This study focuses on the investigation of intelligent form-finding and vibration analysis of a triangular polyhedral tensegrity that is enclosed within a sphere and subjected to external loads. The nonlinear dynamic equations of the system are derived using the Lagrangian approach and the finite element method. The proposed form-finding approach, which is based on a basic genetic algorithm, can determine regular or irregular tensegrity shapes without dimensional constraints. Stable tensegrity structures are generated from random configurations and based on defined constraints (nodes located on the sphere, parallelism, and area of upper and lower surfaces), and shape finding is performed using the fitness function of the genetic algorithm and multi-objective optimization goals. The genetic algorithm's efficacy in determining the shape of structures with unpredictable configurations is evaluated in two distinct scenarios: one involving a known connection matrix and the other involving fixed or random member positions (struts and cables). The shapes obtained from the algorithm suggested in this study are validated using the force density approach, and their vibration characteristics are examined. The findings of the comparative study demonstrate the efficacy of the proposed methodology in determining the vibrational behavior of tensegrity structures through the utilization of intelligent shape seeking techniques.

The free undamped vibration analysis of a shell of general shape is formulated with a degenerated curved lagrangian finite element, without neglecting shear deformations and z/R with consistent mass matrix. The shell element with nine nodes and 45 degree of freedoms (three transverse and two rotations) is applicable for both thin and thick shell analysis. The accuracy and efficiency of this proposed finite element are illustrated by examples and the results are compared with those obtained by other analytical and numerical methods. The comparisons show that the method yields very good results with a relatively small number of elements.

This paper presents the Fourier and wavelet characterization of vibration problem. To determine the natural frequencies, modal damping and mass participation factors of bars, a rod element is established by means of isogeometric formulation. The non-uniform rational Bezier splines (NURBS) is presented to characterize the geometry and the deformation field in isogeometric analysis (IGA). Non-proportional damping has been used to measure the real-state energy dissipation in vibration. Therefore, the stiffness, damping and mass matrices are derived by the NURBS basis functions. The efficiency and accuracy of the present isogeometric analysis is demonstrated by using classical finite element method (FEM) models and closed-form analytical solutions. The frequency content, modal excitation energy and damping are measured as basis values. Results show that the present isogeometric formulation can determine the modal frequencies and inherent damping in an accurate way. Damping as an inherent characteristics of viscoelastic materials is treated in a realistic way in IGA method using non-proportional form. Based on results, k-refinement technique has enhanced the accuracy convergence with respect to other refinement methods. In addition, the half-power bandwidth method gives modal damping for the IGA solution with appropriate accuracy with respect to FEM. Accuracy difference between quadratic and cubic NURBS is significant in IGA h-refinement.

In marine engineering, ship vibration analysis is crucial for ensuring structural integrity, operational safety, and environmental sustainability. Traditional analysis, following classical paradigms established by early contributors such as Todd, Kumai, and Schlick, relies primarily on costly simulations and empirical tests. This study seeks to overcome these limitations by integrating machine learning (ML) methodologies with semi-empirical models to develop a predictive hybrid model, thereby advancing vibration analysis toward a data-driven paradigm. The research is significant for improving ship design, mitigating vibration-related risks, and reducing reliance on resource-intensive approaches, aligning with global efforts to promote energy-efficient and sustainable maritime operations. The proposed hybrid model combines Random Forest (RF) and Logistic Regression (LR), leveraging RF’s capacity for modeling nonlinear relationships and LR’s interpretability for linear adjustments. Trained on Kumai’s seminal dataset and validated on 373 cases spanning 34 ship types, the model accurately predicts critical parameters (α, τ₂, N₂, N₃, and c̄) with exceptional precision. Performance metrics demonstrate strong results, including near-perfect R² values (0.9938 for α) and minimal MSE (0.0000 for α, 0.0701 for N₃). Natural frequency predictions exhibit less than 3% error, as validated against empirical data for crude oil tankers. Feature importance analysis identifies structural parameters (length, displacement, block coefficient) as key predictors, enhancing interpretability for engineering applications. This work bridges the gap between classical vibration theory and modern ML, offering a cost-effective, scalable alternative to conventional simulations. By enabling precise vibration predictions across diverse vessels, the model facilitates predictive maintenance, design optimization, and operational safety. The findings highlight the transformative potential of hybrid ML in maritime engineering, paving the way for digital twins and sustainability-driven ship design.

This study based on free vibration analysis and study the behavior of framed structure under different frequency of vibration using ANSYS software and shaking table. A small scale uni-axial shaking table was prepared in laboratory, which can produce lower to moderate vibration, regarding frequency and velocity. Moment resisting framed structures constructed with connecting beam and column elements of mild steel wire of different dimensions were tested in shaking table and analyzed using ANSYS software. The effect of masses and stiffness of structures on its natural frequency and deflection under certain ground vibration also studied and discussed. The test results showed that, this shaking table is satisfying the general concept of free vibration. The height of structures has an inverse effect on its natural frequency for same lateral stiffness. After several shaking, structure’ s natural frequency started to decreases with their decreasing stiffness. Therefore, the fabricated shaking table can used in free vibration analysis.

Perforated discs have many applications in different parts of industry. By making such disks of functionally graded materials, more capabilities can be obtained from them. Vibration analysis of these kinds of disks can help us make them more efficient. In this paper, modeling and evaluation of disk vibration of functionally graded materials with regard to thickness were carried out using Abaqus software. Since no certain element has been defined regarding functionally graded materials for the design and analysis of a particular element in Abaqus software, molding of such materials has been used in this application. In order to verify the results, the results obtained from ABAQUS analysis have been compared with those available in the literature. The obtained results show that by defining more layers with regard to changes in properties, the obtained results approach the exact solutions.

Transverse vibration of the serpentine belt is effective at noise and durability of it. Therefore, understanding of this phenomenon and studying effective parameters can be used in the process of reducing belt noise and increasing life time. In this paper, transverse vibration of serpentine belt is measured experimentally and analyzed. In the implementation test steps, the displacement of the belt in two positions has been measured. Then, the time signals were transformed to frequency domain. It is derived and observed that the belt vibration is synchronous with engine speed, accordingly order analysis is selected to analysis the vibration signal. Results show that the natural frequency of serpentine belt in the region between A/C compressor and crankshaft pulley changes due to A/C compressor loading, but this parameter is not affected by engine load variations. In the area between automatic tensioner and idler, natural frequency is constant regardless of A/C compressor on-off condition and engine load changing. In all engine rotating speeds, the dominant frequencies are highly closed to the natural frequencies. In some engine speeds, vibration amplitude is high and the frequency of these points are proportionally equal to 2, 3, 4 and other orders of engine speed.

In this article, an attempt has been made to estimate the amount of sound transmission loss in a flat oval channel by applying the approach of statistical energy analysis. Correct estimation of sound transmission loss in an air conditioning channel is of great importance due to the harmful effects of noise pollution in the environment on human health. Simulation with the statistical energy analysis method is a powerful approach to estimate sound and vibration in problems in which we deal with complex and multi-part systems; is considered. In this method, first, a system is divided into several subsystems, and then by writing a matrix equation that includes the energy exchanges between subsystems and energy loss coefficients; It is investigated from the perspective of vibration and sound estimation.On average, the model presented in this research is able to estimate the sound transmission loss in different dimensions of the air conditioning channels according to the experimental results in the accuracy range of ± 2.5 dB. Considering that it seems that the results obtained from modeling with this method are in good agreement with the experimental data; The results of this research can be used as an efficient approach to estimate noise in oval shaped channels stretched in different lengths.