The aim of this research was to design a physically consistent model for the forced torsional vibrations of automotive driveshafts that considered aspects of the following phenomena: excitation due to the transmission of the combustion engine through the gearbox, excitation due to the road geometry, the quasi-isometry of the automotive driveshaft, the effect of nonuniformity of the inertial moment with respect to the longitudinal axis of the tulip–tripod joint and of the bowl–balls–inner race joint, the torsional rigidity, and the torsional damping of each joint. To resolve the equations of motion describing the forced torsional nonlinear parametric vibrations of automotive driveshafts, a variational approach that involves Hamilton’s principle was used, which considers the isometric nonuniformity, where it is known that the joints of automotive driveshafts are quasi-isometric in terms of the twist angle, even if, in general, they are considered CVJs (constant velocity joints). This effect realizes the link between the terms for the torsional vibrations between the elements of the driveshaft: tripode–tulip, midshaft, and bowl–balls–inner race joint elements. The induced torsional loads (as gearbox torsional moments that enter the driveshaft through the tulip axis) can be of harmonic type, while the reactive torsional loads (as reactive torsional moments that enter the driveshaft through the bowl axis) are impulsive. These effects induce the resulting nonlinear dynamic behavior. Also considered was the effect of nonuniformity on the axial moment of inertia of the tripod–tulip element as well as on the axial moment of inertia of the bowl–balls–inner race joint element, that vary with the twist angle of each element. This effect induces parametric dynamic behavior. Moreover, the torsional rigidity was taken into consideration, as was the torsional damping for each joint of the driveshaft: tripod–joint and bowl–balls–inner race joint. This approach was used to obtain a system of equations of nonlinear partial derivatives that describes the torsional vibrations of the driveshaft as nonlinear parametric dynamic behavior. This model was used to compute variation in the natural frequencies of torsion in the global tulip (a given imposed geometry) using the angle between the tulip–midshaft for an automotive driveshaft designed for heavy-duty SUVs as well as the characteristic amplitude frequency in the region of principal parametric resonance together the method of harmonic balance for the steady-state forced torsional nonlinear vibration of the driveshaft. This model of dynamic behavior for the driveshaft can be used during the early stages of design as well in predicting the durability of automotive driveshafts. In addition, it is important that this model be added in the design algorithm for predicting the comfort elements of the automotive environment to adequately account for this kind of dynamic behavior that induces excitations in the car structure.

This paper presents an analysis of the CVJ (constant velocity joint) of automotive driveshafts from a point of view concerning the nonuniformity of isometric properties. In the automotive industry, driveshafts are considered to have constant velocity through its joints: free tripode joints and fixed ball joints, which has been proved by Mtzner’s indirect method and Orain’s direct method for tripod joint. Based on vectorial mechanics, the paper proved the quasi-isometry of velocity for polypod joints such as fixed ball joints. In the meantime, it was computed that the global nonuniformity of constant velocity joints for modern driveshafts based on the Dudita-Diaconescu homokinetic approach for the driveshafts. The nonuniformity of the velocity isometry of driveshafts was computed as a function of the input angular velocity of the driveshaft, angular inclination between the tripod–tulip axis and the midshaft axis and the angular inclination between the bowl axis and midshaft axis. The main aim of this article is how to improve the geometric and kinematic approach to add an important correction when designing the driveshaft dynamics prediction such as: forced torsional vibrations, forced bending–shearing vibrations, and coupled torsional–bending vibrations for the automotive driveshaft in the regions of specific resonances such as principal parametric resonance, internal resonance, combined resonance, and simultaneous resonances. By the way it is added, there are important corrections for the design of driveshafts, for the torsional dynamic behavior prediction, and for bending–shearing dynamic behavior of the driveshafts in the early stages of design. The results presented in the article represent a starting point for future research on dynamic phenomena in the area mentioned previously.

This paper presents a model for the acoustic emission of a circular plate, in the domain of large deflections. The thin circular plate is considered homogeneous, isotropic, and fixed on the boundaries. In the hypothesis of large displacements, the nonlinear von-Karman dynamic model was adopted. The external action is periodic and axisymmetric. An approximate analytical method was developed, based on the Kantorovich method and the asymptotic method, to compute the dynamic response of the plate. Starting from the characteristic parameters of the nonlinear vibrations of the plate, a model of acoustic emitter based on the Rayleigh formulation was developed, to obtain the acoustical pressure and the spatial directivity characteristic. Experimental tests were developed in an anechoic chamber, in order to confirm the model. The physical model of the plate consists of a circular frame having a high rigidity and a brass plate of 0.2-mm width. In the transverse direction, passing through the mass center of the plate, it acts as an excitatory device and the acoustic emission of the plate is analyzed. In this way, the natural frequencies of the plate and the spatial directivity characteristic have been determined and a satisfactory agreement with the theoretical results has been found.

The present work aims to design a robust method to detect and certify the deterministic chaos or ergodic process for the forced torsional vibrations (FTV) of a double tripod industrial driveshaft (DTID) in transition through the principal parametric resonance region (PPRR) which is considered by the researchers in the field as one of the most important resonance regions for the systems having parametric excitations. The DTID’s model for FTV considers the following effects: nonuniformities of inertial characteristics of the DTID’s elements, the harmonic torque excitation induced by the asynchronous electrical motor used for a heavy-duty grain mill, and the harmonic reaction torque generated by different granulation of the substance needed to be milled. Based on these aspects, a model of the FTV for the DTID was designed which was a modified, physically consistent model already used by the authors to investigate the FTV of automotive driveshafts (homokinetic transmission). For the DTID elements, the dynamic instability for nonstationary FTV in the PPRR using time–history analysis (THA) was analyzed—THA represents the phase portraits. Time–history analysis is a detection method for possible chaotic dynamic behavior for the nonstationary FTV (NFTV) in transition through PPRR. If this dynamic behavior was seen, a new robust method LEA–PM was created to certify and confirm the deterministic chaos for the NFTV of DTID. The new method, LEA–PM, is composed of the Lyapunov exponent’s approach (LEA) coupled with the Poincaré Map (PM) applied to the global system of differential equations that describe the FTV of DTID in the PPRR. This new robust method, which embeds LEA and PM, LEA–PM, establishes if the mechanical system has a deterministic chaotic dynamic behavior (strange attractor) or an ergodic dynamic process in this resonant region. LEA represents a new method that includes not only the maximal Lyapunov exponent method (MLEM) but also new mathematical criteria that is “the sum of all Lyapunov exponents has to be negative” which, coupled with MLEM, indicates the presence of deterministic chaos (strange attractors). THA–LEA–PM had been used for the NFTV of DTID computing the phase portraits, the Lyapunov exponents, and representing the Poincaré Maps of the NFTV for the DTID’s elements in transition through PPRR, founding deterministic chaos or ergodic dynamic behavior. Based on the obtained results, numerical simulations revealed the pitting manifestations of the DTID’s elements, typical for the geared systems transmission, mentioned recently in experimental data research for the homokinetic transmissions. Using the new robust method, THA–LEA–PM (time–history analysis coupled with LEA–PM) can be used in future research for chaotic dynamic analysis of DTID’s NFTV transition through superharmonic resonances, subharmonic resonances, combination resonances, and internal resonances. Time–history analysis as a detection method for chaos and LEA–PM as a certifying method for deterministic chaos can be integrated as a design tool for DTID’s FTV control of the homokinetic transmission.

In addition to elastomeric devices, viscous fluid dampers can reduce the vibration transmitted to dynamic systems. Usually, these fluid dampers are rate-independent and used in conjunction with elastomeric isolators to insulate the base of buildings (buildings, bridges, etc.) to reduce the shocks caused by earthquakes by increasing the damping capability. According to the EN 15129 standard, the velocity-dependent anti-seismic devices are Fluid Viscous Dampers (FVDs) and Fluid Spring Dampers (FSDs). Based on experimental data from a dynamic regime of a fluid viscous damper of small dimensions, for which not all the design details are known, to determine the law of behavior for the viscous damper, the characteristics of the damper are identified, including the nonlinear parameter α (exponent of velocity V) of the constitutive law. Note that the magnitude of the fluid damper force depends on both velocity (where the maximum value is 0.52 m/s) and amplitude displacement (±25 mm). Using the Kelvin–Voigt rheological models, the dynamic response of a structure fixed with a fluid viscous device is analyzed, presenting the reaction force and displacement during the parameterized application of an external shock. This new approach for FVDs/FSDs was validated using the standard deviation between the experimental data and the numerical results of the extended Kelvin–Voigt model offering researchers in the field of seismic devices a reliable method to obtain a constitutive law for such devices.