Study of forced vibrations of the Kelvin-Voigt model with an asymmetric spring

Abstract

We study the damping properties of a modified Kelvin-Voigt system characterized by a spring with different moduli of elasticity and a viscous damper under forced vibrations generated by a harmonic force. We solve the problem by using the Cauchy formalism and by analyzing the properties of the fundamental matrix of the system. The oscillograms, phase portraits, and Poincar´e sections corresponding to various parameters of the system are considered.

Wave propagation through an elastically asymmetric architected material

“…The system is forced mainly at frequency ω 0 = 0.03 Hz, resulting in a smooth peak in Φ for the signal entering the bimodular segment at x = 0. Note that the resonance frequencies of the bimodular element is given by [55]), where the main resonance occurs for j = 1 and high-frequency sub-harmonic resonances occur at j > 1, j ∈ N. In the signal spectrum (Figure 6(a)) for the case of wave overlap (Figure 4(b)), a second peak emerges at j = 2 sub-harmonic frequency of elemental cells. This peak, which grows with the propagation distance, presents a sink for the energy transmitted from low frequencies.…”

“…Vibration of heteromodular was studied by many authors, whose contributions are well summarized in [52], where some fundamental results were obtained for gyroscopic and nongyroscopic systems using analytical and numerical tools. The approaches used in the abovecited paper were developed in earlier works on vibration of systems with internal impacts, which render them elastically asymmetric, among them we could cite [53][54][55], more results are summarized in the monograph [56].…”

Wave propagation through an elastically-asymmetric architected material

“…The elastic wave propagation in asymmetric media was studied in [10][11][12][13]. Vibrational analyses of materials with internal impacts, which render them elastically asymmetric, were conducted in [14][15][16].…”

“…The system is forced mainly at frequency ω 0 = 0.03 Hz, resulting in a smooth peak in Φ for the signal entering the bi-modulus section at x = 0. Note that the resonance frequencies of the bi-modulus element is given by [16]), where the main resonance occurs for j = 1 and highsub-harmonic resonances occur at j > 1 and j ∈ N. In the signal spectrum [Fig. 4(a)] for the case of wave overlap [Fig.…”