A thermodynamic approach to mechanical motion is presented, and it is shown that dissipation of energy is the key process through which mechanical motion becomes observable. By studying charged particles moving in conservative central force fields, i...
This article presents alternative Hamiltonian and Lagrangian formalisms for relativistic mechanics using proper time and proper Lagrangian coordinates in 1 + 1 dimensions as parameters of evolution. The Lagrangian and Hamiltonian formalisms for a hyp...
All electromagnetic potentials and space–time metrics of Stäckel spaces of type (2.0) in which the Hamilton–Jacobi equation for a charged test particle can be integrated by the method of complete separation of variables are found. Complete sets of mo...
The common geometrical (symplectic) structures of classical mechanics, quantum mechanics, and classical thermodynamics are unveiled with three pictures. These cardinal theories, mainly at the non-relativistic approximation, are the cornerstones for s...
We show that the classical Hamilton equations of motion can be derived from the energy conservation condition. A similar argument is shown to carry to the quantum formulation of Hamiltonian dynamics. Hence, showing a striking similarity between the q...
Hamiltonian variational principles have provided, since the 1960s, the means of developing very successful wave theories for nonlinear free-surface flows, under the assumption of irrotationality. This success, in conjunction with the recognition that...
In classical mechanics, determining the governing equations of motion using finite element analysis (FEA) of an elastic multibody system (MBS) leads to a system of second order differential equations. To integrate this, it must be transformed into a...
This work aims at investigating the free torsional vibration of one-directional nanostructures with an elliptical shape, under different boundary conditions. The equation of motion is derived from Hamilton’s principle, where Eringen’s non...
The necessary and sufficient conditions of the validity of Hamilton’s variational principle for circuits consisting of (α,β) elements from Chua’s periodical table are derived. It is shown that the principle holds if and only if...
In this paper, vibration of axially moving nanobeams is studied using Eringen’s two-phase nonlocal integral model. Geometric nonlinearity is taken into account for the integral model for the first time. Equations of motion for the beam with sim...
The natural vibration behavior of axially functionally graded (AFG) double nanobeams is studied based on the Euler–Bernoulli beam and Eringen’s non-local elasticity theory. The double nanobeams are continuously connected by a layer of lin...
The vibration characteristics of a nonuniform, flexible and free-flying slender rocket experiencing constant thrust is investigated. The rocket is idealized as a classic nonuniform beam with a constant one-dimensional follower force and with free-fre...
A self-sensing and self-actuating quartz tuning fork (QTF) can be used to obtain its frequency shift as function of the tip-sample distance. Once the function of the frequency shift versus force gradient is acquired, the combination of these two func...
This paper presents a free vibration analysis of functionally graded (FG) polymer composite curved nanobeams reinforced with graphene nanoplatelets resting on a Pasternak foundation. The size-dependent governing equations of motion are derived by app...
This paper presents the main analytical methods, in the context of current developments in the study of complex multibody systems, to obtain evolution equations for a multibody system with deformable elements. The method used for analysis is the fini...
In this paper, a seven-parameter spectral/hp finite element model to obtain natural frequencies in shell type structures is presented. This model accounts for constant and variable thickness of shell structures. The finite element model is based on a...
The purpose of this paper is to study the axisymmetric vibrations of circular three-layered sandwich plates with a frequency-dependent fractional viscoelastic core and elastic face sheets. First, the equations of motion and related boundary condition...
In this study, the non-local Euler-Bernoulli beam theory was employed in the nonlinear free and forced vibration analysis of a nanobeam resting on an elastic foundation of the Pasternak type. The analysis considered the effects of the small-scale of...
This paper presents the dynamic model of a flexible-link, flexible-joint manipulator system with a considerable stiffening effect of the flexible link. A gripper, along with tip mass, is attached at one end of the flexible link. By employing the exte...
This study investigates the combined resonance phenomenon in magneto-electro-elastic (MEE) cylindrical shells under longitudinal and lateral excitations with thermal factors, addressing the complex interaction between mechanical, electrical, and magn...
In this study, the buckling of functionally graded (FG) nanoporous metal foam nanoplates is investigated by combining the refined plate theory with the non-local elasticity theory. The refined plate theory takes into account transverse shear strains...
This paper focuses on the geometrically nonlinear dynamic analyses of a three-layered curved sandwich beam with isotropic face layers and a time-dependent viscoelastic core. The boundary conditions and equations of motion governing the forced vibrati...
Based on the differential quadrature procedure (DQP), the vibrational response of functionally graded (FG) sandwich annular plates enhanced with graphene platelets (GPLs) and with an FG porous core is illustrated in this paper. The current annular pl...
In this present paper, the dynamic stiffness method (DSM) was formulated to investigate the out-of-plane natural vibration of a thin orthotropic plate using the classical plate theory (CPT). Hamilton’s principle was implemented to derive the go...
This contribution presents a finite element shell model capable of performing linear vibration analyses of shell-type structures made of functionally graded material (FGM). The model is based on the seven-parameter spectral/hp finite element formulat...
An efficient isogeometric analysis method (IGA) based on a simple first-order shear deformation theory is presented to study free vibration, static bending response, dynamic response, and active control of functionally graded plates (FGPs) integrated...
The following paper talks about the dynamic modeling and control of robot manipulators using Hamilton’s equations in the screw theory framework. The difference between the proposed work with diverse methods in the literature is the ease of obta...
In this work, we design a control strategy to be applied in a port-Hamilton representation of a liquid-mirror telescope for an alt-azimuth configuration. Starting from a dynamical model for an alt-azimuth liquid-mirror telescope based on Lagrange mec...
Dynamic post-buckling behavior of microscale cylindrical shells reinforced with functionally graded carbon nanotubes (FG-CNTs) and conveying microfluid is discussed for the first time. The microshell is embedded in a Kerr foundation and subjected to...
The dynamic stiffness method is developed to analyze the natural vibration characteristics of functionally graded beams, where material properties change continuously across the beam thickness following a symmetric law distribution. The governing equ...
This paper presents a new four-variable refined plate theory for free vibration analysis of laminated piezoelectric functionally graded carbon nanotube-reinforced composite plates (PFG-CNTRC). The present theory includes a parabolic distribution of t...
This study presents a hyperbolic shear deformation theory for free vibration of functionally graded plates on elastic foundations. The field of displacements is chosen based on the assumptions that axial and transverse displacements consist of compon...
The submerged floating tunnel is a marine transportation infrastructure that links two shorelines. The tunnel tube body’s buoyancy exceeds gravity, with anchoring ensuring equilibrium. Anchoring reliability is crucial. This study presents a thr...
The nonlinear behaviors and energy harvesting of an unsymmetric cross-ply square composite laminated plate with a piezoelectric patch is presented. The unsymmetric cross-ply square composite laminated plate has two stable equilibrium positions by app...
This manuscript develops for the first time a mathematical formulation of the dynamical behavior of bi-directional functionally graded porous plates (BDFGPP) resting on a Winkler–Pasternak foundation using unified higher-order plate theories (U...
In this paper, wave propagation in multi-scale hybrid glass fiber (GF)/carbon nanotube (CNT)/polymer nanocomposite plates is studied for the first time by means of refined higher-order plate theory. The hybrid nanocomposite consists of CNTs and glass...
In this work, an analytical solution for the natural frequencies of elastically supported stepped beams with rigid segments is presented. The elastic end boundary conditions are modeled with a translational stiffness element, a rotational stiffness e...
This research investigates the stabilization and control of an uncertain Euler–Bernoulli nano-beam with fixed ends. The governing partial differential equations of motion for the nano-beam are derived using Hamilton’s principle and the no...
A vibration analysis of a flexible follower in an oscillating follower cam system undergoing a rise-dwell-fall-dwell (RDFD) motion is performed. Owing to the time-dependent boundary effect caused by considering simultaneously the axial and the latera...
This study presents a closed-form solution for the dynamic response of a sandwich beam subjected to arbitrary impact loading, with a particular focus on energy harvesting from an attached piezoelectric layer. A thin piezoelectric patch is bonded to t...
In this paper, transverse vibration analysis of rotating micro-beam is investigated based on the modified couple stress theory. The simply-supported micro-beam is modeled utilizing Euler-Bernoulli and Timoshenko beam theories. The system is rotating...
This paper studies wave propagation in a new structure composed of three layers. The upper and lower layers are made of a piezoelectromagnetic material reinforced with graphene platelets (GPLs) that may be uniformly disseminated or continuously varie...
The nonlinear steady state large amplitude forced vibration response of a laminated composite annular sector plate is presented. The nonlinear governing equation of motion of the laminated composite annular sector plate has been obtained using kinema...
The stability of a nonlinear aero-thermo-elastic panel in supersonic flow is analyzed numerically. In light of Hamilton’s principle, the governing equation of motion for a two-dimensional aero-thermo-elastic panel is established taking geometri...
This paper presents an analytical investigation on the forced vibration characteristics of a rotating functionally graded material (FGM) blade subjected to rub-impact and base excitation. Based on the Kirchhoff plate theory, the rotating blade is mod...
This study investigates the sensitivity of dynamic properties in coupled curved beams reinforced with carbon nanotubes (CNTs) to thermal variations. Temperature-dependent (TD) mechanical properties are considered for poly methyl methacrylate (PMMA) t...
This research’s goal is to model and analyze the forced bending vibrating (FBV) movements for the elements of an automotive driveshaft using a perturbation technique, the asymptotic method approach (AMA), in the region of principal parametric r...
This paper studied the nonlinear vibrations of top-tensioned cantilevered pipes conveying pressurized steady two-phase flow under thermal loading. The coupled axial and transverse governing partial differential equations of motion of the system were...
This article presents a mathematical continuum model to analyze the free vibration response of cross-ply carbon-nanotube-reinforced composite laminated nanoplates and nanoshells, including microstructure and length scale effects. Different shell geom...
A nonlinear finite element model for circular and annular micro-plates under thermal and mechanical loading was developed using a third-order shear deformation theory. In the kinematic assumptions, a change in plate thickness is allowed, and no trans...
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