In this work, a methodology is proposed for formulating general dynamical equations in mechanics under the umbrella of the principle of energy conservation. It is shown that Lagrange’s equation, Hamilton’s canonical equations, and Hamilton-Jacobi’s equation are all formulated based on the principle of energy conservation with a simple energy conservation equation, i.e., the rate of kinetic and potential energy with time is equal to the rate of work with time done by external forces; while D’Alembert’s principle is a special case of the law of the conservation of energy, with either the virtual displacements (‘frozen’ time) or the virtual displacement (‘frozen’ generalized coordinates). It is argued that all of the formulations for characterizing the dynamical behaviors of a system can be derived from the principle of energy conservation, and the principle of energy conservation is an underlying guide for constructing mechanics in a broad sense. The proposed methodology provides an efficient way to tackle the dynamical problems in general mechanics, including dissipation continuum systems, especially for those with multi-physical field interactions and couplings. It is pointed out that, on the contrary to the classical analytical mechanics, especially to existing Hamiltonian mechanics, the physics essences of Hamilton’s variational principle, Lagrange’s equation, and the Newtonian second law of motion, including their derivatives such as momentum and angular momentum conservations, are the consequences of the law of conservation of energy. In addition, our proposed methodology is easier to understand with clear physical meanings and can be used for explaining the existing mechanical principles or theorems. Finally, as an application example, the methodology is applied in fluid mechanics to derive Cauchy’s first law of motion.

Acoustic transducer, which is a core component of acoustic logging tool, determines the development of acoustic logging technology. In order to realize the goal of dipole acoustic logging transducer with the features of low frequency, broadband and high radiation power, a cylindrical oscillating dipole acoustic transducer using an actuator of a group of different trilaminar piezoelectric bending bars is designed and studied. Modal and harmonic response analyses of the whole transducer are conducted by using the finite element method, including analyses of input conductance of transducer in air and water, transmitting voltage response and directivity patterns. Besides, the proposed transducer is fabricated and tested to compare with numerical simulation results. Moreover, the numerical results of the proposed transducer are compared with that of traditional dipole transducer. The comparison result indicates the proposed dipole transducer is characterized by low frequency, broadband, and high radiation power, which is feasible in the application of dipole acoustic logging.

In this article, a novel design of a piezoelectric dipole transducer is proposed for formation acoustic velocity measurement in the vicinity of a borehole with a frequency range of 0.4–6 kHz. The transducer which actuates a cylindrical shell to generate a pure dipole mode wave by using multiple piezoelectric bender bars is analyzed theoretically and simulated numerically by using the finite element method (FEM). Moreover, the transducer is fabricated and tested to compare with the numerical simulation results, which shows that the test and simulation results are in good agreement. Finally, compared with numerical simulation results of the traditional dipole transducer, it is shown that the proposed dipole transducer has higher transmitting sensitivities than commonly used ones, especially in low frequency responses. This work lays a foundation for the new development of the transducer in borehole dipole acoustic shear wave measurements. Especially, in a slow formation where the shear wave velocity is lower than that of compressional wave in the borehole fluid, the transducer could be used for highly efficient shear wave velocity measurements.

The use of tuning forks to measure fluid density and viscosity is widely employed in fields such as food, medicine, textiles, automobiles, petrochemicals, and deep drilling. The explicit analytical model based on the Euler–Bernoulli cantilever-beam theory for the relationship between tuning-fork resonance characteristics and the density and viscosity of fluid is only applicable to the situation where the fluid viscous effect is very small. In this paper, the finite element method is used to simulate the influence of large variations in fluid density and viscosity on the resonance characteristic parameters (resonant frequency and quality factor) of the tuning fork. The numerical simulation results are compared with the analytical analysis results and experimental measurement results. Then, the sensitivity of tuning-fork resonance characteristic parameters to fluid density and viscosity is studied. The results show that compared with the analytical results, the numerical simulation results have a higher degree of agreement with the experimental measurement results. The relative difference in resonant frequency is less than 2%, and the relative difference in quality factor is less than 4%. This indicates that the finite element method includes the influence of fluid viscosity on tuning-fork resonance parameters, which is more in line with the actual conditions than the analytical model. Simulating and analyzing the sensitivity of the tuning fork to fluid density and viscosity by the finite element method, it is possible to consider the situation where fluid density and viscosity vary over a large range. Compared with experimental measurements, this method has higher efficiency and can significantly save time and economic costs. This study can overcome the limitation of existing explicit analytical models, which are only applicable when the viscous effects of the fluid are very small. It enables a more accurate simulation of the coupling vibration between tuning forks and fluids, thereby providing theoretical references for further optimizing tuning-fork structural parameters to enhance the accuracy of measuring fluid characteristic parameters.

In this study, we propose a fast calculation method that utilizes Kirchhoff’s hypotheses and electroelasticity theory to derive the resonant frequency, antiresonant frequency, and effective electromechanical coupling coefficient of a trilaminar bending ring transducer with unequal diameters. The accuracy of the theoretical method is validated through finite element analysis (FEM) and experimental tests. Furthermore, we perform optimization of the effective electromechanical coupling coefficient of the first-order bending vibration of the trilaminar bending ring transducer. Our optimization results indicate that, under the free inner and fixed outer boundary conditions, the effective electromechanical coupling coefficient initially increases to a maximum value and then rapidly decreases as r₁/r₂ increases. This behavior can be attributed to the out-of-phase vibrations and the in-phase electric field excitation on both sides of the bending ring vibration nodal circle. Finally, we present the optimized size configuration required to achieve the maximum effective electromechanical coupling coefficient. This study provides theoretical guidance for the design and optimization of trilaminar bending ring transducers with unequal diameters and has the potential to significantly advance the field of crosswell seismic source technology.