Nonstationary deformation of an elastic plate with a notch under the action of a shock wave

Abstract

The behavior of a thin elastic plate with a rectilinear notch under the action a weak shock wave in air is studied experimentally. A technique is developed for this purpose. The effect of the notch on the strain state of the plate is analyzed Keywords: elastic plate, rectilinear notch, shock wave, experiment technique Introduction. Structural members in the form of plates and shells with various special-purpose or process-induced inhomogeneities (holes, cutouts, notches, cracks etc.) are widely used in many areas of technology. This necessitates studying the influence of such inhomogeneities on the strain state, stability, and fracture of structural members. These issues are well covered in the scientific literature. For example, the influence of an edge crack and a hole on the fracture of plates under tension was examined in [8,10]. In [7], applied theories of shells are used to study the nonstationary dynamics of structurally inhomogeneous shell elements, and experimental results on the effect of shock waves on them are presented. Results on the nonstationary behavior of punched thin plates are given in [4,9]. The photoelastic method was used in [11,12] to study the wave stress field in a plate with a circular hole and in a plate with a curvilinear hole with an edge crack under an impulsive load.Here we will study the influence of a notch on the deformation of thin glass-fiber-reinforced plastic plates under the action of a normally incident shock wave described by a step function. A special technique will be developed. We will experimentally study the nonstationary deformation and analyze the qualitative effect of the notch on the strain state of the plate at the time of maximum deflection caused by the shock wave.1. Technique of Study. The dynamic tests are schematized in Fig. 1, which shows test plate 1with notch 2; shock wave front 3 propagating along shock tube 4 in the direction indicated by arrows; piezoelectric transducers 5, which are elements of a wavefront velocity sensor; oscilloscope 6 recoding the moments the wavefront passes the piezoelectric transducers 5; resistance strain gages 7; computer 8.The test plates are made of SF-1-150 glass-cloth-base laminate (GOST 10316-78) with elastic modulus Å = 2.6×10 10 Pa and density r =1.7 g/cm 3 . The experiments [13] showed that rod and flat structural members of this material do not change their elastic properties under repeated (up to several hundred times) action of weak shock waves causing strains of no larger than 3×10 -3 . Rectangular plates with thickness h = 2.5 mm and sides a = 140 mm and b = 210 mm were rigidly fixed on the short sides between two steel frames 10 mm thick each. The inside dimensions of the frames are 210´140 mm, which coincide with the effective cross-section of the diaphragm-type shock tube; the outside dimensions are 300´230 mm. The plates were fixed with screws and the restrained surfaces were glued with cold-setting epoxy adhesive. The gaps between the long sides of the test plate and the inside of the frame were 0.5 mm appro...

Deformation of an elastic plate with an edge notch under the action of a plane shock wave: experimental research

“…The notch with a length of 0.37 times the length of the clamped edge of the plate increases the period by~25% compared with the solid plate. This value is approximately fourfold greater than that for a central notch with a length equal to half the plate width [6].…”

“…The flexibility matrix with a crack and stiffness coefficients for a rotor were found in [9]. The deformation of elastic plates with a central notch parallel to two clamped edges under the action of a shock wave was experimentally studied in [6].The present paper outlines a procedure and results of experimental study of the influence of an edge notch on the nonstationary behavior of a thin elastic plate clamped at two opposite edges and subjected to the action of a normally incident staircase shock wave.1. Method of Analysis.…”

“…The flexibility matrix with a crack and stiffness coefficients for a rotor were found in [9]. The deformation of elastic plates with a central notch parallel to two clamped edges under the action of a shock wave was experimentally studied in [6].…”

“…An analysis of the oscillograms shows that all elements of the plate with an edge notch (except for the zones near the notch) undergo damped quasiharmonic vibrations after the incidence of a shock wave. As in solid plates [1] and plates with a central notch [6], these vibrations occur about some constant level corresponding to the wavefront pressure rather than about zero. Since even if damping is intensive, the vibration frequency is slightly different from the natural frequency of the corresponding conservative system, we can consider the time between two neighboring peaks to be the period of vibrations T. This time interval was determined for each oscillogram and then the average time over all oscillograms was calculated with an error of ±5%.…”

Vibrations of a rigid body with a controlled frictional electromagnetic seismic damper: nonlinear model

“…Such mechanisms are designed to weaken the coupling between protected structures and ground and to dissipate the energy of seismic disturbances. Controlled semiactive seismic dampers have come to be used in recent decades [13][14][15][16][17]22]. Semiactive control systems fall into the class of systems in which control is used to change the physical and mechanical properties of shock-absorbing elements of damping devices.…”