their paired modes. Natural frequencies and mode shapes of the first 15 elastic modes of the tensegrity column are identified from the experiment, which include modes of the overall structure and its cable members. These identified modes can be classified into five mode groups depending on their types. Five modes are paired between experimental and numerical results with MAC values larger than 78%. Differences between natural frequencies of paired modes of the tensegrity column are less than 15%. The non-contact 3D vibration measurement approach presented in this work can measure responses of nodal points, as well as deformations of cable and strut members, of the tensegrity column, and allows accurate estimation of its 3D full-field modal parameters.