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In this paper we discuss some general properties of viscoelastic models defined in terms of constitutive equations involving infinitely many derivatives (of integer and fractional order). In particular, we consider as a working example the…
Mechanical interactions between rigid rings and flexible cables find broad application in both daily life (hanging clothes) and engineering systems (closing a tether-net). A reduced-order method for the dynamic analysis of sliding rings on…
In this article, we study the free vibration and the mechanical buckling of plates using a three dimensional consistent approach based on the scaled boundary finite element method. The in-plane dimensions of the plate are modeled by…
Perturbative construction of the nonequilibrium steady state of a rotator under a stochastic forcing while subject to torque and friction
The laws of friction are reasonably well understood for the case of blocks in contact with rough plane surfaces. However, as far as bodies with circular sections are concerned, the physics of friction becomes more involving and it is not…
This paper studies the discretization of a homogenization and dimension reduction model for the elastic deformation of microstructured thin plates proposed by Hornung, Neukamm, and Vel\v{c}i\'c in 2014. Thereby, a nonlinear bending energy…
The robust statistical description of dynamical systems under perturbations is a central problem in ergodic theory. In this paper, we investigate the statistical properties of skew-product maps driven by a subshift of finite type with…
This work investigates the dynamics of closed quantum systems in the Bloch vector representation using methods from rigid body dynamics and the theory of integrable systems. To this end, equations of motion for Bloch components are derived…
The fundamental equation describing the rotational dynamics of a rigid body is ${\vec \tau}=d{\vec L} / dt$ which is a straightforward consequence of the Newton's second law of motion and is only valid in an inertial coordinate system.…
A rectangular plate modeling the deck of a suspension bridge is considered. The plate may widely oscillate, which suggests to consider models from nonlinear elasticity. The von K\'arm\'an plate model is studied, complemented with the action…
The purpose of this paper is to present a new mathematical model for the dynamics of thin Cosserat elastic plates. Our approach, which is based on a generalization of the classical Reissner-Mindlin plate theory, takes into account the…
The ability to create dynamic deformations of micron-sized structures is relevant to a wide variety of applications such as adaptable optics, soft robotics, and reconfigurable microfluidic devices. In this work we examine non-uniform…
We develop a reduced model for hard-magnetic, thin, linear-elastic shells that can be actuated through an external magnetic field, with geometrically exact strain measures. Assuming a reduced kinematics based on the Kirchhoff-Love…
A high fidelity model is developed for an elastic string pendulum, one end of which is attached to a rigid body while the other end is attached to an inertially fixed reel mechanism which allows the unstretched length of the string to be…
This paper is devoted to the controllability analysis of a class of linear control systems in a Hilbert space. It is proposed to use the minimum energy controls of a reduced lumped parameter system for solving the infinite dimensional…
In this paper is discussed a class of static spherically symmetric solutions of the general relativistic elasticity equations. The main point of discussion is the comparison of two matter models given in terms of their stored energy…
In analogy with conventional quantum mechanics, non-commutative quantum mechanics is formulated as a quantum system on the Hilbert space of Hilbert-Schmidt operators acting on non-commutative configuration space. It is argued that the…
We describe the equations of motion of an incompressible elastic body $\Omega$ in 3-space acted on by an external pressure force, and the Newton iteration scheme that proves the well-posedness of the resulting initial value problem for its…
This paper presents three different constitutive approaches to model thin rotation-free shells based on the Kirchhoff-Love hypothesis. One approach is based on numerical integration through the shell thickness while the other two approaches…
Natural orbital theory is a computationally useful approach to the few and many-body quantum problem. While natural orbitals are known and applied since many years in electronic structure applications, their potential for time-dependent…