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The purpose of this paper is to study the dynamic vibrations of the tethered satellite system (TSS).

The energy principle and the variational approach are used to establish the dynamic equations of the TSS. By introducing new generalized coordinates, the equations are transformed into the Hamiltonian system. Then, the symplectic Runge-Kutta (SRK) method is used to solve the canonical equations.

The influence of the tether length on the dynamic behavior of the TSS is very important.

The dynamic responses of the TSS are obtained by using the SRK method.

The purpose of this paper is to study the buckling and the vibration of the beam induced by atom/molecule adsorption using the nonlocal Euler‐Bernoulli beam model with initial axial stress.

The nonlocal parameter associated with adsorbed mass and bending rigidity variations of the beam induced by adsorbates are taken into account, and the buckling and dynamic behaviors are obtained via the Hamilton's principle, in which the potential energy between adsorbates and surfaces of the beam, the bending energy, the external work and the kinetic energy are summed as the Lagrangian function.

The results show that, for both buckling and resonant frequency, the nonlocal effect should be considered when the beam scales down to several hundreds of nanometres, especially for higher mode numbers.

The present paper gives the exact expressions for the buckling and resonant frequency of a simple‐supported nonlocal beam with initial axial stress. Different from previous works, the mass increasing and bending rigidity of the beam are found size‐dependent (nonlocal effect), resulting in possible different static and dynamic behaviors of the beam when atom/molecular adsorption occurs. The exact expressions obtained for the buckling and resonant frequency may be helpful to the design and application of micro‐ and nanobeam‐based sensors/resonators.

The purpose of this paper is to analyze the frequency and response of hexagonal cell honeycomb structures under Hamilton system.

Taking orthotropic sandwich cylinder as the analytical model, the basic equilibrium equations are transformed into Hamilton system, where the canonical transformation, the extended Wittrick‐Williams algorithm and the precise integration method can be applied to calculate the frequency and the responses of the honeycomb sandwich structures.

For the cellular structures, the basic frequency is the most important which can be affected greatly by the wave number. It is also found that the displacement mode shape is dominated by the radial displacement and the axial principal stress is much higher than that of the radial or the circumferential principal stress for the sandwich cylinders.

A new solution procedure is proposed for the cellular structures by constructing the Hamilton matrix in the cylindrical coordinates. The analysis system is thus transformed from Lagrange to Hamilton.